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Attack and Defend Maps

GerdIsenberg — Sat, 05 Nov 2016 09:18:44 GMT

Home * Programming * Data * Attack and Defend Maps

		Attack and Defend Maps, also called Attack Tables, refer to data-structures, most often arrays, containing attack or defend information for every pawn or piece and/or the transposed information for each square, which pieces control, that is either attack or defend it. These Maps are useful for evaluation purposes such as safe mobility, SEE and of course move generation. While the piece centric attack information, a set of attacked squares per piece, is often encoded as bitboard, there are more alternatives for storing the square centric information, about attacking pieces.
Samuel Bak - Sheltering Myths, 1998 ^[1]

Maintaining Attacks

Incremental Update

The piece centric and/or square centric information is often initialized at the root and updated incrementally during the search while making and unmaking moves. The idea is that a move has often only a local influence on the attack tables, and that it is usually cheaper to change only those squares which changed from- or to-attacks, rather than all squares from scratch. This is especially true during the opening or early middlegame phase, but does become more expensive in the late middlegame or endings with sliding pieces, especially queens.

On the Fly

Programmers like Joël Rivat ^[2], Robert Hyatt ^[3], Ed Schröder and Gerd Isenberg avoid or have abandoned incrementally updated attack tables and rely on the paradigm to process information if needed. A lot of nodes don't need the attack information at all, or only a small part of it. With all the hash tables, incremental update tends to do some unnecessary work, considering the update costs in "worst case" positions, f.i. queen endings, where one move change the attack information of many squares.

On the other hand, if attack tables are available, one should utilize the information as much as possible for a smarter search and evaluation to gain exponentially. Anyway, one has to be careful with too complicated data structures and update code.

Implementations

Classical Approach

The square centric classical approach with bitboards was used in Chess 4.5 and descibed by Larry Atkin and David Slate ^[4] . The incrementally updated attack tables, from which most move generation is done, are called ATKFR and ATKTO. ATKFR is a set of 64 bitboards which give, for each square, all the squares attacked by the piece, if any, that resides on the square. ATKTO (Square Attacked By) is the transpose of ATKFR, giving for each square, the locations of all pieces that attack that square. For instance the square E4 (T) is attacked by a black rook at E8, a black knight at F6, and defended by a white rook at E1 and a white pawn at D3 ^[5] :

attacks_to[E4]
 . . . . 1 . . .
 . . . . . . . .
 . . . . . 1 . .
 . . . . . . . .
 . . . . T . . .
 . . . 1 . . . .
 . . . . . . . .
 . . . . 1 . . .

Alternatives

There are several alternatives for keeping the square centric information what pieces attack each particular square.

Piece-Sets

A Square Attacked By bitboard aka ATKFR as possible union-set of multiple pawns and pieces of either side require intersections with piece bitboards, or bitscanned square lookups, to determine which pieces and how many attack or defend.

Based on a fixed piece-type and bit-position relation with usual material dispositions (for each side, no more than one queen, two rooks, one bishop per square color, two knights), 32-bit Piece-Sets already inherit the information which pieces (and how many of both sides) attack a particular square, one can even imagine a 16-bit lookup inside a 64KByte table to get an denser attack indicator/count byte for each color a lá Ed Schröder. MS-DOS IsiChess maintained an array of 64 32-bit piece-sets for every square, and an array of up to 32 attack-to bitboards for every piece. However working with piece-sets requires an additional indirection via a Piece-list to get the square of that piece.

Ed's lookup

As described by Ed Schröder in Evaluation in REBEL ^[6] , Rebel uses two board tables for both sides, one byte entry each, the three lower bits contain an attack counter, while the five upper bits indicate the presence of least one pawn or piece attacking/defending:

+------+------+------+------+------+------+------+------+
| BIT0 | BIT1 | BIT2 | BIT3 | BIT4 | BIT5 | BIT6 | BIT7 |
+------+------+------+------+------+------+------+------+
|      Number of     | PAWN |KNIGHT| ROOK | QUEEN| KING |
|      ATTACKERS     |      |BISHOP|      |      |      |
+------+------+------+------+------+------+------+------+

The information might be inaccurate in some cases since it loses some information if multiple pieces of one kind are involved. However, since SEE might be erroneous anyway due to pins, x-rays or overloaded pieces, Ed's scheme seems sufficient for practical purposes - and it is fast. Each byte (for both sides) can act as index inside pre-calculated three-dimensional table to perform an SEE by looking up a target piece or square, attack- and defend-byte:

char see_table [14][256][256];   // 14*64 K = 896 KByte
 
see = see_table[Piece][attackByte][defendByte];

While the counter might be updated incrementally, the piece indicators as possible union of multiple pieces (i.e. two knights and one bishop) is not that simple to update, thus Ed generates those tables in evaluation on the fly by scanning the pieces of the board.

Direction wise

An other alternative to incremental updated attack tables is motivated by direction wise fill algorithms like Kogge-Stone for sliding pieces, and that one may hide memory latencies from probes of the transposition table. Especially pawn attacks are cheap to determine on the fly, and likely reduce the set of capture targets of least valuable pieces defended by pawns, which are otherwise object of Quiescence Search or SEE.

Forums Posts

1995 ...

Chess programming using bitboards by Joël Rivat, rgcc, August 18, 1995
Attack Tables by Roberto Waldteufel, CCC, October 20, 1998

2000 ...

Counting attacked squares: how? by Leen Ammeraal, CCC, January 24, 2002
attacks_from[] and attacks_to[] info by Nagendra Singh Tomar, CCC, October 21, 2002
Attack tables by Andreas Herrmann, CCC, November 20, 2002
The Zappa Attack Table Code by Anthony Cozzie, CCC, May 05, 2004
bitboards and incrementally updated attack tables by Eric Oldre, CCC, June 30, 2004
Attack table by Anonymous, Winboard Forum, October 06, 2004

2005 ...

Attack table musings by GeoffW, Winboard Forum, February 11, 2005
Incremental updating for positional evaluation by Steven Edwards, CCC, March 27, 2008
Piece attacks count by Marco Costalba, CCC, May 18, 2009 » Population Count

2010 ...

Incrementally-updated attack map by Harm Geert Muller, April 21, 2014 » Incremental Updates

References

^ The Game of War from Samuel Bak - represented by Pucker Gallery since 1969
^ Chess programming using bitboards by Joël Rivat, rgcc, August 18, 1995
^ Speed of Move Generator by Valavan Manohararajah, rgcc, August 15, 1995, post 5 by Robert Hyatt where he mentions on the fly generation with rotated bitboards
^ David Slate and Larry Atkin (1977). CHESS 4.5 - The Northwestern University Chess Program. Chess Skill in Man and Machine (ed. Peter W. Frey), pp. 82-118. Springer-Verlag, New York, N.Y. 2nd ed. 1983. ISBN 0-387-90815-3. Reprinted (1988) in Computer Chess Compendium
^ Rotated bitmaps, a new twist on an old idea by Robert Hyatt
^ Evaluation in REBEL (hanging pieces) from How Rebel Plays Chess by Ed Schröder, also available as pdf

What links here?

Page	Date Edited
Andreas Herrmann	Nov 7, 2014
Arasan	Apr 8, 2018
Attack and Defend Maps	Nov 5, 2016
Bebe	Dec 23, 2017
Bitboards	Nov 14, 2017
BlackBishop	Nov 7, 2014
Board Representation	Dec 11, 2017
Bruja	Feb 3, 2015
CAPS	Dec 23, 2017
Check	Feb 1, 2018
Chess (Program)	Dec 22, 2017
Chess 0.5	Nov 20, 2016
Chest	Mar 3, 2015
Combinatorial Logic	Apr 6, 2017
Constellation	Oct 2, 2016
DanChess	Jun 17, 2012
Data	Nov 26, 2017
Deflection	May 21, 2011
Diablo	May 17, 2016
Dorpsgek	Apr 2, 2018
Double Attack	Oct 22, 2014
Encoding Moves	Mar 27, 2016
Eugen	Jan 7, 2016
Eugenio Castillo Jiménez	Jul 23, 2017
Eye Movements	Jul 22, 2015
Floyd	Sep 11, 2016
Golch	Dec 7, 2017
Gromit	Apr 5, 2017
Hagrid	Apr 12, 2016
Horizon	Mar 17, 2013
Incremental Updates	Sep 6, 2017
Interception	May 21, 2011
Interference	May 20, 2011
Joker NL	Sep 15, 2017
José Carlos Martínez Galán	Feb 19, 2017
King Safety	Feb 14, 2018
KnightCap	Nov 6, 2016
Legal Move	Feb 16, 2017
M-20	Oct 9, 2013
Mate at a Glance	Sep 24, 2014
Mediocre	Feb 27, 2015
MessChess	Mar 6, 2014
Mikhail Botvinnik	Jul 15, 2017
Mobility	Jan 17, 2018
Movei	Jan 7, 2016
MVV-LVA	Oct 26, 2017
Neural Networks	Mar 12, 2018
Node Types	Oct 22, 2017
Nullmover	Jul 21, 2013
Ostrich	Dec 28, 2017
Overloading	May 5, 2017
Pandix	Feb 4, 2017
Patzer	Apr 5, 2017
Perceiver	Nov 21, 2017
Peter Fendrich	May 19, 2017
Piece-Sets	Jun 9, 2017
Pioneer	Dec 23, 2017
Population Count	Sep 3, 2017
RDChess	May 3, 2013
Rookie	Jan 7, 2016
SEE - The Swap Algorithm	Jun 5, 2017
SnailChess	Nov 26, 2014
Snitch	Apr 7, 2016
SOMA	Mar 25, 2015
Spartacus	Oct 17, 2016
Spector	Nov 11, 2016
Square Attacked By	Jan 20, 2018
Square Control	Sep 15, 2016
Static Exchange Evaluation	Dec 14, 2017
Sunsetter	Jun 1, 2017
Tao	Jan 8, 2016
Vladimir Butenko	Aug 12, 2013
Woodpusher	Dec 12, 2016
Zach Wegner	Jan 7, 2016
Zappa	Oct 24, 2017

Up one Level

Bitboards

GerdIsenberg — Tue, 14 Nov 2017 20:13:35 GMT

Home * Board Representation * Bitboards

		Bitboards, also called bitsets or bitmaps, are among other things used to represent the board inside a chess program in a piece centric manner. Bitboards, are in essence, finite sets of up to 64 elements - all the squares of a chessboard, one bit per square. Other board games with greater board sizes may be use set-wise representations as well ^[1], but classical chess has the advantage that one 64-bit word or register covers the whole board. Even more bitboard friendly is Checkers with 32-bit bitboards and less piece-types than chess ^[2] ^[3] .
Samuel Bak - Boards Meeting ^[4]

The Board of Sets

To represent the board we typically need one bitboard for each piece-type and color - likely encapsulated inside a class or structure, or as an array of bitboards as part of a position object. A one-bit inside a bitboard implies the existence of a piece of this piece-type on a certain square - one to one associated by the bit-position.

Bitboard Basics

Of course bitboards are not only about the existence of pieces - it is a general purpose, set-wise data-structure fitting in one 64-bit register. For example, a bitboard can represent things like attack- and defend sets, move-target sets and so on.

General Bitboard Techniques

The fundamental bitboard basics.

Pattern and Attacks

This is basically about chess, how to calculate attack-sets and various pattern for evaluation and move generation purposes.

Move Generation Issues

Bitboard aspects on move generation and static exchange evaluation (SEE).

Miscellaneous

Defining Bitboards

To be aware of their scalar 64-bit origin, we use so far a type defined unsigned integer U64 in our C or C++ source snippets, the scalar 64-bit long in Java. Feel free to define a distinct type or wrap U64 into classes for better abstraction and type-safety during compile time. The macro C64 will append a suffix to 64-bit constants as required by some compilers:

typedef unsigned __int64 U64;    // for the old microsoft compilers
typedef unsigned long long  U64; // supported by MSC 13.00+ and C99
#define C64(constantU64) constantU64##ULL

Bitboard-History

The general approach of bitsets was proposed by Mikhail R. Shura-Bura in 1952 ^[5] ^[6]. The bitboard method for holding a board game appears to have been invented also in 1952 by Christopher Strachey using White, Black and King bitboards in his checkers program for the Ferranti Mark 1 ^[7], and in the mid 1950's by Arthur Samuel in his checkers program as well. In computer chess, bitboards were first described by Georgy Adelson-Velsky et al. in 1967 ^[8] , reprinted 1970 ^[9] . Bitboards were used in Kaissa and in Chess. The invention and publication of Rotated Bitboards by Robert Hyatt ^[10] and Peter Gillgasch with Ernst A. Heinz in the 90s was another milestone in the history of bitboards. Steffan Westcott's innovations, too expensive on 32-bit x86 processors, should be revisited with x86-64 and SIMD instructions in mind. With the advent of fast 64-bit multiplication along with faster memory, Magic Bitboards as proposed by Lasse Hansen ^[11] and refined by Pradu Kannan ^[12] have surpassed Rotated.

Analysis

The use of bitboards has spawned numerous discussions about their costs and benefits. The major points to consider are:

Bitboards can have a high information density.
Single populated or even empty Bitboards have a low information density.
Bitboards are weak in answering questions like what piece if any resides on square x. One reason to keep a redundant mailbox board representation with some additional update costs during make/unmake.
Bitboards can operate on all squares in parallel using bitwise instructions. This is one of the main arguments used by proponents of bitboards, because it allows for a flexibility in evaluation.
Bitboards are rather handicapped on 32 bit processors, as each bitwise computation must be split into two or more instructions ^[13] . As most modern processors are now 64 bit, this point is somewhat diminished ^[14] .
Bitboards often rely on bit-twiddling and various optimization tricks and special instructions for certain hardware architectures, such as bitscan and population count. Optimal code requires machine dependent header-files in C/C++. Portable code is likely not optimal for all processors.
Some operations on bitboards are less general, f.i. shifts. This requires additional code overhead.

Publications

1970 ...

Georgy Adelson-Velsky, Vladimir Arlazarov, Alexander Bitman, Alexander Zhivotovsky and Anatoly Uskov (1970). Programming a Computer to Play Chess. Russian Mathematical Surveys, Vol. 25, pp. 221-262.
David Slate and Larry Atkin (1977). CHESS 4.5 - The Northwestern University Chess Program. Chess Skill in Man and Machine, reprinted (1988) in Computer Chess Compendium » Chess

1980 ...

Zdenek Zdráhal, Ivan Bratko, Alen Shapiro (1981). Recognition of Complex Patterns Using Cellular Arrays. The Computer Journal, Vol. 24, No. 3, pp. 263-270
Stuart Cracraft (1984). Bitmap move generation in Chess. ICCA Journal, Vol. 7, No. 3
Burton Wendroff (1985). Attack Detection and Move Generation on the X-MP/48. ICCA Journal, Vol. 8, No. 2
Arch D. Robison, Brian J. Hafner, Steven Skiena (1989). Eight Pieces Cannot Cover a Chess Board. The Computer Journal, Vol. 32, No. 6, pdf

1990 ...

Ernst A. Heinz (1997). How DarkThought Plays Chess. ICCA Journal, Vol. 20, No. 3 » DarkThought
Robert Hyatt (1999). Rotated Bitmaps, a New Twist on an Old Idea. ICCA Journal, Vol. 22, No. 4 » Rotated Bitboards ^[15]

2000 ...

David Rasmussen (2004). Parallel Chess Searching and Bitboards. Master's thesis, ps » Parallel Search
Borko Bošković, Sašo Greiner, Janez Brest, Viljem Žumer (2005). The Representation of Chess Game. Proceedings of the 27th International Conference on Information Technology Interfaces
Pablo San Segundo, Ramón Galán (2005). Bitboards: A New Approach. AIA 2005
Pablo San Segundo, Ramón Galán, Fernando Matía, Diego Rodríguez-Losada, Agustín Jiménez (2006). Efficient Search Using Bitboard Models. ICTAI 2006, pdf
Fridel Fainshtein (2006). An Orthodox k-Move Problem-Composer for Chess Directmates. M.Sc. thesis, Bar-Ilan University, pdf, Appendix D - 64-bit Representation, pp. 105
Fridel Fainshtein, Yaakov HaCohen-Kerner (2006). A Chess Composer of Two-Move Mate Problems. ICGA Journal, Vol. 29, No. 1, pdf, Appendix E: 64-bit representation, pp. 22
Reijer Grimbergen (2007). Using Bitboards for Move Generation in Shogi. ICGA Journal, Vol. 30, No. 1, pdf » Move Generation, Shogi
James Glenn, David Binkley (2008) An Investigation of Hierarchical Bit Vectors. New Topics in Theoretical Computer Science, pdf
Shi-Jim Yen, Jung-Kuei Yang (2009). The Bitboard Design and Bitwise Computing in Connect Six. 14th Game Programming Workshop
Fritz Reul (2009). New Architectures in Computer Chess, Ph.D. Thesis, pdf

2010 ...

Stefano Carlini (2010). Arimaa, a New Challenge for Artificial Intelligence. M.Sc. thesis, University of Modena and Reggio Emilia, pdf » Chapter 4, Bitboards in Arimaa
Shi-Jim Yen, Jung-Kuei Yang, Kuo-Yuan Kao, Tai-Ning Yang (2012). Bitboard Knowledge Base System and Elegant Search Architectures for Connect6. Knowledge-Based Systems, Vol. 34 » Connect6
Cameron Browne, Stephen Tavener (2013). Life in the Fast Lane. AI Factory » Conway's Game of Life within a Bitboard
Cameron Browne (2014). Bitboard Methods for Games. ICGA Journal, Vol. 37, No. 2

Forum Posts

1994

bitboard move generation by Robert Hyatt, rgc, October 25, 1994
bitboard move generator by Joël Rivat, rgc, November 13, 1994
bitboard position evaluations by Robert Hyatt, rgc, November 17, 1994 » Evaluation

1995 ...

Chess programming using bitboards by Joël Rivat, rgcc, August 18, 1995
Bit Board Bonkers?? by Dave, rec.games.chess.computer, July 28, 1997
Efficient Bitboard Implementation on 32-bit Architecture by Roberto Waldteufel, CCC, October 25, 1998
Bitboard question by Werner Inmann, CCC, December 02, 1998
Bitboards by Frank Phillips, CCC, December 05, 1998
bitboards in java? by vitor, CCC, April 06, 1999 » Java
BitBoards by Frank Phillips, CCC, May 29, 1999
Bitboard user's information request by Robert Hyatt, CCC, October 05, 1999 » Rotated Bitboards ^[16]

2000 ...

To bitboard or not to bitboard? by Tord Romstad, CCC, August 30, 2003
How important are Bitboards? by Martin Schreiber, CCC, February 29, 2004
Two questions for bitboard experts by Tord Romstad, Winboard Forum, November 06, 2004 » In Between, Piece-Lists

2005 ...

Bitboard question by Tord Romstad, Winboard Forum, March 14, 2006
Speedup with bitboards on 64-bit CPUs by Tord Romstad, CCC, April 27, 2007
Speedup by bitboards by Onno Garms, Winboard Forum, July 13, 2007
BitBoard representations of the board by Uri Blass, CCC, October 14, 2007
Bitboards / move generation on larger boards by Gregory Strong, CCC, January 09, 2009
Bitboard techniques in Xiangqi by Harm Geert Muller, CCC, February 12, 2009 » Chinese Chess
Bitboards using 2 DOUBLE's ? by Carey, CCC, June 02, 2009 » Double

2010 ...

Bitboard implementation, how much time? by Ed Schröder, CCC, January 22, 2012
64 bits for 64 squares ? by Thomas Petzke, mACE Chess, April 28, 2013 » Population Count
Bitboard Tricks for Large Chess Variants by Ed Trice, CCC, November 01, 2014

2015 ...

Bitboard database code samples by Steven Edwards, CCC, May 25, 2015 » Symbolic
M42 - A C++ library for Bitboard attack mask generation by Syed Fahad, CCC, April 30, 2016 ^[17]
Checkers Bitboard representation by Pranav Deshpande, CCC, July 02, 2017 » Checkers
Bitboards and Java by Fred Hamilton, CCC, November 14, 2017 » Java

Viewer & Calculator

External Links

References

^ Reijer Grimbergen (2007). Using Bitboards for Move Generation in Shogi. ICGA Journal, Vol. 30, No. 1, pdf
^ Checker Bitboards Tutorial by Jonathan Kreuzer
^ Checkers Bitboard representation by Pranav Deshpande, CCC, July 02, 2017
^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ Lazar A. Lyusternik, Aleksandr A. Abramov, Victor I. Shestakov, Mikhail R. Shura-Bura (1952). Programming for High-Speed Electronic Computers. (Программирование для электронных счетных машин)
^ Andrey Ershov, Mikhail R. Shura-Bura (1980). The Early Development of Programming in the USSR. in Nicholas C. Metropolis (ed.) A History of Computing in the Twentieth Century. Academic Press, preprint pp. 43
^ On Bitboards for White, Black and Kings to represent the checkers board, see David Link Video at 1:04:02
^ Early Reference on Bit-Boards by Tony Warnock from rec.games.chess, October 29, 1994
^ Georgy Adelson-Velsky, Vladimir Arlazarov, Alexander Bitman, Alexander Zhivotovsky and Anatoly Uskov (1970). Programming a Computer to Play Chess. Russian Mathematical Surveys, Vol. 25, pp. 221-262.
^ Robert Hyatt (1999). Rotated Bitmaps, a New Twist on an Old Idea. ICCA Journal, Vol. 22, No. 4
^ Fast(er) bitboard move generator by Lasse Hansen, Winboard Forum, June 14, 2006
^ List of magics for bitboard move generation by Pradu Kannan, Winboard Forum, August 23, 2006
^ Efficient Bitboard Implementation on 32-bit Architecture by Roberto Waldteufel, CCC, October 25, 1998
^ Speedup by bitboards by Onno Garms, Winboard Forum, July 13, 2007
^ Bitboard user's information request by Robert Hyatt, CCC, October 05, 1999
^ Robert Hyatt (1999). Rotated Bitmaps, a New Twist on an Old Idea. ICCA Journal, Vol. 22, No. 4
^ M42 by Syed Fahad

Up one level

Candidates (Bitboards)

GerdIsenberg — Sat, 11 Nov 2017 09:57:18 GMT

Home * Board Representation * Bitboards * Pawn Pattern and Properties * Candidates

		Candidates, pawns that can force themselves to become passed pawns simply with a series of pawn moves. Candidates are half-open pawns with no mechanical but dynamical obstructions. Specifially, the pawn must be on a half-open file, and the number of defender pawns that can help the pawn advance are greater than or equal to the number of pawns which attack the pawn or squares in front of it.
Samuel Bak - The Designated ^[1]

Candidate and Faker

While the intersection of the frontspan with opposing pawns is empty, the intersection of front attackspans with opposing pawns is not (otherwise it would already a passer). The opposing pawns as member of the front attackspan(s), stand sentinel over one or more squares in the frontfill of the open pawn, and are about to capture the open pawn, if it may advance into - or already is - a lever. Those opposing pawns are called sentries.

If the open pawn has one or more helper-pawns on adjacent files, which are able to recapture the sentry, the candidate is a real one and is guaranteed to force a passer. Otherwise, without enough support from helpers, the candidate is only a faker.

The following diagrams shows advanced candidates and fakers, assuming black to move:

candidates b6, f4   fakers -
sentries   c7, g2   more sentries
helper     c5, g4   than helpers
. . . . | . . .     . . . . | . . .
. . b . . . . .     b . b . . . . .
. w . . . . . .     . w . . . . . .
. . w . . . . .     . . w . . . . .
. . . . . b b .     . . . . . b b .
. . . . . . . .     . . . . . . . .
. . . . . . w .     . . . . w . w .
. . . | . . . .     . . . | . . . .

The white candidate on b6 is already in lever-distance with the sentry c7. The sentry c7 is likely forced to capture - otherwise b6 captures or pushes to become a passer. The white helper immediately recaptures and takes the role of the former candidate and becomes a passer. The black candidate on f4 can also force a passer. The helper on g4 compensates the sentry on g2. Usually, the candidate has to push forward, not the helper.

In the second diagram both candidates are pseudo-candidates or fakers, since there are more sentries than helpers - a7xb6 is required - otherwise, after c7xb6, c5-c6 would allow the helper to advance to a passer.

Advanced Candidates

Advanced candidates, already inside or about to enter the opponent side of the board are the most important to consider in evaluation. Even more if the interspan of sentries and helper is already one - and it is only about the control of the stop-square - or if the candidate is already part of a lever, the number of attacks and defenses.

In such cases, due to the forced nature of exchanging candidate, sentry and helper, only two or up to five plies are necessary to establish a passer. In fact those candidates may even be more worth than pawns already a passer - specially if the opponent king is outside the candidates square - or if the outside candidate may deflect the opponent king.

One may argue that a candidate already in lever distance with the sentry should be covered by quiescence search - since it is a capture/recapture sequence. Therefor more important to evaluate are the candidate-helper-duo/trio against one or two sentries, which is likely a kind of static exchange evaluation of the candidate's stop-square.

. . . . . . . .
. . s . . s . s   sentries
. . . . . . . .
. c h . . h c h   candidates with helpers
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .

To cover sets of advanced white candidates with attacked but sufficient defended stops already on the on the 5th rank, one may use some code like this. Feel free to introduce branches, e.g. if there are no white pawns on the fifth rank. Anyway, wSafePawnSquares might be used elsewhere, e.g. to decide whether helper pawns may advance to defend candidate's stop.

U64 wCandidatesOn5th(U64 wpawns, U64 bpawns) {
   const U64 rank5     = C64(0x000000ff00000000);
   U64 bPawnAnyAttacks = bPawnAnyAttacks(bpawns);
   U64 wSafeSquares    = wSafePawnSquares(wpawns, bpawns);
   U64 wSafeAttacked   = bPawnAnyAttacks  &  wSafeSquares;
   U64 blackFrontSpan  = (bpawns >> 8)    | (bpawns >> 16); // only for 5th rank
   return wpawns & rank5 &~blackFrontSpan & (wSafeAttacked >> 8);
}

Less Advanced

If it is about the long-term evaluation of telestop -squares - or the need of advancement of helper(s) to defend the stop-square, things become more complicated and one probably better relies on search and some general bonus to advance half-free pawns and advanced duos. Feel free to cover attackspan-related stuff for less advanced candidates respectively helpers and helper's helpers.

d4 is candidate     d4 is faker         d4 faker due to     d4 is candidate
                                        helper's sentry     due to helper's helper f2
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . s . s . . .     . . s . s . . .     . . s . s . . .     . . s . s . . .
. . . . . . . .     . . . . . . . .     . . . . . hs. .     . . . . . hs. .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . c . . . .     . . . f . . . .     . . . f . . . .     . . . c . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . h . h . . .     . . h . . . . .     . . h . h . . .     . . h . h hh. .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .

The Sneaker

Also known as a hidden passed pawn. A kind of candidate in disguise is an unfree pawn or faker that may become a passer through a sacrificial combination. In the diagram white may sacrifice the faker with b5-b6 - allowing black to establish a passer on b6 - but the sneaker on c6 becomes a much more advanced passer with a frontspan of only two against five:

. . . . . . . .
. . b . . . . .
. . w . . . . .
. w . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .

A sneaker is likely advanced (opponent side of the board), rammed and defended, but no lever. No other opposing pawn controls it's stop or telestop squares.

External Links

Pawn Power in Chess by Hans Kmoch - Glossary of Terms - Chess Forums - Chess.com ^[2]
Candidates Tournament from Wikipedia
Jango Edwards - Harry Christmas, September 10, 2009, Zeche Carl ^[3], Essen, YouTube Video

References

^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ Hans Kmoch (1959, 1990). Pawn Power in Chess. New York: Dover, 1990. Previous ed.: New York: McKay, 1959. ISBN 0-486-26486-6
^ Zeche Carl is part of The Industrial Heritage Trail

What links here?

Page	Date Edited
Attack Spans	Mar 4, 2010
Backward Pawns (Bitboards)	May 5, 2017
Candidate Passed Pawn	Nov 11, 2017
Candidates (Bitboards)	Nov 11, 2017
Faker	Nov 11, 2017
Hans Kmoch	Nov 11, 2017
Hidden Passed Pawn	Nov 11, 2017
Murka	Nov 11, 2016
Passed Pawns (Bitboards)	Aug 23, 2010
Pawn Attacks (Bitboards)	Mar 4, 2010
Pawn Pattern and Properties	Nov 11, 2017
Pawn Spans	Jul 22, 2010
PawnKing	Sep 5, 2014

Up one Level

Check

GerdIsenberg — Thu, 01 Feb 2018 19:43:04 GMT

Home * Chess * Check

		Inside a game of chess, a check occurs if a king is under immediate attack by one (or two) opponent pieces. If the king has no way to remove it from attack on the next move, the check is even checkmate. Since check is crucial concerning the outcome of game and the horizon effect, check extensions might be applied to evade the check.
Samuel Bak - Lighthouse ^[1]

Kind of Checks

Single Check

The king is attacked by one opponent piece, either by the piece which just moved directly attacking the king, or alternatively a discovered check where a distant sliding piece attacks the king by opening the ray in opponent king direction with another piece.

Double Check

A double check occurs if the moving piece directly attacks the king but also discovers a distant sliding attacker.

In Check Detection

Whether the side to move is in check is essential to know inside the search for various reasons. It might be checkmate, and most pseudo-legal moves generated may be illegal, leaving the king attacked. Null move would yield in an illegal position as well, at or below the horizon we don't want to stand pat if material balance or static evaluation is far greater than beta.

By last Move

The cheapest and most straightforward way to detect checks is to consider the previous move just made by the opponent. It might be a direct check or discovered check, so one has to test whether piece on target square attacks the king, or whether piece on origin square is attacked by an own sliding piece on an otherwise open ray in opponent king direction ^[2]. If the last move was an en passant capture, one has to consider a few more complicated cases of possible discovered checks, since the captured pawn is not on the target square, and two pawns disappear from the 4th (5th) rank.

Attack Tables

Based on the design and data structure of a chess program, an incremental updated attack and defend map may immedeatly answer whether the king is under attack of one or even two opponent pieces.

On the Fly

With bitboards one may determine a square attacked as mentioned in checks and pinned pieces.

Getting out of check

While in check, it is recommended to perform a specialized Move Generation for check evasion of either a reasonable subset of all pseudo-legal moves or even a strict legal move generation:

Double Check

Only king moves to non attacked squares, sliding check x-rays the king

Single Check

Capture of checking piece. The capturing piece is not absolutely pinned
King moves to non attacked squares, sliding check x-rays the king
Interposing moves in case of distant sliding check. The moving piece is not absolutely pinned.

Perpetual Check

A perpetual check occurs if one player forces an "endless" series of checks with repeated reversible moves, finally resulting in a draw by threefold repetitions.

Publications

Richard L. Smith, Fernand Gobet, Peter Lane (2009). Checking chess checks with chunks: A model of simple check detection. ICCM 2009 » CHREST, Chunking

Forum Posts

1997 ...

quiescence search by Andrew Tridgell, rgcc, April 16, 1997 » Quiescence Search, Crafty

2000 ...

Checks in the Qsearch by Scott Gasch, CCC, June 28, 2002 » Quiescence Search
Idea for check function by Zach Wegner, CCC, November 14, 2002
Fast check detection in bitboard engine by Jean-Francois Romang, CCC, December 10, 2003
Rebel's long checks concept in QS by milix, CCC, January 23, 2004 » Rebel, Quiescence Search
Qsearch Checks by Tor Lattimore, CCC, August 29, 2004 » Quiescence Search
Checks in QSearch by Dan Honeycutt, Winboard Programming Forum, November 23, 2004 » Checks in Quiescence Search

2005 ...

in check test by Anonymous , Winboard Forum, July 07, 2005
How to Best Limit Checks in the Quiescence ? by Stuart Cracraft, CCC, August 20, 2007 » Checks in Quiescence Search
discovered check definition by Uri Blass, CCC, September 12, 2007 » Discovered Check
checks in q-search by Robert Hyatt, CCC, September 02, 2008

2010 ...

Standpat and check by Vlad Stamate, CCC, February 06, 2010 » Standing Pat
Detecting Checks by beneficii, Winboard Programming Forum, November 27, 2010
out of check move ordering by Don Dailey, CCC, March 12, 2011 » Move Ordering
checks in quies by Larry Kaufman, CCC, March 22, 2012 » Quiescence Search
What is (in your opinion) the best check validation method? by goodgame0111, OpenChess Forum, February 24, 2014
Spite checks by Harm Geert Muller, CCC, May 13, 2014

2015 ...

Check-extension in QS by Harm Geert Muller, CCC, April 03, 2015 » Checks in Quiescence Search
Ostrich tactics and pointless checks by Colin Jenkins, CCC, May 29, 2015 » Horizon Effect
Checks in qsearch - must-have or optional? by Martin Fierz, CCC, March 15, 2016 » Checks in Quiescence Search
perpetual check position by Erin Dame, CCC, August 16, 2016
Spite checks, again by Harm Geert Muller, CCC, October 23, 2016

External Links

References

^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ Idea for check function by Zach Wegner, CCC, November 14, 2002

What links here?

Page	Date Edited
AI Chess	Jan 7, 2016
Anastasios Milikas	Nov 29, 2017
Andrew Tridgell	Aug 3, 2015
Anechka	Mar 20, 2014
Atomic Chess	Nov 26, 2016
BCP	Dec 30, 2015
Bebe	Dec 23, 2017
BELCT 2001	Apr 4, 2017
Blockade	Oct 19, 2017
Bobby	Jan 7, 2016
BootChess	May 16, 2017
BP	Jan 7, 2016
Carballo	Oct 2, 2016
Check	Feb 1, 2018
Check Extensions	Apr 19, 2018
Checkmate	Apr 13, 2018
Checks and Pinned Pieces (Bitboards)	Aug 14, 2013
Cheng	Jul 30, 2017
Chess	Jan 21, 2018
Chess Champion Mark V	Sep 7, 2017
Chess Game	Mar 28, 2017
Chess Wizard	Dec 22, 2014
chess22k	Apr 23, 2018
ChessBrainVB	Jun 24, 2017
Crafty	Jan 28, 2018
CXG Sphinx	Jun 23, 2017
Cyrus 68K	Jan 7, 2016
Dabbaba	Oct 21, 2014
Dan Honeycutt	Mar 13, 2014
Diablo	May 17, 2016
Dictionary	Aug 24, 2017
DirGolem	Jun 5, 2016
Discovered Check	Feb 1, 2018
Djinn	Feb 8, 2016
Double Attack	Oct 22, 2014
Double Check	Apr 4, 2013
Dragon FR	Sep 9, 2016
Draw	Apr 14, 2018
DrunkenMaster	Nov 1, 2016
Encoding Moves	Mar 27, 2016
Erin Dame	Dec 2, 2017
Eveann	Apr 3, 2017
FCP	Jun 15, 2013
Fidelity	Jan 7, 2016
Fortress	Feb 1, 2018
Futility Pruning	Aug 30, 2017
Genie	Feb 7, 2016
George Baylor	Sep 22, 2014
Ghost	Feb 2, 2018
Gibbon	Dec 23, 2014
HAL	Jun 14, 2016
Harm Geert Muller	Mar 31, 2018
Horizon Effect	Sep 10, 2017
Interference	May 20, 2011
Kaissa	Apr 9, 2018
King	Feb 26, 2013
Knowledge	Jul 22, 2017
Lachex	Jan 7, 2016
Larry Kaufman	Jan 28, 2018
Laser	Dec 27, 2017
Late Move Reductions	Sep 25, 2017
Legal Move	Feb 16, 2017
Losing Chess	Sep 18, 2017
Martin Fierz	Apr 26, 2018
Mate Search	Oct 22, 2016
Mater	Apr 26, 2016
Maverick	Jan 7, 2016
MessChess	Mar 6, 2014
Monarch	Nov 19, 2014
Move Generation	Jan 29, 2018
Move Ordering	Feb 27, 2018
Moves	Feb 19, 2018
Murka	Nov 11, 2016
One Reply Extensions	Dec 31, 2014
Overloading	May 5, 2017
Pawn Race	Dec 16, 2017
Pertti Saariluoma	Jun 13, 2017
Pin	Mar 7, 2017
Point Value	Mar 31, 2018
ProChess IT	Sep 30, 2015
Pseudo-Legal Move	May 23, 2015
python-chess	Nov 4, 2017
Querg	Dec 11, 2013
Quiescence Search	Aug 19, 2017
Quiet Moves	Mar 4, 2010
Rebel	Feb 25, 2018
Repetitions	Jan 16, 2018
Retrograde Analysis	Mar 21, 2017
RISC 2500	Jan 7, 2016
Scott Gasch	Nov 29, 2016
SCP	Jun 16, 2016
Search Explosion	Mar 30, 2017
SEE	Jan 14, 2013
SEX Algorithm	Nov 25, 2014
Skewer	Oct 22, 2014
Stalemate	Feb 21, 2018
Static Exchange Evaluation	Dec 14, 2017
Stuart Cracraft	May 19, 2017
SuperChess	Dec 7, 2016
Tactical Moves	Sep 22, 2010
Tactics	Jan 12, 2018
Tao	Jan 8, 2016
Test-Positions	Feb 25, 2018
Tor Lattimore	Jan 13, 2013
Turochamp	Dec 14, 2017
Undermining	Jun 10, 2012
Vlad Stamate	Dec 31, 2014
WildCat	Nov 11, 2016
Winter	Jan 23, 2018
Zappa	Oct 24, 2017
Zeus	Jan 3, 2018

Up one Level

Direction

GerdIsenberg — Thu, 06 Oct 2016 21:33:05 GMT

Home * Chess * Squares * Direction

		The Direction is a information of the geometrical relation of two squares on a chessboard without the information of distance. Mathematically, direction may be uniquely specified by a unit vector, or equivalently by the angle with respect to a specified set of axes.
Samuel Bak - Directions ^[1]

Move Directions

Ray Directions

Knight Directions

Directions between any Squares

In Degrees

In Begrees

Lookup

Lookup by 0x88 Difference

Move Directions

Directions on the chessboard are usually related to from- to-coordinates of moves, that is four orthogonal and four diagonal ray-directions plus the eight directions a knight may move. Following Compass roses give the directions and single step increments of an 8x8 Board.

Ray Directions

  northwest    north   northeast
  noWe         nort         noEa
          +7    +8    +9
              \  |  /
  west    -1 <-  0 -> +1    east
              /  |  \
          -9    -8    -7
  soWe         sout         soEa
  southwest    south   southeast

Knight Directions

        noNoWe    noNoEa
            +15  +17
             |     |
noWeWe  +6 __|     |__+10  noEaEa
              \   /
               >0<
           __ /   \ __
soWeWe -10   |     |   -6  soEaEa
             |     |
            -17  -15
        soSoWe    soSoEa

Directions between any Squares

In Degrees

Based on arctangent of the quotient of file- and rank-distance, one may calculate following 15 times 15 sheet with all possible angels which might occur between any squares in Degree (rounded to integer). Inner squares whose angle occur on farther squares are left blank, so each angle given is distinct, 144 from 224 (15x15-1), move directions are given in bold:

315	319	324	330	337	344	352	0	8	16	23	30	36	41	45
311		320	326	333	342	351	\|	9	18	27	34	40		49
306	310		321	329	338	349	\|	11	22	31	39		50	54
300	304	309		323		346	\|	14		37		51	56	60
293	297	301	307				\|				53	59	63	67
286	288	292					\|					68	72	74
278	279	281	284				\|				76	79	81	82
270	-	-	-	-	-	-	+	-	-	-	-	-	-	90
262	261	259	256				\|				104	101	99	98
254	252	248					\|					112	108	106
247	243	239	233				\|				127	121	117	113
240	236	231		217		194	\|	166		143		129	124	120
234	230		219	211	202	191	\|	169	158	149	141		130	126
229		220	214	207	198	189	\|	171	162	153	146	140		131
225	221	216	210	203	196	188	180	172	164	157	150	144	139	135

In Begrees

Enumerating all distinct integer degrees of the above rose in order but without any gaps, leaves a circle with 144 board degrees (Begrees) - only the 16 angels with modulo 9 equals zero are actually covered by move directions (bold). A possible application of Begrees is to select moves with a direction to an "interesting" area of the board, specified by some center- or gravity square.

126	127	131	134	136	139	143	0	1	5	8	10	13	17	18
125		128	132	135	138	142	\|	2	6	9	12	16		19
121	124		129	133	137	141	\|	3	7	11	15		20	23
118	120	123		130		140	\|	4		14		21	24	26
116	117	119	122				\|				22	25	27	28
113	114	115					\|					29	30	31
109	110	111	112				\|				32	33	34	35
108	-	-	-	-	-	-	+	-	-	-	-	-	-	36
107	106	105	104				\|				40	39	38	37
103	102	101					\|					43	42	41
100	99	97	94				\|				50	47	45	44
98	96	93		86		76	\|	68		58		51	48	46
95	92		87	83	79	75	\|	69	65	61	57		52	49
91		88	84	81	78	74	\|	70	66	63	60	56		53
90	89	85	82	80	77	73	_72	_71	_67	_64	_62	_59	_55	_54

Opposed to the compass-rose above, all inner squares are filled with Begrees as well.

126	127	131	134	136	139	143	0	1	5	8	10	13	17	18
125	126	128	132	135	138	142	0	2	6	9	12	16	18	19
121	124	126	129	133	137	141	0	3	7	11	15	18	20	23
118	120	123	126	130	135	140	0	4	9	14	18	21	24	26
116	117	119	122	126	132	138	0	6	12	18	22	25	27	28
113	114	115	117	120	126	135	0	9	18	24	27	29	30	31
109	110	111	112	114	117	126	0	18	27	30	32	33	34	35
108	108	108	108	108	108	108	+	36	36	36	36	36	36	36
107	106	105	104	102	99	90	72	54	45	42	40	39	38	37
103	102	101	99	96	90	81	72	63	54	48	45	43	42	41
100	99	97	94	90	84	78	72	66	60	54	50	47	45	44
98	96	93	90	86	81	76	72	68	63	58	54	51	48	46
95	92	90	87	83	79	75	72	69	65	61	57	54	52	49
91	90	88	84	81	78	74	72	70	66	63	60	56	54	53
90	89	85	82	80	77	73	_72	_71	_67	_64	_62	_59	_55	_54

Lookup

Since the computation is quite expensive, a two dimensional table with pre-calculated values might be used for that purpose. The enumerated type enumDir might contain only ray- or move directions, Degrees, Begrees, or a structure combining them.

enumDir arrDirection[64][64]; // 4 KByte
 
enumDir direction(enumSquare sq1, enumSquare sq2) {
   return arrDirection[sq1][sq2];
}

Lookup by 0x88 Difference

The 0x88 square relation permits a denser lookup approach. The difference of valid 0x88 coordinates of two squares is unique with respect to distance and direction. That way, one can greatly reduce the size of the lookup array to only 240 instead of 4096 elements. Some additional computation required, if one has to convert usual square coordinates to 0x88. If one already relies on 0x88 coordinates, it becomes even cheaper:

enumDir arrDirectionBy0x88Diff[240];
 
unsigned int x88diff(enumSquare sq1, enumSquare sq2) {
   return sq2 - sq1 + (sq2|7) - (sq1|7) + 120;
}
 
enumDir direction(enumSquare sq1, enumSquare sq2) {
   return arrDirectionBy0x88Diff[x88diff(sq1, sq2)];
}

Forum Posts

Extract direction (ray) informations from two squares by Mathieu Pagé, CCC, June 18, 2013 » Rays, Square Attacked By

External Links

Direction from Wikipedia
Relative direction from Wikipedia
Windward and leeward from Wikipedia
Starboard from Wikipedia
Port (nautical) from Wikipedia
Origins of the Compass Rose by Bill Thoen
Boxing the compass from Wikipedia
Weather Report - Directions, 73rd NDR-Jazzworkshop, IFA Berlin, September 03, 1971, YouTube Video
Joe Zawinul, Wayne Shorter, Miroslav Vitouš, Alphonse Mouzon, Dom Um Romão, & guests John Surman, Eje Thelin, Alan Skidmore

References

^ The Game of War from Samuel Bak - represented by Pucker Gallery since 1969

What links here?

Page	Date Edited
0x88	Nov 28, 2016
10x12 Board	Feb 19, 2018
8x8 Board	Aug 29, 2017
Abyss	Aug 5, 2017
AlphaZero	Feb 10, 2018
Array	Dec 1, 2016
Atlas	Nov 5, 2017
AVX2	Aug 8, 2017
Backtracking	Dec 16, 2017
Battery	Jan 29, 2017
Belle	Jan 18, 2018
Check	Feb 1, 2018
Checks and Pinned Pieces (Bitboards)	Aug 14, 2013
Connectivity	Mar 6, 2016
DayDreamer	Aug 22, 2016
Direction	Oct 6, 2016
DirGolem	Jun 5, 2016
Discovered Attack	Nov 8, 2010
Distance	Sep 25, 2015
Dumb7Fill	May 27, 2016
Encoding Moves	Mar 27, 2016
Fill Algorithms	Nov 6, 2013
Freccia	Dec 26, 2017
General Setwise Operations	Feb 25, 2018
GiuChess	May 8, 2017
Gullydeckel	Oct 28, 2015
Joker IT	Sep 16, 2017
King	Feb 26, 2013
King Pattern	Nov 15, 2013
Knight Pattern	Feb 23, 2015
Kogge-Stone Algorithm	Sep 17, 2016
Kurt	Apr 20, 2014
Legal Move	Feb 16, 2017
Manhattan-Distance	May 19, 2014
Mate at a Glance	Sep 24, 2014
Mate-in-two	Oct 14, 2016
Mater	Apr 26, 2016
Nibble	Jan 25, 2015
OliThink	May 19, 2017
On an empty Board	Mar 18, 2014
Othello	Jan 4, 2018
Pawn Fills	Jul 18, 2014
Pawn Pushes (Bitboards)	Apr 5, 2013
Piece-Lists	Feb 13, 2017
Pieces versus Directions	Oct 6, 2016
Pin	Mar 7, 2017
Pseudo-Legal Move	May 23, 2015
Purple Haze	Oct 26, 2017
Rays	Oct 20, 2016
Rule of the Square	Sep 6, 2014
SBAMG	Dec 4, 2016
Sensor Chess	Jun 7, 2013
Sliding Piece Attacks	May 27, 2016
Space	Jan 18, 2018
Square Attacked By	Jan 20, 2018
Square Mapping Considerations	Feb 28, 2018
Squares	Feb 15, 2015
Table-driven Move Generation	Feb 19, 2017
Thor's Hammer	Nov 23, 2013
Vanilla Chess	Jan 13, 2013
Vector Attacks	Dec 15, 2017
X-ray	Apr 12, 2017
X-ray Attacks (Bitboards)	Mar 31, 2015

Up one Level

Dispersion and Distortion

GerdIsenberg — Sat, 11 Nov 2017 09:15:45 GMT

Home * Board Representation * Bitboards * Pawn Pattern and Properties * Dispersion and Distortion

		Dispersion and Distortion, Kmoch's terms ^[1] ^[2] for pawn structure weaknesses due to vertical or horizontal splitting caused by captures or advancement. The proposed functions may be used via an additional scaling or indirection, f.i. to index a table with concrete penalties.
Samuel Bak - Luna ^[3]

Dispersion

Dispersion is Kmoch's term for vertical splitting of pawns (most commonly, isolation) caused by captures. Having three or four islands while the opponent has one or two - assuming about the same number of pawns for both sides - may be considered in evaluation. But this is also implicitly done by evaluating double- or triple and isolated or the balance of weak pawns in general. Some arbitrary dispersion measure, intended as evaluation term.

int dispersion(U64 pawns)
{
   BYTE fileset  = (BYTE) soutFill(pawns);
   int  ni = popCount(islandsEastFiles(fileset));
   int  np = popCount(wpawns);
   return abs(3*ni*ni - np);
}
 
BYTE islandsEastFiles(BYTE f) {return f & ((f ^ (f >> 1));}

The higher the worse.

  \  number if islands
   \     1   2   3   4
np  \    3  12  27  48
_____\________________
 1   |   2   -   -   -
 2   |   1  10   -   -
 3   |   0   9  24   -
 4   |   1   8  23  44
 5   |   2   7  22  43
 6   |   3   6  21  42
 7   |   4   5  20  41
 8   |   5   4  19  40

Distortion

Distortion is Kmoch's term for horizontal splitting of pawns caused by advances. One may use something like this based on rearfill, xor and population count to get an idea of distortion. It considers the rank-difference of two file-adjacent pawns (if any) as distortion penalty - the higher the worse. Half-isolated or even isolated pawns contribute a distortion penalty according to the size of their rearfill from 2 to 7 for each empty neighboring file, which discourages advancement of such pawns, interacting with terms considerring (half-) isolated pawns. Alternatively, for a "reverse" distortion penalty to encourage advancement of half-isolanis, one may use frontfill instead with a slightly different semantic is case of doubled pawns.

int wDistortion(U64 wpawns) {
   U64 fill  = wRearFill(wpawns); // wFrontFill
   U64 delta = (fill ^ (fill<<1)) & C64(0xfefefefefefefefe));
   return popCount(delta);
}

High distortion sample:

wpawns              rearFill            rearFill << 1      xor & ~A-File
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . 1 . 1 . 1 .     . . 1 . 1 . 1 .     . . . 1 . 1 . 1     . . 1 1 1 1 1 1
. . . . . . . .     . . 1 . 1 . 1 .     . . . 1 . 1 . 1     . . 1 1 1 1 1 1
1 . . . . . . .     1 . 1 . 1 . 1 .     . 1 . 1 . 1 . 1     . 1 1 1 1 1 1 1
. . . . . . . .     1 . 1 . 1 . 1 .     1 1 . 1 . 1 . 1     . 1 1 1 1 1 1 1
. 1 . 1 . 1 . 1     1 1 1 1 1 1 1 1     1 1 1 1 1 1 1 1     . . . . . . . .
. . . . . . . .     1 1 1 1 1 1 1 1     . 1 1 1 1 1 1 1     . . . . . . . .
 
                                                            26 bits sets

External Links

References

^ Hans Kmoch (1959, 1990). Pawn Power in Chess. New York: Dover, 1990. Previous ed.: New York: McKay, 1959. ISBN 0-486-26486-6
^ Pawn Power in Chess by Hans Kmoch - Glossary of Terms - Chess Forums - Chess.com
^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota

What links here?

Page	Date Edited
Dispersion and Distortion	Nov 11, 2017
Hans Kmoch	Nov 11, 2017
Pawn Islands (Bitboards)	May 4, 2017
Pawn Pattern and Properties	Nov 11, 2017
Space-Time Tradeoff	Jun 17, 2015
Weak Pawns	Dec 19, 2013

Up one Level

Endgame Tablebases

GerdIsenberg — Tue, 06 Mar 2018 21:48:25 GMT

Home * Knowledge * Endgame Tablebases

		Endgame Tablebases, (EGTBs or EGTs) precalculated endgame tables generated by an exhaustive retrograde analysis. During its game play and/or search, recognizing a specific material composition, a chess program can probe, or in principle compute these tables to determine the outcome of positions definitively and act as an oracle providing the optimal moves. The tables are usually divided into separate files for each material configuration and side to move. What all different formats of tablebases have in common is that every possible piece placement has its own, unique index number which represents the position where the information about the position is located in the file. Positions with non-null castling rights could be represented in an EGT but typically are not. The term Tablebase opposed to endgame database was coined by Steven Edwards by means of a data vector and a single file access for both sides to move, when he introduced his Edwards' Tablebases, addressing several shortcomings of Ken Thompson's earlier database of positions with the weaker and hence potentially losing side to move only ^[1] .
Samuel Bak - Persistence ^[2]

Selected Publications

Metrics

DTM

Depth to Mate
'Mate' is the ultimate goal and ends the game. For each position that is represented, 'DTM' indicates the theoretical value, and the number of winner's moves to 'Mate' if won/lost - assuming that the winner is minimizing and the loser is maximizing DTM.

DTC

Depth to Conversion
'Conversion' is the changing of the force on the board, by capture and/or Pawn-conversion. For each position that is represented, 'DTC' indicates the theoretical value, and the number of winner's moves to the goal of 'Won Conversion' if won/lost - assuming that the winner is minimizing and the loser is maximizing DTC. DTC £ DTM.

DTZ

Depth to Zeroing (of the ply count)
The ply-count is zeroed if and only if a Pawn is pushed or a capture is made. For each position that is represented, 'DTZ' indicates the theoretical value, and the number of winner's moves to the goal of 'Win and ply-count zeroed' if won/lost - assuming that the winner is minimizing and the loser is maximizing DTZ. DTZ £ DTC £ DTM.

DTZ50

Depth to Zeroing (of the ply count) in the context of the 50-Move Rule
The DTC, DTM and DTZ metrics do not consider the current FIDE 50-move rule whereby a game in which no irreversible moves have been played for 100 plies can be claimed as a draw by the player 'on move'. In this metric, in addition to the DTC/DTM/DTZ draws, positions requiring more than 50 winner's moves to zero the ply-count are defined as draws. DTZ £ DTZ50 if DTZ50 ¹ draw. 'DTZ50' is one of a set of 'DTZk' rules: a k-move rule effectively applies if there are only k moves left before a draw-claim might be made. k1 £ k2 implies DTZk2 £ DTZk1 if DTZk1 ¹ draw.

Note that, because depth is measured in winner's moves rather than plies, this metric does not define as draw a position in which 50 winner's moves and 51 loser's moves are required to zero the ply-count, despite the fact that the loser would claim a draw after 100 plies had been played in that endgame.

DTR

Depth by the (k-move) Rule
'The Rule' referred to here is a notional set of k-move rules. For each position that is represented, 'DTR' indicates the theoretical value and, for won/lost positions, the least k for which DTZk is not draw - assuming that the winner is minimising and the loser is maximising DTR. DTZ £ DTR. No DTR EGTs have been created to date ^[3] .

DTZR

Depth to Zeroing move, give that DTR is being minimaxed
If DTR = draw, then DTZR = draw. Otherwise, Otherwise DTRZR indicates the theoretical value, and the number of winner's moves to the zeroing of the ply count, given that the two sides are minimaxing first DTR and then DTZR. DTZR would be used in conjunction with DTR to progress a deep win in the context of a k-move rule because DTR can remain unchanged over a sequence of moves. DTZR £ DTR but it is not always the case that DTZ £ DTZR as may seem intuitively obvious: the loser may zero the move-count to maximise DTR.

Summary

To summarize the different metrics of tablebases, each metric has its strengths and weaknesses. Nalimov's DTM EGTs are widely and commercially available, and used by many chess engines or chess GUIs. DTC EGTs are more easily computed and stored as they involve smaller depth-ranges and are more compressible. For endgames with less or equal than 5 pieces on the board, KNNKP comes closest to requiring more than one Byte per position to store DTM: maxDTM = 115 (1-0) and 73 (0-1) necessitating 190 values in the EGT. For KPPKP, maxDTM = 127 (1-0) but only 42 (0-1). But for certain 6 piece endgames, one Byte is not enough: maxDTM = 262 for a KRNKNN position. The DTC and DTZ metrics increasingly postpone the need for two Bytes per position in an uncompressed EGT, but KRBNKQN has maxDTC = maxDTZ = 517 (0-1), both wtm and btm.

In extremis, he unmoderated use of DTM, DTC or DTZ EGTs will let slip a winnable position in the context of the 50-move rule ... hence the marginal need for the DTR and DTZR metrics, coupled with the ability to recompute DTR/DTZR EGTs in the context of a limited move-budget.

Bitbases

see main article Endgame Bitbases

Inside the search much denser tables with value {won, draw, loss, invalid} or boolean {win, not_win} information are sufficient with respect to bounds. Denser tables are more efficiently used, given that memory and cache are limited resources. Boolean Win/Not_Win Bitbases require only one bit per position (and if necessary, further enquiry if draw is to be distinguished from loss with respect to bounds). Value Bitbases require two bits per position.

Indexing

Every position is assigned to an unique index to specify the location of the information stored about it. There are two main aims when generating the index number. The easier the algorithm to generate the index from any given position, the faster will be the probing of the tablebase as well as the generation of it. But the second aim is to get a relatively small range of index-numbers, to keep the size of the file as small as possible.

The most straight forward way would be to for every piece on the board use 6 bit (1-64 squares)

index = position_white_King + position_black_King * 64
 
for each piece {
    index = index * 64 + position
}

This can be optimized in several ways.
A chess board can be rotated and mirrored (if pawns are on the board only a vertical reflection is possible).

Pieces may not stand on the same square.
For pieces of the same type, different arrangements can be left away.
The side to move may not give check.
The distance between the two Kings must be greater than one.

Brief Info

of some popular Endgame tablebases:

Format	Metric	1st published	5 men	6 men	7 men
Thompson	DTC	1991	2.5 GiB (not completed)	-	-
Edwards	DTM	1994	56 GiB (estimated)	-	-
Nalimov	DTM	1998	7.1 GiB	1.2 TiB	-
Scorpio	WDL	2005	214 MiB	48.1 GiB	-
Gaviota	DTM	2008	6.5 GiB	-	-
Lomonosov	DTM	2012	-	-	140 TiB
Syzygy	WDL + DTZ50	2013	939 MiB	150.2 GiB	-

Formats

Generators

7-man EGTBs

2005

In 2005, Yakov Konoval started to collaborate with Marc Bourzutschky on constructing 7-man EGTBs. Yakov wrote the generator and Marc a verification program and some utilities for extracting the data. In October 2005, Yakov Konoval and Marc Bourzutschky announced that a position in the ending of a KRRNkrr requires 290 moves to convert to a simpler winning endgame ^[4] . The old record was 243 moves from a position in a rook and knight versus two knights endgame, discovered by Lewis Stiller in 1991 ^[5] .

2006

In March 2006, the wizards of 7-men endgames, Marc Bourzutschky and Yakov Konoval found a 330 moves win in KQBNkqb ^[6] and in May 2006 a 517 moves win in KQNkrbn ^[7] .

2012

In July 2012, Vladimir Makhnychev and Victor Zakharov from Moscow State University completed 4+3 DTM-tablebases (525 endings including KPPPKPP). The next set of 5+2 DTM-tablebases was completed during August 2012 ^[8] . The tablebases are named Lomonosov Tablebases, using the Lomonosov Supercomputer.

2013

Convekta Ltd. announced the release of Lomonosov Tablebases. Until December 31, 2013, the tablebases will be available online through ChessOk products ^[9] .

Selected Publications

1965 ...

Richard E. Bellman (1965). On the application of dynamic programming to the determination of optimal play in chess and checkers. Proceedings of the National Academy of Sciences of the United States of America. pdf

1970 ...

Thomas Ströhlein (1970). Untersuchungen über kombinatorische Spiele. Ph.D. Thesis, Technical University of Munich (German)
Edward Komissarchik, Aaron L. Futer (1974). Ob Analize Ferzevogo Endshpilya pri Pomoshchi EVM. (Analysis of a queen endgame using an IBM computer) Problemy Kybernetiki, Vol. 29, pp. 211-220. English translation by C. Posthoff, revised in ICCA Journal, Vol. 9, No. 4 (1986)

1975 ...

A. G. Alexandrov, A. M. Baraev, Ya. Yu. Gol'fand, Edward Komissarchik, Aaron L. Futer (1977). Computer analysis of rook end game. Avtomatika i Telemekhanika, No. 8, 113–117
A. G. Alexandrov, Vladimir Arlazarov, A. M. Baraev, Ya. Yu. Gol'fand, V. N. Deza, T. P. Il’ina, Edward Komissarchik, Anatoly Uskov, I. A. Faradzhev, Aaron L. Futer (1977). Processing of large files of information on the example of the analysis of the rook’s end game. Programming and Computer Software, No. 3
Thomas Ströhlein, Ludwig Zagler (1977). Analyzing games by Boolean matrix iteration. Discrete Mathematics, Vol. 19, No. 2
Thomas Ströhlein, Ludwig Zagler (1978). Ergebnisse einer vollstandigen Analyse von Schachendspielen: König und Turm gegen König, König und Turm gegen König und Laufer. Report, Institut für Informatik, Technical University of Munich (German)
Max Bramer (1978). Computer-Generated Databases for the Endgame in Chess. Technical Report. Milton Keynes, Open University Faculty of Mathematics.
Aaron L. Futer (1978). Programming endgames with few pieces. Soviet Physics. Doklady, No. 23
Vladimir Arlazarov, Aaron L. Futer (1979). Computer Analysis of a Rook End-Game. Machine Intelligence 9 (eds. Jean Hayes Michie, Donald Michie and L.I. Mikulich), pp. 361-371. Ellis Horwood, Chichester. Reprinted in Computer Chess Compendium

1985 ...

Jaap van den Herik, Bob Herschberg (1985). The Construction of an Omniscient Endgame Data Base. ICCA Journal, Vol. 8, No. 2
John Roycroft (1985). Chess-Endgame Data-Base`Oracles': Necessary and Desirable Features. ICCA Journal, Vol. 8, No. 2
Harry Nefkens (1985). Constructing Data Bases to Fit a Microcomputer. ICCA Journal, Vol. 8, No. 4

1986

Jaap van den Herik, Bob Herschberg (1986). A Data Base on Data Bases. ICCA Journal, Vol. 9, No. 1
John Roycroft, Ken Thompson (1986). Queen and Pawn on a2 against Queen. Chess Endgame Consultants and Publishers, London
John Roycroft, Ken Thompson (1986). Queen and Pawn on a6 against Queen. Chess Endgame Consultants and Publishers, London
John Roycroft, Ken Thompson (1986). Queen and Pawn on b7 against Queen. Chess Endgame Consultants and Publishers, London
Jaap van den Herik (1986). Roycroft's 5-Man Chess Endgame Series. ICCA Journal, Vol. 9, No. 3
Ken Thompson (1986). Retrograde Analysis of Certain Endgames. ICCA Journal, Vol. 9, No. 3, pdf
Edward Komissarchik, Aaron L. Futer (1986). Computer Analysis of a Queen Endgame. ICCA Journal, Vol. 9, No. 4 ^[10]
Ken Thompson (1986). An Example of QPvQ. ICCA Journal, Vol. 9, No. 4
Hans Zellner (1986). Compressing Databases Down to Micro Size. ICCA Journal, Vol. 9, No. 4

1987

Hans Zellner (1987). KBBK Squeezed into a Micro. ICCA Journal, Vol. 10, No. 1
Jaap van den Herik, Bob Herschberg (1987). The KBBKN Statistics: New Data from Ken Thompson. ICCA Journal, Vol. 10, No. 1
Bob Herschberg, Jaap van den Herik (1987). More Truth on KBBK Database Results. ICCA Journal, Vol. 10, No. 2
Hans Zellner, Jaap van den Herik, Bob Herschberg (1987). Corrections and Substantiations to KBNK. ICCA Journal, Vol. 10, No. 3
Sito Dekker, Jaap van den Herik, Bob Herschberg (1987). Complexity Starts at Five. ICCA Journal, Vol. 10, No. 3
Lars Rasmussen (1987). Correcting grandmasters' Analyses in Elementary Endgames. ICCA Journal, Vol. 10, No. 4
Jaap van den Herik, Bob Herschberg, Najib Nakad (1987). A Six-Men-Endgame Database: KRP(a2)KbBP(a3). ICCA Journal, Vol. 10, No. 4, pdf
Sito Dekker, Jaap van den Herik, Bob Herschberg (1987). Perfect Knowledge and Beyond. Report 37-87, Delft University of Technology, Delft.
John Roycroft (1987). Expert Against Oracle. Machine Intelligence 11

1988

Jaap van den Herik, Bob Herschberg (1988). Computer Checks on Human Analyses of the KRKB Endgame. ICCA Journal, Vol. 11, No. 1
Lars Rasmussen (1988). Ultimates in KQKR and KRKN. ICCA Journal, Vol. 11, No. 1
Lewis Stiller (1988). Massively Parallel Retrograde Endgame Analysis. BUCS Tech. Report #88-014, Boston University, Computer Science Department.
Jaap van den Herik, Bob Herschberg, Najib Nakad (1988). A Reply to R. Sattler's Remarks on the KRP(a2)KbBP(a3) Database. ICCA Journal, Vol. 11, No. 2/3, pdf
Lars Rasmussen (1988). A Database for KRKP. ICCA Journal, Vol. 11, No. 4

1989

Christopher A. Marris (1989). Compressing a Chess-Endgame Database. ICCA Journal, Vol. 12, No. 1
David Forthoffer, Lars Rasmussen, Sito Dekker (1989). A Correction to some KRKB-Database Results. ICCA Journal, Vol. 12, No. 1
Edmar Mednis (1989). Rook and Bishop versus Rook: The Controversial Endgame. ICCA Journal, Vol. 12, No. 1
Lewis Stiller (1989). Parallel Analysis of Certain Endgames. ICCA Journal, Vol. 12, No. 2
Hans Zellner (1989). The KPK Database Revisited. ICCA Journal, Vol. 12, No. 2
Sito Dekker, Jaap van den Herik, Bob Herschberg (1989). Perfect Knowledge and Beyond. Advances in Computer Chess 5
Bob Herschberg, Jaap van den Herik, Patrick Schoo (1989). Verifying and Codifying Strategies in the KNNKP(h) Endgame. ICCA Journal, Vol. 12, No. 3, pdf
Hans Zellner (1989). KBBKN on a Micro. ICCA Journal, Vol. 12, No. 3
John Roycroft (1989). The Computer is at it again - Interfering with the Endgame! Britisch Chess Magazine, Vol. 109, No. 10

1990 ...

Bob Herschberg, Jaap van den Herik, Patrick Schoo (1990). Verifying and Codifying Strategies in a Chess Endgame. Computers, Chess, and Cognition, pp. 183-196
John Roycroft (1990). How to Treat Endgame Databases. ICCA Journal, Vol. 13, No. 2
Ken Thompson (1990). KQPKQ and KRPKR Endings. ICCA Journal, Vol. 13, No. 4
John Roycroft (1990). Identifying Three Types of Zugzwang. ICCA Journal, Vol. 13, No. 4 » Zugzwang

1991

Ken Thompson (1991). Chess Endgames Vol. 1. ICCA Journal, Vol. 14, No. 1
Ken Thompson (1991). New Results for KNPKB and KNPKN Endgames. ICCA Journal, Vol. 14, No. 1
Edmar Mednis (1991). Database Results for KQKRN and KQKRB annotated. ICCA Journal, Vol. 14, No. 2
John Roycroft (1991). A Postscript to the Computer's Involvement. Britisch Chess Magazine, Vol. 111, No. 2
Lewis Stiller (1991). Some Results from a Massively Parallel Retrograde Analysis. ICCA Journal, Vol. 14, No. 3
John Roycroft (1991). A Side-Effect of new Database Knowledge. ICCA Journal, Vol. 14, No. 3
John Roycroft (1991). A Use for Endgame Databases? ICCA Journal, Vol. 14, No. 4
John Roycroft, Don Beal (1991). To Make Dumb Endgame Databases Speak. Advances in Computer Chess 6

1992

Lewis Stiller (1992). KQNKRR. ICCA Journal, Vol. 15, No. 1
John Nunn (1992). Perfect Prose. ICCA Journal, Vol. 15, No. 2
Lars Rasmussen (1992). Queen versus Rook and Pawn. ICCA Journal, Vol. 15, No. 2

1993

Burton Wendroff, Tony Warnock, Lewis Stiller, Dean Mayer, Ralph Brickner (1993). Bits and pieces: constructing chess endgame databases on parallel and vector architectures. Appl. Num. Math. 12, pp. 285-295, zipped ps
Christian Posthoff, Michael Schlosser, Jens Zeidler (1993). Search vs. Knowledge? - Search and Knowledge! In: Proc. 3rd KADS Meeting, Munich, March 8-9 1993, Siemens AG, Corporate Research and Development, 305-326, 1993.
John Nunn (1993). Extracting Information from Endgame Databases. ICCA Journal, Vol. 16, No. 4

1994

Ingo Althöfer, Bernhard Walter (1994). Weak Zugzwang: Statistics on some Chess Endgames. ICCA Journal, Vol. 17, No. 2
John Nunn (1994). More, and More Perfect Prose. ICCA Journal, Vol. 17, No. 2
John Nunn (1994). Extracting Information from Endgame Databases. Advances in Computer Chess 7
Christian Posthoff, Michael Schlosser, Rainer Staudte, Jens Zeidler (1994). Transformations of Knowledge. Advances in Computer Chess 7
Grit Lachmann (1994). Verarbeitung von Wissen aus Endspieldatenbanken. Master's thesis, Chemnitz University of Technology (German)

1995 ...

Steven Edwards and the Editorial Board (1995). An Examination of the Endgame KBNKN. ICCA Journal, Vol. 18, No. 3
Henri Bal, Victor Allis (1995). Parallel Retrograde Analysis on a Distributed System. Supercomputing ’95, San Diego, CA.

1996

Dietmar Lippold (1996). Legality of Positions of Simple Chess Endgames. zipped pdf ^[11]
Ken Thompson (1996). 6-Piece Endgames. ICCA Journal, Vol. 19, No. 4
Lewis Stiller (1996). Multilinear Algebra and Chess Endgames. Games of No Chance edited by Richard J. Nowakowski, pdf

1997

Dietmar Lippold (1997). The Legitimacy of Positions in Endgame Databases. ICCA Journal, Vol. 20, No. 1
Ken Thompson (1997). 6-Piece Endgames. Advances in Computer Chess 8
Johannes Fürnkranz (1997). Knowledge Discovery in Chess Databases: A Research Proposal. Technical Report OEFAI-TR-97-33, Austrian Research Institute for Artificial Intelligence, zipped ps, pdf ^[12]

1999

Ernst A. Heinz (1999). Endgame Databases and Efficient Index Schemes for Chess. ICCA Journal, Vol. 22, No. 1, ps
Ernst A. Heinz (1999). Knowledgeable Encoding and Querying of Endgame Databases. ICCA Journal, Vol. 22, No. 2, ps
Christoph Wirth, Jürg Nievergelt (1999). Exhaustive and Heuristic Retrograde Analysis of the KPPKP Endgame. ICCA Journal, Vol. 22, No. 2
Eugene Nalimov, Christoph Wirth, Guy Haworth (1999). KQQKQQ and the Kasparov-World Game. ICCA Journal, Vol. 22, No. 4
Ulrich Thiemonds (1999). Ein regelbasiertes Spielprogramm für Schachendspiele. University of Bonn, Diploma thesis, zipped ps (German)
Chrilly Donninger (1999). Der Fortschritt ist nicht aufzuhalten - Chrilly Donninger über Endspieldatenbanken. CSS 6/99, pdf (German)

2000 ...

Haw-ren Fang, Tsan-sheng Hsu, Shun-Chin Hsu (2000). Construction of Chinese Chess Endgame Databases by Retrograde Analysis. CG 2000
Ken Thompson (2000). The Longest: KRNKNN in 262. ICGA Journal, Vol. 23, No. 1
Peter Karrer (2000). KQQKQP and KQPKQP≈.ICGA Journal, Vol. 23, No. 2 ^[13]
Guy Haworth (2000). Chess Endgames: Currents and Futures. 5th Computer Olympiad Workshop
Thomas Lincke, Ambros Marzetta (2000). Large Endgame Databases with Limited Memory Space. 5th Computer Olympiad Workshop
Thomas Lincke, Ambros Marzetta (2000). Large Endgame Databases with Limited Memory Space. ICGA Journal, Vol. 23, No. 3
Eugene Nalimov, Guy Haworth, Ernst A. Heinz (2000). Space-Efficient Indexing of Chess Endgame Tables. ICGA Journal, Vol. 23, No. 3, postscript

2001

John Tamplin, Guy Haworth (2001). Ken Thompson's 6-man Tables. ICGA Journal, Vol. 24, No. 2
Harold van der Heijden (2001). Endgame Tables and Endgame Study Composition. ICGA Journal, Vol. 24, No. 2
Noam Elkies (2001). Endgame Tables and Chess Composition. ICGA Journal, Vol. 24, No. 2
Ren Wu, Don Beal (2001). Fast, Memory-efficient Retrograde Algorithms. ICGA Journal, Vol. 24, No. 3 ^[14] ^[15]
Ren Wu, Don Beal (2001). Parallel Retrograde Analysis on Different Architectures. IEEE 10th Conference in High Performance Distributed Computing pp. 356-362, August 2001
Eugene Nalimov, Guy Haworth, Ernst A. Heinz (2001). Space-efficient Indexing of Endgame Tables for Chess. Advances in Computer Games 9
Guy Haworth (2001). Four Notes on Chess Endgames. 6th Computer Olympiad Workshop, ppt
Guy Haworth (2001). Discarding Like Pieces. 6th Computer Olympiad Workshop
Guy Haworth (2001). Depth by The Rule. 6th Computer Olympiad Workshop
Guy Haworth (2001). 3-5-Man Chess Data. 6th Computer Olympiad Workshop
Guy Haworth (2001). 3-5-Man Mutual Zugzwangs in Chess. 6th Computer Olympiad Workshop
Guy Haworth (2001). Discarding Like Pieces. ICGA Journal, Vol. 24, No. 3
Guy Haworth (2001). Depth by The Rule. ICGA Journal, Vol. 24, No. 3
Guy Haworth, Peter Karrer, John Tamplin, Christoph Wirth (2001). 3-5-man chess: Maximals and mzugs. ICGA Journal, Vol. 24, No. 4

2002

Guy Haworth (2002). Secrets of Pawnless Endings. ICGA Journal, Vol. 25, No. 2
Eugène Nalimov (2002). Chess Endgame Tablebases. Invited Lecture, 7th Computer Olympiad Workshop
Guy Haworth (2002). Reference Fallible Endgame Play. 7th Computer Olympiad Workshop, pdf
Ren Wu, Don Beal (2002). A memory efficient retrograde algorithm and its application to solve Chinese Chess endgames. More Games of No Chance edited by Richard J. Nowakowski

2003

John Tamplin, Guy Haworth (2003). Chess Endgames: Data and Strategy. Advances in Computer Games 10
Guy Haworth, Rafael B. Andrist (2003). Model Endgame Analysis. Advances in Computer Games 10
Jonathan Schaeffer, Yngvi Björnsson, Neil Burch, Rob Lake, Paul Lu, Steve Sutphen (2003). Building the Checkers 10-Piece Endgame Databases. Advances in Computer Games 10. pdf » Checkers
Guy Haworth (2003). Reference Fallible Endgame Play. ICGA Journal, Vol. 26, No. 2
Ed Trice, Gil Dodgen (2003). The Perfect 7-Piece Checkers Database. ICGA Journal, Vol. 26, No. 4 » Checkers

2004

Haw-ren Fang (2004). Rule-Tolerant Verification Algorithms for Completeness of Chinese-Chess Endgame Databases. CG 2004
Eiko Bleicher (2004). Building Chess Endgame Databases for Positions with many Pieces using A-priori Information. Lehrstuhl Mathematische Optimierung, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, Jena, Germany, as pdf

2005 ...

Joe Hurd (2005). Formal Verification of Chess Endgame Databases. in Joe Hurd, Edward Smith, Ashish Darbari Theorem proving in higher order logics: Emerging trends proceedings. Technical Report PRG-RR-05-02, Oxford University Computing Laboratory, pdf
Jesper Torp Kristensen (2005). Generation and compression of endgame tables in chess with fast random access using OBDDs. Master thesis, Supervisor Peter Bro Miltersen, Aarhus University, pdf ^[16]
Guy Haworth (2005). 6-Man Chess Solved. ICGA Journal, Vol. 28, No. 3
Marc Bourzutschky, John Tamplin, Guy Haworth (2005). Chess endgames: 6-man data and strategy. Theoretical Computer Science, Vol. 349, No. 2
Rafael B. Andrist, Guy Haworth (2005). Deeper model endgame analysis. Theoretical Computer Science, Vol. 349, No. 2
Guy Haworth (2005). Chess Endgame News. ICGA Journal, Vol. 28, No. 4
Yngvi Björnsson, Jonathan Schaeffer, Nathan Sturtevant (2005). Partial Information Endgame Databases. Advances in Computer Games 11, pdf, pdf

2006

Guy Haworth (2006). Chess Endgame News. ICGA Journal, Vol. 29, No. 1
Guy Haworth (2006). Chess Endgame News. ICGA Journal, Vol. 29, No. 2
Guy Haworth (2006). Chess Endgame News. ICGA Journal, Vol. 29, No. 3

2008

Bo-Nian Chen, Pangfeng Liu, Shun-Chin Hsu, Tsan-sheng Hsu (2008). Knowledge Inferencing on Chinese Chess Endgames. CG 2008

2009

Guy Haworth (2009). Chess Endgame Update. ICGA Journal, Vol. 32, No. 4

2010 ...

Bo-Nian Chen, Pangfeng Liu, Shun-Chin Hsu, Tsan-sheng Hsu (2010). Conflict Resolution of Chinese Chess Endgame Knowledge Base. Advances in Computer Games 12, pdf
Joe Hurd, Guy Haworth (2010). Data Assurance in Opaque Computations. Advances in Computer Games 12, pdf
Matej Guid, Martin Možina, Aleksander Sadikov, Ivan Bratko (2010). Deriving Concepts and Strategies from Chess Tablebases. Advances in Computer Games 12, pdf
Eiko Bleicher, Guy Haworth (2010). 6-Man Chess and Zugzwangs. Advances in Computer Games 12
Bo-Nian Chen, Pangfeng Liu, Shun-Chin Hsu, Tsan-sheng Hsu (2010). Knowledge Abstraction in Chinese Chess Endgame Databases. CG 2010
Ping-hsun Wu, Ping-yi Liu, Tsan-sheng Hsu (2010). An External-memory Retrograde Analysis Algorithm, slides as pdf
Eiko Bleicher, Guy Haworth, Harold van der Heijden (2010). Data-Mining Chess Databases. ICGA Journal, Vol. 33, No. 4

2011

Guy Haworth (2011). Chess Endgame News. ICGA Journal, Vol. 34, No. 2

2013

Guy Haworth (2013). Chess Endgame News. ICGA Journal, Vol. 36, No. 1
Guy Haworth (2013). Chess Endgame News. ICGA Journal, Vol. 36, No. 2
Abdallah Saffidine, Nicolas Jouandeau, Cédric Buron, Tristan Cazenave (2013). Material Symmetry to Partition Endgame Tables. CG 2013
John Nunn (2013). Discoveries in R+2P vs. R+P Endings. ICGA Journal, Vol. 36, No. 3
Guy Haworth (2013). Chess Endgame News. ICGA Journal, Vol. 36, No. 3
Karsten Müller, Guy Haworth (2013). Rook vs. Bishop. ICGA Journal, Vol. 36, No. 4
Bo-Nian Chen, Hung-Jui Chang, Shun-Chin Hsu, Jr-Chang Chen, Tsan-sheng Hsu (2013). Multilevel Inference in Chinese Chess Endgame Knowledge Bases. ICGA Journal, Vol. 36, No. 4 » Chinese Chess
Guy Haworth (2013). Chess Endgame News. ICGA Journal, Vol. 36, No. 4
Guy Haworth (2013). Haworth’s Law. ICGA Journal, Vol. 36, No. 4
Victor Zakharov, Vladimir Makhnychev (2013). Creating tables of chess 7-piece endgames on the Lomonosov supercomputer. Superkomp’yutery, No. 15

2014

Bo-Nian Chen, Hung-Jui Chang, Shun-Chin Hsu, Jr-Chang Chen, Tsan-sheng Hsu (2014). Advanced Meta-knowledge for Chinese Chess Endgame Knowledge Bases. ICGA Journal, Vol 37, No. 1 » Chinese Chess
Guy Haworth (2014). Chess Endgame News. ICGA Journal, Vol. 37, No. 1 » Syzygy Bases
Guy Haworth (2014). Chess Endgame News. ICGA Journal, Vol. 37, No. 2 » Syzygy Bases
Guy Haworth (2014). Chess Endgame News. ICGA Journal, Vol. 37, No. 3 » Syzygy Bases

2015 ...

Nikolaos Papahristou, Ioannis Refanidis (2015). Constructing Pin Endgame Databases for the Backgammon Variant Plakoto. Advances in Computer Games 14 ^[17]
Guy Haworth (2015). Chess Endgame News. ICGA Journal, Vol. 38, No. 1 » Crafty, FinalGen
Galen Huntington, Guy Haworth (2015). Depth to Mate and the 50-Move Rule. ICGA Journal, Vol. 38, No. 2 » Fifty-Move Rule ^[18]
Michael Hartisch, Ingo Althöfer (2015). Optimal Robot Play in Certain Chess Endgame Situations. ICGA Journal, Vol. 38, No. 3

2016

Victor Zakharov, Michael G. Malkovsky, Vladislav Y. Shchukin (2016). Compression of underdetermined data in a 7-piece chess table. Moscow University Computational Mathematics and Cybernetics, Vol. 40, No. 1 ^[19]

2017

Karsten Müller (2017). Tablebases, Fermat, Knights and Knightmares. ICGA Journal, Vol. 39, No. 2
Guy Haworth (2017). Chess Endgame News. ICGA Journal, Vol. 39, No. 2

Forum Posts

1995 ...

endgame databases and Kasparov by Feng-Hsiung Hsu, rgc, April 25, 1995
Tablebases and castling? by Ronald de Man, rgcc, May 12, 1997
Steve Edward's Endgame Tablebase generator is now available for WIN95 by Mike Byrne, CCC, November 01, 1997
Questions about Endgame tablebases by Alexander Nitschke, rgcc, March 19, 1998
Tablebases by Eugene Nalimov, CCC, August 28, 1998 » Nalimov Tablebases
Ideas to reduce size of tablebases by Rémi Coulom, CCC, August 31, 1998
endgame databases by Robert Hyatt, rgcc, October 13, 1998
Interesting endgame database probe problem by Robert Hyatt, CCC, February 04, 1999
overlapping tablebase lookup by Jay Scott, CCC, February 09, 1999

2000 ...

Tablebase Access Code by Roberto Waldteufel, CCC, April 26, 2000 » Rabbit
EGTB: Better algorithm by Urban Koistinen, CCC, April 07, 2001 ^[20]
Re: How endgame tablebases work by Bruce Moreland, rgcc, July 19, 2001
PONDER=ON and TableBases on 1 PC by Matthias Gemuh, CCC, July 27, 2001 » Pondering
Nalimov's EGTBs (long post with code) by Heiner Marxen, CCC, October 13, 2001
Incomplete egtbs can be harmful by Leen Ammeraal, CCC, November 06, 2001
Generating egtbs ICGAJ by Tony Werten, CCC, December 04, 2001 ^[21] ^[22]
Wu/Beal predates Koistinen by Guy Haworth, CCC, December 04, 2001
3-3 tablebase (with pawns) suggestion by Shane Hudson, CCC, December 23, 2001
Interesting EGTB bug by Tom Likens, CCC, April 16, 2002
How to handle EGTB stalemates by Tom Likens, CCC, March 02, 2003 » Stalemate
EGTB generation with 1 bit per position? by Martin Fierz, CCC, March 25, 2003
Frank Phillips' KNNKP position revisited ... by Guy Haworth, CCC, September 18, 2003 ^[23]

2005 ...

EGTB question by Stef Luijten, Winboard Forum, January 09, 2006
EGTB compression by Stef Luijten, Winboard Forum, February 10, 2006
utility for testing tablebases integrity by Victor Zakharov, CCRL Discussion Board, October 24, 2007
EGTB compression (H. G. Muller tablebase...) by Dann Corbit, CCC, January 25, 2008
DTR is no good! by Harm Geert Muller, CCRL Discussion Board, September 24, 2008
Gaviota's Endgame Tablebases by Miguel A. Ballicora, CCC, December 07, 2008 » Gaviota Tablebases
Creating EGTBs by Carey, CCC, December 21, 2008
Other endgame tablebase generators by Denis P. Mendoza, CCC, January 23, 2009

2010 ...

Some tablebase formats by BB+, OpenChess Forum, November 25, 2010
Retrograde tablebase methods by BB+, OpenChess Forum, November 26, 2010

2011

Gaviota tablebases, probing code v4 (UPDATE) by Miguel A. Ballicora, CCC, March 11, 2011
Large tablebases by BB+, OpenChess Forum, April 21, 2011
Mapping the 7-men computation by Astokes, CCRL Discussion Board, September 21, 2011
Poor Man Table Base by Ed Schroder, CCC, December 13, 2011
Number sequence puzzle by Steven Edwards, CCC, December 16, 2011 ^[24]
Tablebase class name list available by Steven Edwards, CCC, December 19, 2011 » CookieCat

2012

Compression of chess databases by Edmund Moshammer, CCC, July 09, 2012
pawn enumeration by Daniel Shawul, CCC, July 24, 2012

2013

New 6-piece tablebases by Ronald de Man, CCC, April 01, 2013 » Syzygy Bases
Complete 7-piece tablebases are out! by Albert Silver, CCC, April 12, 2013 ^[25]
Multithreaded LRU by Alvaro Cardoso, CCC, October 06, 2013 » Memory
What happens using egbb by Kai Laskos, CCC, October 12, 2013 » Scorpio Bitbases
tablebase caching / mmap() / page cache by Ronald de Man, CCC, October 13, 2013 » Memory, Syzygy Bases
How to encode endgame tablebases by Mr. beo, Rybka Forum, October 18, 2013
Could EGTB make an Engine "weaker"? by Bill Henry, CCC, October 23, 2013
evaluating tablebases draws by Uri Blass, CCC, November 23, 2013 » Draw Evaluation
Table Base Cache Size question by Rob Nicholas, CCC, December 05, 2013 » Memory

2014

Scorpio 6men EGBB Now available by Joshua Shriver, CCC, January 14, 2014 » Scorpio Bitbases
On-demand tablebase generation by Evert Glebbeek, CCC, January 19, 2014
Endgame tablebase generation for newbies by Alberto Sanjuan, CCC, April 04, 2014
A different tablebase encoding format by Steven Edwards, CCC, August 10, 2014
Tablebase access using a Solid State Disk by Steven Edwards, CCC, October 16, 2014 » Memory

2015 ...

how to probe egtb from console? by Marco Belli, CCC, May 15, 2015 » CLI
Yet another KPK endgame table generator: pfkpk by Marcel van Kervinck, CCC, September 05, 2015 » KPK Bitbase ^[26]
Is there tools to get the longest DTM/DTC for elementary EG? by Vincent Lejeune, CCC, September 07, 2015
7 men Rook endgames H4 vs SF in recent TCEC stage 1b by Nay Lin Tun, CCC, September 07, 2015 » Rook Endgame, TCEC Season 8

2016

Nalimov EGTB problem related to DTM? by Kai Laskos, CCC, February 14, 2016 » Nalimov Tablebases, DTM
Re: Nalimov EGTB problem related to DTM? by Ronald de Man, CCC, February 14, 2016
6-men tablebase wanted by Harm Geert Muller, CCC, March 03, 2016
Good testsets for tablebases testing by Sergei S. Markoff, CCC, May 15, 2016 » Test-Positions
EPD to test EGTB probe code by Sergei S. Markoff, CCC, May 24, 2016
11-men tablebases (XQ) by Harm Geert Muller, CCC, May 23, 2016 » Xiangqi
Natural TB by Marco Costalba, CCC, May 29, 2016 » Syzygy Bases, Stockfish
How texel probes endgame tablebases by Peter Österlund, CCC, July 16, 2016 » Gaviota Tablebases, Syzygy Bases, Texel
Getting engines to use TBs in Arena by Brendan J. Norman, CCC, July 19, 2016 » Arena
Syzygy and draw by repetition by Jon Dart, CCC, July 22, 2016 » Draw, Repetitions, Syzygy Bases
Verifiability of endgame tablebases by Joan Charmant, CCC, July 23, 2016

2017

Checkers Is Strongly-Solved for 8-pieces by Ed Trice, CCC, February 12, 2017 » Checkers
Search Halting Criteria When Probing Tablebases by Ed Trice, CCC, March 02, 2017
Probe EGT in quiescence? by Nguyen Pham, CCC, May 20, 2017 » Quiescence Search, Xiangqi
Incorporating Endgame tablebases by Pranav Deshpande, CCC, May 24, 2017
EGTB probe in search by Erin Dame, CCC, July 30, 2017
Natural TB (take 2) by Marco Costalba, CCC, August 22, 2017 » Syzygy Bases, Stockfish
understanding DTZ by Alexandru Mosoi, CCC, October 06, 2017 » DTZ, Syzygy Bases, Fathom

2018

A new design for Xianqgi (Chinese chess) Endgame Tablebase by Nguyen Pham, CCC, January 16, 2018 » Chinese Chess
Question about EGT formats by Harm Geert Muller, CCC, January 26, 2018
The history of Syzygy tablebases by Isaac Haïk Dunn, CCC, March 06, 2018 » Syzygy Bases

External Links

ICGA: Chess Endgames compiled by Guy Haworth and colleagues
Endgame tablebase from Wikipedia
Endgame Tablebases and Bitbases List from Computer-Chess Wiki by Ron Murawski
QUEEN vs. ROOK by Warren Stenberg and Edware J. Conway, reprinted from the January, 1979 issue of the Minnesota Chess Journal, The Usenet Oldnews Archive, Compilation Copyright (C) 1981, 1996 Bruce Jones, Henry Spencer, David Wiseman » ACM 1978, Belle, Walter Browne
Gilith - Chess Endgames by Joe Leslie-Hurd
Endgame Tablebases - gaviota chess engine by Miguel A. Ballicora ^[27]
Compression Schemes for Gaviota Tablebases
Computing endgames with few men by Urban Koistinen ^[28] ^[29] ^[30]
Koistinen/Endgame · GitHub
End-Game Table Bases by Harm Geert Muller
The Leapfrog Tablebase Generator by Harm Geert Muller
Hoffman by Brent Baccala
Endgame databases by Emil Vlasák
CCRL Discussion Board - Endgame Tablebases
Guide to the use of Computer Chess Endgame Tablebases from FAQ on Winboard and Chess Engines by Aaron Tay
Can use of endgame tablebases weaken play? from FAQ on Winboard and Chess Engines by Aaron Tay
Can We Solve Chess One Day? | Gödel's Lost Letter and P=NP by Dick Lipton, May 12, 2010
7-man TB - Google+
syzygy1/tb · GitHub by Ronald de Man ^[31]
dshawul/Scorpio · GitHub includes Six men egbb code » Scorpio Bitbases ^[32]
kervinck/pfkpk · GitHub » KPK Bitbase by Marcel van Kervinck ^[33]

ChessBase

Engines and endgame tablebases by Albert Silver, ChessBase News, December 12, 2013
Perfect endgame play – with tablebases, ChessBase News, April 21, 2015
Just one of 17,823,400,766 positions by Frederic Friedel, ChessBase News, April 23, 2015

ChessOK

Lomonosov Endgame Tablebases

Online Lookup

Lomonosov - online 7-man tablebases
Endgame Nalimov Tablebases Online by ChessOK
Nalimov EGTB from GMchess.com
Nalimov Tablebase server (DTM) by Lokasoft
Web Query for Nalimov Endgame Tablebases (DTM) from Knowledge4IT by Eiko Bleicher
Chess Archives - Endgames (DTC, DTM, DTZ, DTZ-50) hosted by John Tamplin
Schach Endspiele (DTM) (German) by Joachim Rack

Download

Endgame Tablebases Online - 6-men endgame analysis free for everyone by Kirill Kryukov (3,4,5,6 pieces - via emule)
Index of /tablebases by kingliveson
tablebase.sesse.net by Sesse

Statistics

References

^ Ernst A. Heinz (1999). Endgame Databases and Efficient Index Schemes for Chess. ICCA Journal, Vol. 22, No. 1, ps
^ Persistence, Oil on Canvas, 200 x 160 cm, Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ DTR is no good! by Harm Geert Muller, CCRL Forum, September 24, 2008
^ Subject: KRRNKRR win in 290: a new record by Marc Bourzutschky from CCC, October 16, 2005
^ Chess endgame from Wikipedia
^ 311. 31 March 2006: White plays and wins in 330 moves by Tim Krabbé
^ OPEN CHESS DIARY 316. 26 May 2006: A 517-move win by Tim Krabbé
^ Endgame tablebase from Wikipedia - Background
^ Lomonosov Endgame Tablebases - ChessOK
^ Subject: brute-force vs. intuition in math & chess by Bill Dubuque, August 1996
^ Jesper Torp Kristensen (2005). Generation and compression of endgame tables in chess with fast random access using OBDDs. Master thesis
^ Knowledge discovery from Wikipedia
^ Kasparov versus the World from Wikipedia
^ Generating egtbs ICGAJ by Tony Werten, CCC, December 04, 2001, with reference to Computing endgames with few men by Urban Koistinen
^ Wu / Beal retrograde analisys algorithm by Alvaro Jose Povoa Cardoso, Winboard Forum, March 10, 2007
^ OBDD - Ordered Binary Decision Diagram from Wikipedia
^ Plakoto from Wikipedia
^ Endgame tablebases with the fifty-move rule by Galen Huntington
^ tablebase compression / academic integrity by Ronald de Man, CCC, May 19, 2016
^ Computing endgames with few men by Urban Koistinen
^ Ren Wu, Don Beal (2001). Fast, Memory-efficient Retrograde Algorithms. ICGA Journal, Vol. 24, No. 3
^ Computing endgames with few men by Urban Koistinen
^ Easy mate by Frank Phillips, CCC, September 13, 2003 » Checkmate
^ A018214 - OEIS | Alkane (or paraffin) numbers
^ Lomonosov Endgame Tablebases - ChessOK
^ kervinck/pfkpk · GitHub
^ Gaviota tablebases, probing code v4 (UPDATE) by Miguel A. Ballicora, CCC, March 11, 2011
^ EGTB: Better algorithm by Urban Koistinen, CCC, April 07, 2001
^ Generating egtbs ICGAJ by Tony Werten, CCC, December 04, 2001
^ Ren Wu, Don Beal (2001). Fast, Memory-efficient Retrograde Algorithms. ICGA Journal, Vol. 24, No. 3
^ New 6-piece tablebases by Ronald de Man, CCC, April 01, 2013
^ Scorpio 6men EGBB Now available by Joshua Shriver, CCC, January 14, 2014
^ Yet another KPK endgame table generator: pfkpk by Marcel van Kervinck, CCC, September 05, 2015

What links here?

Page	Date Edited
ACM 1978	Dec 23, 2017
Advances in Computer Chess 8	Jun 26, 2017
Albert Silver	Feb 25, 2018
Alberto Sanjuan	Nov 3, 2014
Albrecht Heeffer	Sep 6, 2016
Alexandru Mosoi	Jan 8, 2018
Alvaro Cardoso	Jan 12, 2018
Arena	Mar 16, 2018
Belle	Jan 18, 2018
Beowulf	May 5, 2017
Bernhard Walter	Dec 31, 2015
BMI2	Mar 6, 2018
Bo-Nian Chen	Jul 17, 2017
Brendan J. Norman	Jan 11, 2018
Brute-Force	Jul 27, 2017
Carey Bloodworth	Jul 19, 2016
Check Check	Jan 8, 2016
Checkers	Dec 23, 2017
Checkmate	Apr 13, 2018
Chenard	Sep 5, 2015
Chess for Android	Mar 1, 2018
Chess Game	Mar 28, 2017
Chess Problems, Compositions and Studies	Feb 19, 2018
ChessBase (Database)	Feb 26, 2018
ChessGUI	Jan 17, 2018
Chessmaster	Jan 21, 2018
ChessOK	Jul 30, 2013
Chinese Chess	Jan 16, 2018
Chiron	Sep 24, 2017
Christoph Wirth	Jan 8, 2017
CLI	Jan 20, 2018
Connection Machine	Oct 12, 2016
CookieCat	Nov 15, 2016
Corresponding Squares	Oct 9, 2017
Crafty	Jan 28, 2018
DarkThought	Jul 3, 2018
Data	Nov 26, 2017
Databases	Mar 18, 2018
David Forthoffer	Apr 25, 2016
Denis Onneweer	Oct 3, 2012
Diagonal Mirroring	Jun 29, 2013
Dictionary	Aug 24, 2017
Dietmar Lippold	Mar 22, 2014
Djinn	Feb 8, 2016
Draw	Apr 14, 2018
Draw Evaluation	Mar 12, 2018
Ed Trice	Feb 21, 2018
Edmund Moshammer	Sep 23, 2017
Edwards' Tablebases	Sep 26, 2016
Emil Vlasák	Sep 30, 2015
Endgame	Sep 18, 2017
Endgame Bitbases	Apr 5, 2017
Endgame Tablebases	Mar 6, 2018
Engine Testing	Feb 1, 2018
Ernst A. Heinz	Mar 6, 2017
Evert Glebbeek	Sep 25, 2017
Ferret	Jan 7, 2016
Fifty-move Rule	Aug 9, 2017
FinalGen	Aug 14, 2016
Floyd	Sep 11, 2016
Frank Phillips	Sep 26, 2016
Frederic Friedel	Jan 6, 2018
Freezer	Aug 14, 2016
GAFS	Aug 14, 2016
Galahad	Jan 8, 2015
Galen Huntington	Dec 21, 2015
Galjoen	Mar 19, 2018
Gaviota Tablebases	Apr 22, 2018
Gerard Zielinski	Sep 25, 2014
Gijsbert Wiesenekker	Jan 17, 2018
Gil Dodgen	Mar 1, 2017
Grit Lachmann	Apr 26, 2014
GUI	Mar 16, 2018
Günter Rehburg	Nov 5, 2010
Guy Haworth	Nov 20, 2017
Hans Zellner	Jun 12, 2016
Harold van der Heijden	Jan 8, 2014
Hash Table	Jan 1, 2018
Hiarcs	Feb 25, 2018
Horizontal Mirroring	Jun 29, 2013
ICGA	Jul 8, 2017
ICGA Journal	Dec 21, 2017
Ikarus	Jul 5, 2016
Interior Node Recognizer	Mar 12, 2018
Ioannis Refanidis	Jan 19, 2016
Jesper Torp Kristensen	Oct 10, 2013
Joachim Rang	Mar 19, 2014
Joe Culberson	Dec 13, 2016
Joe Leslie-Hurd	Aug 15, 2013
John Nunn	Dec 9, 2017
John Roycroft	Apr 24, 2016
John Tamplin	Jan 9, 2017
Joshua Shriver	Nov 24, 2017
Kenneth Wingate Regan	Feb 19, 2018
Kirill Kryukov	Apr 16, 2014
Knowledge	Jul 22, 2017
KPK	May 12, 2016
KRK	Nov 26, 2016
Kuang-Che Wu	Dec 26, 2016
Lars Rasmussen	Apr 25, 2016
Leila	May 8, 2017
Lomonosov Supercomputer	May 19, 2016
Lomonosov Tablebases	May 20, 2016
Losing Chess	Sep 18, 2017
Ludwig Zagler	Sep 6, 2017
Marc Bourzutschky	Dec 16, 2013
Marco Belli	Jan 6, 2018
Mark Watkins	Dec 6, 2017
Martin Fierz	Apr 26, 2018
Match Statistics	Mar 31, 2018
Mate Search	Oct 22, 2016
Mathematician	Apr 9, 2018
Matthias Gemuh	Jan 21, 2018
Memory	Dec 8, 2017
Michael G. Malkovsky	May 20, 2016
Michael Hartisch	Aug 11, 2017
Miguel A. Ballicora	Jun 19, 2017
Much	Jun 7, 2016
Najib Nakad	Oct 22, 2014
Nalimov Tablebases	Dec 23, 2016
Nimzo	Dec 30, 2017
Nullmover	Jul 21, 2013
Oracle	Sep 4, 2016
Pandix	Feb 4, 2017
Patrick Schoo	May 25, 2016
Patzer	Apr 5, 2017
Paul Lu	Dec 13, 2016
Pepito	Nov 27, 2014
Peter Karrer	Jan 9, 2017
Peter van Diepen	Nov 5, 2015
Pharaon	Sep 2, 2017
Ping-hsun Wu	Jun 8, 2015
Pondering	Dec 9, 2017
Protector	Oct 12, 2017
python-chess	Nov 4, 2017
Quiescence Search	Aug 19, 2017
Rabbit	Oct 5, 2014
Rafael B. Andrist	May 30, 2017
Rémi Coulom	Feb 5, 2018
Ren Wu	Jul 23, 2017
Réti Endgame Study	Feb 25, 2014
RetroChess	Feb 2, 2014
Retrograde Analysis	Mar 21, 2017
Rob Lake	Dec 5, 2016
Roberto Waldteufel	Jun 5, 2013
Ronald de Man	Nov 20, 2017
Rook Endgame	Sep 18, 2017
Score	Apr 14, 2018
Scorpio Bitbases	Mar 12, 2018
Shess	Jan 7, 2016
Shun-Chin Hsu	Jul 22, 2017
Sidonia	May 19, 2016
Sito Dekker	Apr 25, 2016
SOS	Apr 5, 2017
Space-Time Tradeoff	Jun 17, 2015
Stalemate	Feb 21, 2018
Steven Edwards	Aug 26, 2017
Syzygy Bases	Apr 19, 2018
Test-Positions	Feb 25, 2018
Thomas Ströhlein	May 24, 2016
Thompson's Databases	Dec 24, 2014
Thread	Apr 22, 2018
Tom Likens	Mar 7, 2017
Tsan-sheng Hsu	Jul 17, 2017
UCI	Mar 4, 2018
Ulrich Thiemonds	Apr 26, 2014
User Interface	Feb 21, 2018
Vertical Flipping	Oct 10, 2013
Victor Zakharov	May 20, 2016
Vladimir Makhnychev	Nov 29, 2016
WCCC 2002	Nov 24, 2017
WChess	Jan 7, 2016
Wilhelm	Oct 6, 2015
Workshop Chess and Mathematics	Mar 5, 2015
XieXie	Jul 26, 2017
Yakov Konoval	Apr 28, 2009
YChess	Feb 25, 2018
Zeus	Jan 3, 2018

Up one level

Fruit

GerdIsenberg — Tue, 27 Sep 2016 14:02:25 GMT

Home * Engines * Fruit

		Fruit, until Version 2.1 open source, is a groundbreaking UCI compatible chess engine developed by primary author Fabien Letouzey. It made its first appearance to the public in March 2004, when Fruit was a basic program with a very simple evaluation and basic search. However, since then it made progress adding about 100 Elo to each new release (1.5, 2.0, 2.1 and Fruit 2.2) ^[1]. The release of Fruit until version 2.1 under the GNU General Public License was a "revolution" in computer chess in 2005 - an open source engine was "suddenly" competitive with the long time leading programs Shredder and Junior, as demonstrated at the WCCC 2005, where Fruit became runner up behind Zappa. After the strong Massy 2005 over the board debut, and the great success of Reykjavik, where Fabien Letouzey met his professional colleagues, he decided to close the source ^[2] and to go commercial ^[3] - while Fruit derivatives have already appeared based on the source code of Fruit 2.1, most notably Toga ^[4] by Thomas Gaksch, and Gambit Fruit by Ryan Benitez, who in late 2005 joint forces with Fabian for the commercial endeavor. Fabien finished his commercial computer chess career so far in 2007 ^[5]. Fruit 2.3+ is non GPL with full rights given to Ryan Benitez who continued the Fruit development porting it to bitboards ^[6], while Fruit 2.1 is now owned by the Free Software Foundation ^[7], released as GNU Chess 6 ^[8].
Samuel Bak - Still Life with Ego, 2003 ^[9]

Tournament Play

Fruit had its strong debut at CCT7, February 2005, and over the board at Massy 2005 in June 2005, with the then surprising shared second place, tied with Chess Wizard behind AnMon. After the mentioned breakthrough at the WCCC 2005 in Reykjavík, Fruit played the DOCCC 2005, operated by new book author Jeroen Noomen, who short later left the team for Rybka, the IPCCC 2005 b, CCT8 and the DOCCC 2006. Fruit continued to play CCT Tournaments from CCT10 in 2008.

Photos & Games

Stefan Meyer-Kahlen and Fabien Letouzey, Shredder - Fruit, WCCC 2005 ^[10]

[Event "WCCC 2005"]
[Site "Reykjavík, Iceland"]
[Date "2005.08.16"]
[Round "5"]
[White "Shredder"]
[Black "Fruit"]
[Result "0-1"]
 
1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 Nc6 5.Nc3 a6 6.Be2 d6 7.Be3 Nf6 8.f4 Be7 9.O-O Qc7 
10.Qe1 O-O 11.Kh1 Nxd4 12.Bxd4 b5 13.Qg3 Bb7 14.a3 Bc6 15.Bd3 Rfd8 16.Rae1 Qb7 17.Bxf6
Bxf6 18.e5 Be7 19.Ne4 dxe5 20.fxe5 Rd5 21.Re2 Rf8 22.Nf6+ Bxf6 23.Rxf6 Rd4 24.Rh6 g6 
25.Rh4 Rxh4 26.Qxh4 Qb6 27.Qf4 Rd8 28.Rf2 Rd7 29.c3 Qc7 30.Qe3 Qd8 31.Bf1 Rd1 32.Kg1 Qd5
33.Re2 a5 34.Qf2 b4 35.axb4 axb4 36.cxb4 h6 37.Re1 Rxe1 38.Qxe1 Qd4+ 39.Qf2 Qxb4 40.h3 
Be4 41.Kh2 Bd5 42.Bd3 Qb7 43.Qf6 Qb6 44.Qh4 Qb8 45.Qf6 Qb7 46.Bb1 Qd7 47.Qh4 Qc7 48.Qf4 
Ba8 49.b4 Qb7 50.Qd2 Kg7 51.Qb2 Qb5 52.Kg1 h5 53.Ba2 Qd3 54.Qf2 Kg8 55.Kh2 Be4 56.Qb2 h4 
57.b5 g5 58.Qf2 Qc3 59.b6 Kf8 60.Kg1 Qa1+ 61.Kh2 Qxe5+ 62.Kg1 Qa1+ 63.Kh2 Qc3 64.Kg1 Ke7 
65.Kh2 f5 66.Kg1 Kd7 67.Kh2 Kc6 68.Qe2 Kxb6 69.Qf2+ Kc6 70.Qe2 Kd6 71.Bc4 Qe5+ 72.Kg1 Qd4+ 
73.Kh2 g4 74.hxg4 fxg4 75.Qxg4 Qxc4 76.Qxh4 Qe2 77.Qd8+ Kc6 78.Qc8+ Kb5 79.Qb8+ Kc4 80.Qc7+ 
Kd3 81.Qd6+ Bd5 82.Qa6+ Kd2 83.Qa5+ Kc2 84.Qa4+ Bb3 85.Qd4 e5 86.Qa7 e4 87.Qc5+ Bc4 88.Qa3 
Qd3 89.Qa5 e3 90.Qa4+ Qb3 91.Qe8 e2 92.Qe4+ Kb2 93.Qh4 Qc3 94.Qf2 0-1

Innovations

Fruit was and still is one of the most influential didactic open source programs. It first uses a 16x12 Vector attack board representation, since Version 1.5 a 16x16 board to have a symmetric treatment of files and ranks ^[11] . Its structure and C source code was very clean and apparently bug-free due to runtime checking a lot of preconditions using debug asserts. While late move reductions (LMR) might be used in other programs before, Fabien's history based implementation in conjunction with history leaf pruning made LMR very popular. Another Fruit innovation, despite not absolutely new and already a known issue, and related to what is mentioned in evaluation philosophy, was tapered evaluation to avoid discontinuity ^[12] .

Fruit Team

Beside Fabien Letouzey as primary author and opening book author Marc Lacrosse, Ryan Benitez joined the Fruit-Team in December 2005. Before he developed Gambit Fruit with some interesting changes on the basis of the last open-source-version 2.1 ^[13]. Joachim Rang was the main tester of Fruit since its first public appearance, tuned parameters, and tested evaluation and search features ^[14] .

Fruit 64

Ryan Benitez continued the development on the non public Fruit in 2007 ^[16]. He converted the board representation from vector attacks to bitboards, and naturally, Fruit has become a new evaluation to go along with that ^[17]. Fruit by Fabien Letouzey and Ryan Benitez played the CCT10, the CCT11, where it became shared winner along with Bright after the later Rybka disqualification ^[18], and the CCT13 in 2011.

Influence

Many programmers took a lot of ideas and implementation details from Fruit, as noted by Vasik Rajlich ^[19] :

Alexander Schmidt:

The increase in playing strength of the latest chess engines is unbelieveable. We have since some time with Fruit 2.1 by Fabien Letouzey a very strong open source engine. Do you see a relation between the published sources of such a strong engine and the increase of strength in computer chess in general? How much influence do the ideas of Fruit have on the future of computerchess?

Vasik Rajlich:

Yes, the publication of Fruit 2.1 was huge. Look at how many engines took a massive jump in its wake: Rybka, Hiarcs, Fritz, Zappa, Spike, List, and so on. I went through the Fruit 2.1 source code forwards and backwards and took many things.

Fruit Reloaded

In March 2014, ten years after the initial Fruit 1.0 release, Daniel Mehrmann initiated a "let's update Fruit" called Fruit Reloaded ^[20]. With some help from Ryan Benitez, the aim is to add SMP to Fruit and upgrade search and evaluation with modern techniques ^[21] ^[22]. Simultaneously, Fabien Letouzey waved goodbye to Fruit and published his new open source engine Senpai, also with Ryan Benitez and Joachim Rang involved ^[23].

Derivatives

Publications

Mark Watkins (2011). A comparison of Rybka 1.0 Beta and Fruit 2.1, pdf, February 12, 2011 Version ^[24]
Mark Watkins (2011). A comparison of Rybka 1.0 Beta and Fruit 2.1, pdf, February 24, 2011 Version
Mark Watkins (2011). A comparison of Rybka 1.0 Beta and Fruit 2.1, pdf, March 11, 2011 Version » Rybka
Jaap van den Herik, Krzysztof Siewicz (2011). Open Source has a Price. ICGA Journal, Vol. 34, No. 2

Forum Posts

2004

Fruit Results, by Afzal Siddique, CCC, March 10, 2004
Fruit: first observations. Not a coconut yet, a budding pomegranate? by Đorđe Vidanović, CCC, March 10, 2004
Fruit - Question for Fabien by Dan Honeycutt, CCC, March 11, 2004 » Node Types, Transposition Table, Principal variation, Principal Variation Search
What makes Fruit so strong? by Steve Maughan, March 12, 2004
Fruit, trying to answer various missed posts by Fabien Letouzey, CCC, March 15, 2004
Fruit 1.0 UCI (with source code) now available by Fabien Letouzey, CCC, March 17, 2004
Fruit 1.0 64-bit by Slater Wold, CCC, March 26, 2004
Fruit 1.5 UCI available (Windows/Linux/MacOS + source code)! by Fabien Letouzey, CCC, June 04, 2004
Fruit 1.5 released! by Joachim Rang, CCC, June 05, 2004
Fruit 1.5 Hash Hit Percentage by Robert Allgeuer, CCC, June 19, 2004
null move question(Fruit) by Jan K., CCC, July 22, 2004
Fruit 2.0 released! by Joachim Rang, CCC, December 24, 2004

2005

Fruit2 = Ruffian with source code! by Jouni Uski, CCC, January 04, 2005
Fruit 2 and endgame play by Jouni Uski, CCC, January 12, 2005
Fruit's Board Representation? by Steve Maughan, Winboard Programming Forum, April 27, 2005
why is Patriot 2.0 beta ? by Matthias Gemuh, CCC, May 16, 2005 » Patriot
Re: why is Patriot 2.0 beta ? by Fabien Letouzey, CCC, May 17, 2005
Re: What makes Fruit and Fruit-Toga so strong? by Fabien Letouzey, CCC, June 15, 2005
understanding fruit by Uri Blass, Winboard Programming Forum, June 18, 2005
Temptation for Fabien: going commercial by Matthias Gemuh, CCC, June 20, 2005
Fruit on Pocket PC by Alain Zanchetta, CCC, July 27, 2005 » CEBoard, Pocket PC
Re: Some details by Joachim Rang, CCC, August 09, 2005
Re: Fruit Reykjavic by Fabien Letouzey, CCC, August 24, 2005
Fruit commercial by Fabien Letouzey, CCC, September 16, 2005
Re: Fact is also that Fruit went commercial by Eduard Nemeth, CCC, November 09, 2005
Re: Gambit Fruit ? by Ryan B., CCC, November 15, 2005
Has anyone tested Gambit Fruit with Rebel Reductions on? by Ryan B., CCC, November 15, 2005 » Reductions, Rebel ^[25]
To Fruit's author Fabien Letouzey and commercial manager Joachim Rang by Marc Lacrosse, CCC, November 17, 2005
Gambit Fruit Beta 3 available by Ryan B., CCC, November 19, 2005
A. STEEN vs. FRUIT 2.2.1 {Posted at request of Graham Banks & M. Monge} by A. Steen, CCC, November 24, 2005
Unmasking the Secrets of Rybka and Fruit by Stuart Cracraft, CCC, December 15, 2005
Secrets of Rybka and Fruit from my point of view by Sergei Markoff, CCC, December 15, 2005

2006

SSDF(Fruit 2.2.1 - Ruffian 1.0.1)A1200, 2½-2½, ended 26-14 by Tony Hedlund, CCC, January 09, 2006 » SSDF, Ruffian
not correct information in fruit's site by Uri Blass, CCC, January 09, 2006
congratulations to gambit-fruit! by Thorsten Czub, CCC, January 13, 2006 » Gambit Fruit
Rybka and Fruit on Chessbase by Walter Faxon, CCC, January 14, 2006 » Rybka, ChessBase
SSDF(Fritz 9 - Fruit 2.2.1)A1200, 1.5-1.5, ended 21-19 by Tony Hedlund, CCC, January 14, 2006 » SSDF, Fritz
SSDF Fruit 2.2.1 A1200 - Junior 7.0 A1200 Ended: 38.5-8.5 by Paul Petersson, CCC, January 22, 2006 » SSDF, Junior
SSDF(Hiarcs 10 - Fruit 2.2.1)A1200, 1-2, ended 19-21 by Tony Hedlund, CCC, January 29, 2006 » SSDF, Hiarcs
What are the moves of the loss of fruit against hiarcs? by Uri Blass, CCC, February 26, 2006 » CCT8
Fruit depth by Stuart Cracraft, CCC, March 06, 2006 » Depth, Branching Factor
Toga II 1.2 Beta2a based on Fruit released by Thomas Gaksch, CCC, March 08, 2006

2007

SSDF(Hiarcs 11.1 - Fruit 2.2.1)A1200, 12-7, ended 24-24 by Tony Hedlund, April 28, 2007 » SSDF, Hiarcs
SSDF(Zap!Chess Zanzibar-Fruit 2.2.1)A1200 3½-2½ ende 22½-17½ by Tony Hedlund, June 24, 2007 » SSDF, Zappa
Fruit, Rybka, Strelka final conclusion! (I hope) by Michael Sherwin, CCC, July 13, 2007 » Rybka, Strelka
What is Fruit? Fabien explains! by Michael Sherwin, CCC, July 14, 2007
Fruit and History Reductions by Ed Schröder, CCC, July 19, 2007 » Late Move Reductions
Fruit availability - 2 questions by Kaj Soderberg, CCC, July 20, 2007
Re: Fruit availability - 2 questions by Ryan Benitez, CCC, July 21, 2007
Fruit is already a free chess engine... by Dr.Wael Deeb, CCC, July 23, 2007
Fruit 2.2.1 : 2687 by Patrick Buchmann, CCC, July 24, 2007
Fruit 2.3 released by Ryan Benitez, CCC, July 26, 2007
Fruit 2.3 : 2689 by Patrick Buchmann, CCC, July 31, 2007
Fruit 2.3.1 released by Ryan Benitez, CCC, August 02, 2007 ^[26]
Fruit 2.3.1 : 2673 by Patrick Buchmann, CCC, August 06, 2007
Is Toga still weaker than Fruit? by Jouni Uski, CCC, August 23, 2007
Fruit2.3.1 stalemate bug by Uri Blass, CCC, October 21, 2007
Question to co-Author of Fruit and Chess64, Ryan Benitez by Swaminathan, CCC, November 03, 2007
Fruit SMP 2.3.4e Beta by Daniel Charles, CCC, December 15, 2007

2008

Re: How many "official" Toga projects there is now by Ryan Benitez, CCC, January 24, 2008
Has Fruit finaly surpassed Rybka!? by Dr.Wael Deeb, CCC, March 11, 2008
Fruit 2.1 pruning by kongsian, CCC, July 15, 2008 » Pruning
Fruit 2.1 vs Strelka 2.0 by Norman Schmidt, CCC, August 18, 2008
counting similiarities between strelka2.0 and fruit2.1 by Uri Blass, CCC, August 22, 2008
Strelka = Rybka 1.0 =Fruit 2.1 = Toga?? Oh how disappointing by Oliver Brausch, CCC, October 21, 2008 » Strelka, Rybka, Toga
Chess engine oldies upgrades by Denis P. Mendoza, Toga Developers Discussion Board, December 30, 2008 » Gambit Fruit

2009

posix source for GambitFruit4bxSE ? by Martin Helmer, CCC, January 28, 2009
Fruit vs. Toga poll by Miguel A. Ballicora, CCC, March 11, 2009
Re: Fruit vs. Toga poll by Ryan Benitez, CCC, March 19, 2009
Error in Fruit 2.1 source? by Ernest Bonnem, CCC, March 25, 2009
Re: When will come a new Toga Engine? by Ryan Benitez, CCC, April 10, 2009
Toga / Fruit historical question by Vladimir Medvedev, CCC, August 25, 2009

2010

Question about Fruit 2.1 code by Harm Geert Muller, CCC, April 14, 2010
Cluster Toga based on Fruit Source Code by Kai Himstedt, CCC, June 07, 2010 » Cluster Toga
Question about Fruit by Peter Kasinski, CCC, December 02, 2010
Brief Q&A about Rybka 1.0 Beta and Fruit 2.1 by BB+, OpenChess Forum, December 14, 2010

2011

Interview with Fabien (from the year 2005) ... by Frank Quisinsky, CCC, January 25, 2011
GNU Chess 6 (= Fruit) by Harm Geert Muller, CCC, January 25, 2011 ^[27]
Feb 12 version: Rybka 1.0 Beta / Fruit 2.1 document by BB+, OpenChess Forum, February 12, 2011
Attack of the clones | ChessVibes by David Levy, 19 February, 2011
Programmers write open letter about Rybka-Fruit issue | ChessVibes by Peter Doggers, March 01, 2011
Open letter to the ICGA about the Rybka-Fruit issue by Harvey Williamson, Hiarcs Forum, March 01, 2011
Programmers Open Letter to ICGA on Rybka/Fruit by BB+, OpenChess Forum, March 01, 2011 » ICGA Investigations
Loop 2007 / Fruit 2.1 by BB+, OpenChess Forum, Apr 18, 2011 » Loop

2012 ...

Fruit/Rybka timeline by BB+, OpenChess Forum, January 09, 2012
Fruit 1.0 anniversary by Fabien Letouzey, CCC, March 17, 2014

External Links

Chess Engine

Fruit

Fruit - pure playing strength
Fruit Chess Engine by Fabien Letouzey - Fruit 2.1 source
Fruit 2.3.1 from Superchessengine.com by Daniel Charles
GNU Chess - Free Software Foundation
Fruit's ICGA Tournaments
Fruit (chess engine) from Wikipedia
The alternative to Crafty, Interview with Fabien Letouzey by Frank Quisinsky April 05, 2005, from Free chess graphical user interface (GUI) Arena for chess engines, News-Ticker, Page 7, 96, FQ, also hosted by Ed Schröder ^[28]
Attack of the clones | ChessVibes by David Levy, 19 February, 2011 » Rybka, Strelka
Fruit 2.1 in CCRL 40/40
Fruit 2.1 in CCRL 40/4

Fruit reloaded

Misc

References

^ Fruit - pure playing strength - Team / History
^ Re: Fruit Reykjavic by Fabien Letouzey, CCC, August 24, 2005
^ Fruit commercial by Fabien Letouzey, CCC, September 16, 2005
^ Toga II by Thomas Gaksch and Fabien Letouzey
^ Fruit - pure playing strength
^ Re: How many "official" Toga projects there is now by Ryan Benitez, CCC, January 24, 2008
^ Re: When will come a new Toga Engine? by Ryan Benitez from CCC, April 10, 2009
^ GNU Chess 6 (= Fruit) by Harm Geert Muller, CCC, January 25, 2011
^ Major Works from Samuel Bak - represented by Pucker Gallery since 1969
^ Photo by Gerd Isenberg
^ Re: Fruit's Board Representation? by Fabien Letouzey, Winboard Forum, April 28, 2005
^ Secrets of Rybka and Fruit from my point of view by Sergei Markoff, CCC, December 15, 2005
^ Gambit fruit from Superchessengine.com by Daniel Charles
^ Fruit - pure playing strength - Team / History
^ To Fruit's author Fabien Letouzey and commercial manager Joachim Rang by Marc Lacrosse, CCC, November 17, 2005
^ Re: Question to co-Author of Fruit and Chess64, Ryan Benitez by Ryan Benitez, CCC, November 03, 2007
^ Re: Fruit vs. Toga poll by Ryan Benitez, CCC, March 19, 2009
^ CCT11: Bright by Allard Siemelink and Fruit by Fabien Letouzey are Co-Champions
^ Interview with Vasik Rajlich by Christopher Conkie, Michael Diosi, Frank Quisinsky & Alexander Schmidt, December 20, 2005, hosted by Ed Schröder
^ Fruit 1.0 anniversary by Fabien Letouzey, CCC, March 17, 2014
^ Akusari/Fruit-reloaded-public · GitHub
^ Fruit Reloaded - Computer Chess Programming hosted by Steve Maughan
^ Senpai 1.0 (new engine) by Fabien Letouzey, CCC, March 17, 2014
^ Feb 12 version: Rybka 1.0 Beta / Fruit 2.1 document by Mark Watkins, OpenChess General Forum, February 12, 2011
^ Programmer Corner - How Rebel Plays Chess - Reductions by Ed Schröder, pdf reprint
^ Fruit 2.3.1 from Superchessengine.com by Daniel Charles
^ GNU Chess - Free Software Foundation
^ Interview with Fabien (from the year 2005) ... by Frank Quisinsky, CCC, January 25, 2011

What links here?

Page	Date Edited
Alain Zanchetta	Feb 20, 2018
Arena	Mar 16, 2018
Bison	Sep 29, 2016
Bright	Oct 25, 2016
CCT10	May 5, 2013
CCT11	Feb 17, 2015
CCT13	Dec 6, 2013
CCT16	May 13, 2014
CCT7	Dec 16, 2017
CCT8	Apr 6, 2013
Chess-64	Mar 21, 2014
Chris Whittington	Dec 9, 2017
Cipollino	Jul 11, 2017
Claims of Rybka Originality	May 17, 2016
Clones	Jan 16, 2017
Cluster Toga	Jan 7, 2016
Crafty	Jan 28, 2018
Cyclone	Nov 24, 2013
Dan Honeycutt	Mar 13, 2014
Daniel Mehrmann	Dec 13, 2015
David Levy	Jan 3, 2017
DOCCC 2005	Aug 15, 2015
DOCCC 2006	Aug 27, 2016
Ed Schroder	Feb 26, 2018
Eigenmann Endgame Test	Jun 1, 2017
Engines	Mar 10, 2018
Enhanced Transposition Cutoff	May 19, 2017
Ethereal	Mar 20, 2018
Evaluation of Pieces	Jan 8, 2018
Evaluation Philosophy	Sep 29, 2014
Fabien Letouzey	Feb 5, 2018
Fabien Rybka Letter	Feb 23, 2014
Fonzy Bluemers	Sep 5, 2013
Frank Quisinsky	May 3, 2017
Fritz Reul	Nov 28, 2016
Fruit	Sep 27, 2016
Fruit Reloaded	Dec 8, 2017
Futility Pruning	Aug 30, 2017
Gabor Szots	Oct 1, 2014
Gambit Fruit	Mar 29, 2013
Gavon	Apr 30, 2018
Giancarlo Delli Colli	Jun 27, 2017
Gibbon	Dec 23, 2014
Glaurung	Mar 14, 2017
GNU Chess	Jan 21, 2018
Graham Banks	Nov 27, 2015
GridChess	Jul 13, 2016
History Leaf Pruning	Apr 15, 2013
IGWT 2013	Jun 23, 2014
IPCCC 2005 b	Apr 15, 2013
Jan Kaan	Feb 4, 2018
Joachim Rang	Mar 19, 2014
Jouni Uski	Sep 28, 2017
Kai Himstedt	Jun 28, 2016
Kaissa (BY)	May 16, 2016
King Safety	Feb 14, 2018
Kiwi	Sep 2, 2016
Kramnik versus Deep Fritz 2006	Nov 28, 2017
Krzysztof Siewicz	Aug 9, 2014
Late Move Reductions	Sep 25, 2017
Lion	Sep 27, 2016
Loop (Program)	Mar 14, 2017
Marc Lacrosse	Aug 22, 2016
Mark Watkins	Dec 6, 2017
Massy 2005	Jan 29, 2013
Matthew R. Brades	Jun 9, 2017
Matthias Gemuh	Jan 21, 2018
Maurizio Monge	Nov 27, 2015
Michael Sherwin	Dec 18, 2017
Milos Stanisavljevic	May 23, 2016
Node Types	Oct 22, 2017
Norman Schmidt	Oct 12, 2017
Null Move Pruning	Dec 2, 2017
Open Source Engines	Jul 14, 2015
Patriot	Sep 27, 2016
Peter Berger	Feb 29, 2016
Piece-Square Tables	Mar 31, 2018
PocketGrandmaster	Sep 17, 2015
Point Value	Mar 31, 2018
Point Value by Regression Analysis	Aug 26, 2017
Principal variation	Dec 4, 2017
Principal Variation Search	Oct 22, 2017
Protector	Oct 12, 2017
Pruning	Jan 1, 2018
PuppetMaster	Sep 17, 2015
Quantifying Evaluation features	Jun 6, 2012
Revelation	Jul 15, 2016
Revelation II	Jan 8, 2018
Rodent	Jan 11, 2018
Rook on Open File	Apr 24, 2017
Ross Boyd	Mar 12, 2018
Ruffian	Jun 6, 2017
Ryan Benitez	May 16, 2015
Rybka	Mar 27, 2017
Rybka Controversy	Jan 18, 2018
Salvo Spitaleri	Mar 11, 2013
Senpai	Nov 10, 2017
Sergei Markoff	Mar 12, 2018
Spark	Oct 19, 2017
Steve Maughan	Jan 31, 2018
Stockfish	Apr 7, 2018
Strelka	May 17, 2016
Swaminathan Natarajan	Jun 17, 2015
Tapered Eval	Jan 9, 2018
Thinker	Jan 7, 2016
Thomas Gaksch	Jan 8, 2016
Toga	Dec 28, 2017
tomitankChess	Dec 8, 2017
Tony Hedlund	Jun 19, 2017
Transposition Table	Apr 19, 2018
Unstoppable Passer	Jun 21, 2016
Vadim Demichev	Jul 26, 2013
Vasik Rajlich	Sep 23, 2017
Vector Attacks	Dec 15, 2017
Vladimir Yelin	May 16, 2016
WCCC 2005	Dec 27, 2016
WCCC 2006	Jan 28, 2018
Who's Who	Sep 6, 2017
Wii Chess	Jun 3, 2016
World Computer Chess Championship	Mar 6, 2018
Zach Wegner	Jan 7, 2016
Đorđe Vidanović	Feb 20, 2017

Up one Level

Fruit Reloaded

GerdIsenberg — Fri, 08 Dec 2017 20:28:31 GMT

Home * Engines * Fruit * Reloaded

		Fruit Reloaded, an independent fork of Fruit 2.1, started by Daniel Mehrmann in 2012 ^[1] as a "let's update Fruit" project, published in March 2014 as announced by Fabien Letouzey ^[2]. Like its predecessor, Fruit Reloaded is UCI compliant and open source licensed under the GPL v3 ^[3]. Sources are available from a GitHub repository ^[4]. With some help from Ryan Benitez, the aim was to add a parallel search and to upgrade search and evaluation with recent techniques, still following the clean coding style of Fabien's work. Beside newly added, tweaked or tuned selectivity and evaluation features, Fruit Reloaded can now probe Nalimov Tablebases and Scorpio Bitbases, configurable by appropriate UCI options. Binaries are available for Windows, Linux, Mac OS X and Android platforms, hosted by Steve Maughan's Computer Chess Programming ^[5].
Samuel Bak - Backstage, 1997 ^[6]

Forum Posts

Fruit 1.0 anniversary by Fabien Letouzey, CCC, March 17, 2014
Fruit reloaded 2.1: Android builds available by Daniel Mehrmann, CCC, April 11, 2014
Fruit reloaded needs some testers and devs by Daniel Mehrmann, CCC, April 16, 2014
Fruit Reloaded smooth scaling by Dann Corbit, CCC, May 13, 2015
Fruit reloaded v 3.2.1 released by Daniel Mehrmann, CCC, December 08, 2017 » TCEC Season 10

External Links

Chess Engine

Misc

Fruit from Wikipedia
Fruit (disambiguation) from Wikipedia
reload - Wiktionary
Reload from Wikipedia
Billy Cobham - Cat in the Hat, Fruit from the Loom (2007), YouTube Video ^[7]

References

^ Fruit-reloaded-public/readme.txt at master · Akusari/Fruit-reloaded-public · GitHub
^ Fruit 1.0 anniversary by Fabien Letouzey, CCC, March 17, 2014
^ Fruit-reloaded-public/LICENSE at master · Akusari/Fruit-reloaded-public · GitHub
^ Akusari/Fruit-reloaded-public · GitHub
^ Fruit Reloaded - Computer Chess Programming hosted by Steve Maughan
^ Backstage, 1997, Oil on linen, from Major Works from Samuel Bak - represented by Pucker Gallery since 1969
^ The Cat in the Hat - Wikipedia

What links here?

Page	Date Edited
Daniel Mehrmann	Dec 13, 2015
Engine releases	Apr 23, 2018
Engines	Mar 10, 2018
Fabien Letouzey	Feb 5, 2018
Fruit	Sep 27, 2016
Fruit Reloaded	Dec 8, 2017
Late Move Reductions	Sep 25, 2017
PT 49	Oct 22, 2015
Ryan Benitez	May 16, 2015
TCEC Season 10	Jan 3, 2018
TCEC Season 8	Nov 30, 2015
TCEC Season 9	Nov 6, 2017

Up one Level

Hyperbola Quintessence

camleon — Sat, 25 Mar 2017 14:31:28 GMT

Home * Board Representation * Bitboards * Sliding Piece Attacks * Hyperbola Quintessence

Hyperbola Quintessence applies the o^(o-2r)-trick also for vertical or diagonal negative Rays - by reversing the bit-order of up to one bit per rank or byte with a vertical flip aka x86-64 bswap ^[1] . It is somehow a resurrection of the reverse bitboards idea of Ryan Mack's Hyperbola Project on the fly, and was created by Gerd Isenberg. Improvements by Aleks Peshkov ^[2] made it applicable and competitive.

Code samples and bitboard diagrams rely on Little endian file and rank mapping.

Samuel Bak - Reflexion, 1990 ^[3]

Reverse Math

Source Code

Generalized set-wise attacks

x86-64 assembly

Java

AMD's SIMD Future in 2011

Reverse Math

Assume following masked occupancy on a file, diagonal or anti-diagonal - for simplicity as a flat byte (in a real bitboard with masked files or diagonals you have 6..8 scratch-bits between the bits of this byte). Thus, vertical flip reverses the bits of this byte.

o' = reverse(o)
r' = reverse(r)
 
       normal    reversed
 o     11010101  10101011 o' occupancy including slider
 r     00010000  00001000 r' slider
 o-r   11000101  10100011 o'-r'  1. sub clears the slider
 o-2r  10110101  10011011 o'-2r' 2. sub borrows "one" from next blocker
       |......|  \....../
normal 10110101   \..../
       11011001 <--XXXX   re-reverse
single
xor    01101100 -> to get the attack set

The first subtraction of (o-2r) is done implicitly by masking off the line, removing the slider from the occupied set. The second subtraction borrows a "one" from the next nearest blocker in msb-direction, falling through all unset bits outside the line. Of course, if no blocker is available, it borrows a "one" in usual arithmetical manner from the hidden 2^N. Only the changed bits (from original o, o') are the appropriate sliding attacks, including the blocker but excluding the slider. The result finally needs to be intersected with the same line mask as previously the occupancy, to clear the wrapped borrow one bits outside the file or diagonal. The fine optimization by Aleks Peshkov covers the final union of positive and negative ray-attacks. Since opposed ray-directions are always disjoint sets, using xor instead of bitwise or safes two instructions per line-attack. That is because bit-reversal or any mirroring or flipping is own inverse and distributive over xor.

reverse(a ^ b) == reverse (a) ^ reverse(b)

thus

lineAttacks = o^(o-2r) ^ reverse((o'-2r')^o')
lineAttacks = o^(o-2r) ^ reverse( o'-2r') ^ reverse(o')
lineAttacks = o^(o-2r) ^ reverse( o'-2r') ^ o

and finally

lineAttacks =   (o-2r) ^ reverse( o'-2r')

Beside shorter code this reduces register pressure - and clearly outperforms kindergarten bitboards - ipc-wise, in code size and memory requirements.

Source Code

C

The three C-routines only differ by the line-mask applied:

U64 diagonalAttacks(U64 occ, enumSquare sq) {
   U64 forward, reverse;
   forward = occ & smsk[sq].diagonalMaskEx;
   reverse  = _byteswap_uint64(forward);
   forward -= smsk[sq].bitMask;
   reverse -= _byteswap_uint64(smsk[sq].bitMask);
   forward ^= _byteswap_uint64(reverse);
   forward &= smsk[sq].diagonalMaskEx;
   return forward;
}
 
U64 antiDiagAttacks(U64 occ, enumSquare sq) {
   U64 forward, reverse;
   forward  = occ & smsk[sq].antidiagMaskEx;
   reverse  = _byteswap_uint64(forward);
   forward -= smsk[sq].bitMask;
   reverse -= _byteswap_uint64(smsk[sq].bitMask);
   forward ^= _byteswap_uint64(reverse);
   forward &= smsk[sq].antidiagMaskEx;
   return forward;
}
 
U64 fileAttacks(U64 occ, enumSquare sq) {
   U64 forward, reverse;
   forward  = occ & smsk[sq].fileMaskEx;
   reverse  = _byteswap_uint64(forward);
   forward -= smsk[sq].bitMask;
   reverse -= _byteswap_uint64(smsk[sq].bitMask);
   forward ^= _byteswap_uint64(reverse);
   forward &= smsk[sq].fileMaskEx;
   return forward;
}
 
U64 bishopAttacks(U64 occ, enumSquare sq) {
   return diagonalAttacks (occ, sq)
        + antiDiagAttacks (occ, sq);
}

For better locality of the line-attacks on the otherwise empty board, we may use an properly aligned array of structs.

struct
{
   U64 bitMask;         // 1 << sq for convenience
   U64 diagonalMaskEx;
   U64 antidiagMaskEx;
   U64 fileMaskEx;
} smsk[64]; // 2 KByte

Using x86-64 bswap makes it quite competitive for bishops and files, on AMD K8 or K10 it has a latency of one cycle with a throughput of 1/3, like other cheap instructions. However, Intel is tad slower - while the recent Core 2 duo processors perform 128-bit SIMD-instructions with 128-bit alus, that is bitwise logical instructions with a latency of one cycle and throughput of 1/3, the general purpose bswap-instruction takes four cycles with a throughput of one. In Intel 64 and IA32 Architectures Optimization Reference Manual ^[4] , it is therefor recommend (5.6.5. endian conversion) to use the SSSE3 pshufb instruction to swap bytes, available through intrinsic ^[5] , see SSSE3 Hyperbola Quintessence for bishop attacks.

As long there is no fast bit reversal instruction, there is no general solution for all four lines, and the rook attack-getter still needs some standard technique for the rank-attacks. Tim Cooijmans proposed to map the rank to the main diagonal before applying HQ, and to re-map the calculated attacks back to the original rank ^[6] .

Generalized set-wise attacks

Hyperbola quintessence can be generalized to work on whole sets of sliding pieces instead on individual pieces, whose ranks to be masked. The problem arising, when not masking the rank of the piece is that attacks wrap around the board during subtraction. This is shown below:

     ........       ........                            11111111
     ........       ........                            11111111
     ........       ........                            11111111
 r = ........ , o = ........ this leads to   o - 2*r =  11111111
     ........       ........                            11111111
     ........       ........                            11111111
     ....1...       ....1...                            11111...
     ........       ........                            ........
 
instead of
 
........
........
........
........
........
........
11111...
........

This is not the intended result. It can be avioded, by bitwise adding an overflow barrier on the right-hand side. Afterwards this barrier needs to be removed from the attack set:

u64 right = 0x0101010101010101ULL;
 
     ......1.      1..1..1.                              1...1111
     ....1...      1...1...                              .1111..1
     ......1.      11....1.                              1.111111
r =  .....1..  o = .11..1..   now: ((o | right) - 2*r) = .1.111.1
     ........      ........                              ........
     ......1.      ......1.                              1111111.
     .......1      .......1                              1111111.
     1.......      1.......                              1......1
 
Note, that the 4th rank was not flooded by the subtraction! Next, the blockers are removed as usual:
 
                          ...111.1
                          1111...1
                          .11111.1
o ^ ((o | right) - 2*r) = ..111..1
                          ........
                          111111..
                          11111111
                          .......1
 
The last step is to remove the barrier at the right side that became visible after the last operation.
 
                                     ...111..
                                     1111...
                                     .11111..
(o ^ ((o | right) - 2*r) & ~right =  ..111...
                                     ........
                                     111111..
                                     1111111.
                                     ........
 
This is the correct attack set for the left direction.

the complete algorithm for the left direction is therefore:

const u64 right = 0x0101010101010101ULL;
 
u64 leftAttacks = ((o ^ ((o | right) - 2*r) & ~right);

For the right-hand direction, the bits need to be reversed rank-wise.

x86-64 assembly

The VC2005 generated x86-64 assembly of bishopAttacks indicates what ipc-monster Hyperbola Quintessence is:

occ$ = 16
sq$ = 24
?bishopAttacks@@YA_K_KI@Z PROC
  00000   40 53                push    rbx
  00002   8b c2                mov    eax, edx
  00004   4c 8d 15 00 00 00 00 lea    r10, OFFSET FLAT:?smsk
  0000b   48 c1 e0 05          shl    rax, 5
  0000f   4a 8b 5c 10 08       mov    rbx, QWORD PTR [rax+r10+8]  ; diagonalMaskEx
  00014   4e 8b 4c 10 10       mov    r9,  QWORD PTR [rax+r10+16] ; antidiagMaskEx
  00019   4e 8b 14 10          mov    r10, QWORD PTR [rax+r10]    ; r := 1 << sq
  0001d   4c 8b db             mov    r11, rbx                    ; diagonalMaskEx
  00020   49 8b d1             mov    rdx, r9                     ; antidiagMaskEx
  00023   4d 8b c2             mov    r8, r10                     ; r := 1 << sq
  00026   48 23 d1             and    rdx, rcx                    ; anti & occ
  00029   4c 23 d9             and    r11, rcx                    ; dia  & occ
  0002c   49 0f c8             bswap  r8                          ; r'
  0002f   48 8b c2             mov    rax, rdx                    ; ant
  00032   49 8b cb             mov    rcx, r11                    ; dia
  00035   49 2b d2             sub    rdx, r10                    ; ant - r
  00038   48 0f c8             bswap  rax                         ; ant'
  0003b   48 0f c9             bswap  rcx                         ; dia'
  0003e   4d 2b da             sub    r11, r10                    ; dia - r
  00041   49 2b c0             sub    rax, r8                     ; ant' - r'
  00044   49 2b c8             sub    rcx, r8                     ; dia' - r'
  00047   48 0f c8             bswap  rax                         ;(ant' - r')'
  0004a   48 0f c9             bswap  rcx                         ;(dia' - r')'
  0004d   48 33 c2             xor    rax, rdx                    ; ant := (ant' - r')' ^ (ant - r)
  00050   49 33 cb             xor    rcx, r11                    ; dia := (dia' - r')' ^ (dia - r)
  00053   49 23 c1             and    rax, r9                     ; ant &= antidiagMaskEx
  00056   48 23 cb             and    rcx, rbx                    ; dia &= diagonalMaskEx
  00059   48 03 c1             add    rax, rcx                    ; attacks := dia + ant
  0005c   5b                   pop    rbx
  0005d   c3                   ret    0
?bishopAttacks@@YA_K_KI@Z ENDP

Java

Java programmer may try Long.reverseBytes:

    static private final long[] bitMask = {
        0x0000000000000001, 0x0000000000000002, 0x0000000000000004, 0x0000000000000008,
        0x0000000000000010, 0x0000000000000020, 0x0000000000000040, 0x0000000000000080,
        ...
    };
 
    static private final long[] diagonalMaskEx = {
        0x8040201008040200, 0x0080402010080400, 0x0000804020100800, 0x0000008040201000,
        0x0000000080402000, 0x0000000000804000, 0x0000000000008000, 0x0000000000000000,
        ...
    };
 
    /**
     * @param occ - occupancy
     *        sq  - from square
     * @return diagonal attacks from sq with occupancy occ
     */
    static public long diagonalAttacks(long occ, int sq)
    {
       long forward = occ & diagonalMaskEx[sq];
       long reverse = Long.reverseBytes(forward);
       forward -= bitMask[sq];
       reverse -= bitMask[sq^56];
       forward ^= Long.reverseBytes(reverse);
       forward &= diagonalMaskEx[sq];
       return forward;
    }

Long.reverse for a generalized attack getter even for ranks is too expensive, except a JVM can use a machine instruction rather than a bit-reversal routine:

    /**
     * @param occ  - occupancy
     *        line - {0..3} {rank, file, diagonal, antidiagonal}
     *        sq   - from square
     * @return attacks from sq on line with occupancy occ
     */
    static public long attacks(long occ, int line, int sq)
    {
       long forward = occ & maskEx[sq][line];
       long reverse = Long.reverse(forward);
       forward -= bitMask[sq];
       reverse -= bitMask[sq^63];
       forward ^= Long.reverse(reverse);
       forward &= maskEx[sq][line];
       return forward;
    }

AMD's SIMD Future in 2011

In 2007 AMD announced the hypothetical SSE5 instruction set ^[7] with a PPERM instruction ^[8] , which would be able to reverse vectors of two bitboards. In May 2009 AMD revised SSE5, to become more compatible with Intel's Advanced Vector Extensions, and also expanding the SIMD-register width from 128 to 256-bit, the renamed XOP instruction set ^[9] . However, the successor of the planned PPERM SSE5-instruction is now called VPPERM, but still works on 128-bit XMM registers ^[10] . VPPERM instruction requires four operands (xmm-registers):

 VPPERM dest, src1, src2, selector

For each of 16 destination bytes the corresponding selector-byte addresses one of 32 input bytes (from src1, src2) and a logical operation including bit-reversal:

char src[32];   // src2:src1
char select[16];
char dest[16];
for (int i = 0; i < 16; i++) {
   char opera = select[i] >>> 5; // unsigned shift
   char idx32 = select[i] & 31;
 
   switch ( opera ) {
      case 0: dest[i] =  src[idx32]; break;
      case 1: dest[i] = ~src[idx32]; break;
      case 2: dest[i] =  bitreverse( src[idx32]); break;
      case 3: dest[i] = ~bitreverse( src[idx32]); break;
      case 4: dest[i] = 0x00; break;
      case 5: dest[i] = 0xFF; break;
      case 6: dest[i] =  src[idx32] >> 7;  break; // signed shift
      case 7: dest[i] = ~src[idx32] >> 7;  break; // signed shift
   }
}

Since VPPERM can simultaneously reverse bits and bytes, it can for instance reverse two bitboards in one run, even from different sources, to make Hyperbola Quintessence work for all four lines.

Forum Posts

Re: BitBoard Tests Magic v Non-Rotated 32 Bits v 64 Bits by Aleks Peshkov, CCC, August 25, 2007
Hyperbola Quiesscene: hardly any improvement by trojanfoe, CCC, January 13, 2009
Comparison of bitboard attack-getter variants by Sven Schüle, CCC, January 04, 2016
Re: The wrong way by Aleks Peshkov, CCC, January 05, 2016 » SSSE3 Hyperbola Quintessence

External Links

Sliding Pieces (Part 1) - Advanced Java Chess Engine Tutorial 8 by Jonathan Warkentin
Hyperbola Quintessence for rooks along ranks by Tim Cooijmans, April 6, 2014 ^[11]

Hyperbola

Quintessence

Misc

Focus - Hocus Pocus, Pinkpop Festival 1972, Geleen, YouTube Video

References

^ _byteswap_uint64 Visual C++ Developer Center - Run-Time Library Reference
^ Re: BitBoard Tests Magic v Non-Rotated 32 Bits v 64 Bits by Aleks Peshkov, CCC, August 25, 2007
^ The Game of War from Samuel Bak - represented by Pucker Gallery since 1969
^ Intel 64 and IA32 Architectures Optimization Reference Manual (pdf)
^ _mm_shuffle_epi8 Visual C++ Developer Center - Run-Time Library Reference
^ Hyperbola Quintessence for rooks along ranks by Tim Cooijmans, April 6, 2014
^ 128-Bit SSE5 Instruction Set from AMD Developer Central
^ SSE5 permutations
^ XOP instruction set from Wikipedia
^ Volume 6: 128-Bit and 256-Bit XOP, FMA4 and CVT16 Instructions (pdf), see VPPERM pg. 221
^ Re: Comparison of bitboard attack-getter variants by Matthew R. Brades, CCC, January 04, 2016

What links here?

Page	Date Edited
Aleks Peshkov	Jan 13, 2016
Amoeba	Mar 19, 2018
Dumb	Mar 10, 2018
Efficient Generation of Sliding Piece Attacks	Nov 5, 2016
Endianness	Jan 25, 2015
Fill Algorithms	Nov 6, 2013
First Rank Attacks	Aug 28, 2010
Flipping Mirroring and Rotating	Oct 14, 2016
General Setwise Operations	Feb 25, 2018
Hiding the Implementation	Feb 3, 2011
Hyperbola Quintessence	Mar 25, 2017
Java	Feb 25, 2018
Jonathan Warkentin	Jun 29, 2014
Karlo Bala Jr.	Feb 19, 2017
Kindergarten Bitboards	Aug 1, 2017
Kogge-Stone Algorithm	Sep 17, 2016
Parallel Prefix Algorithms	Jun 22, 2016
Reverse Bitboards	Aug 29, 2015
Ryan Mack	Jan 18, 2011
SBAMG	Dec 4, 2016
SIMD techniques	Nov 26, 2017
Sliding Piece Attacks	May 27, 2016
SSSE3	Aug 8, 2017
Subtracting a Rook from a Blocking Piece	Dec 2, 2016
Syed Fahad	Jan 1, 2017
XOP	Aug 8, 2017

Up one Level

Influence Quantity of Pieces

GerdIsenberg — Fri, 21 Jul 2017 17:35:24 GMT

Home * Chess * Pieces * Influence Quantity

		The influence quantity of pieces is defined by their number of unique moves with respect to their from- and to-square coordinates, the cardinality of the set of all possible moves, or potential, global mobility ^[1]. It might be used to enumerate and encode all those moves, i.e. associating each move, per piece and in total, with a unique number for minimal perfect hashing opposed to intermittent Butterfly boards. For instance a pawn (including promotions) has 48 (86) single pushes and 84 (27*6) captures, plus 8 possible double pushes on each file, which results in a influence quantity of 140 of either white or black pawns.The influence quantities of all pieces are divisible by four times seven (28), excluding pawn and king even by sixteen times seven (112). While obviously the number of queen quantities is the sum of rook- and bishop quantities, it is at the first glance somehow surprising that the rook quantity is the sum of bishop- and knight quantities.
Samuel Bak - Group Portrait, 1998 ^[2]

Moves per Origin

Whole Board Diagrams

Board Circles

Quantities and Point Values

Divisibility by Seven

Moves per Origin

Following table gives the distinct number of moves per piece and origin square and their sums from the lower left quarter of a board (a1-d4) and in total for the whole board:

    Knight          King            Bishop          Rook            Queen
     4  6  8  8      5  8  8  8      7  9 11 13     14 14 14 14     21 23 25 27
     4  6  8  8      5  8  8  8      7  9 11 11     14 14 14 14     21 23 25 25
     3  4  6  6      5  8  8  8      7  9  9  9     14 14 14 14     21 23 23 23
     2  3  4  4      3  5  5  5      7  7  7  7     14 14 14 14     21 21 21 21
 
sum 13 19 26 26     18 29 29 29     28 34 38 40     56 56 56 56     84 90 94 96
    84 = 3 * 4*7   105 = 3 *5*7   140 = 5 * 4*7   224 = 8 * 4*7   364 = 13 * 4*7
   336             420            560             896            1456

Whole Board Diagrams

Whole board tables cover pawn, knight, king and sliding pieces, and their file-, rank and total sums:

White pawn total                      white pawn a2                         white pawn d2
+---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |     |   |   |   |   |   |   |   |   |     |   |   |   |   |   |   |   |   |
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22  | 2 | 3 | 3 | 3 | 3 | 3 |   |   | 17  | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22  | 2 | 3 | 3 | 3 | 3 |   |   |   | 14  | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22  | 2 | 3 | 3 | 3 |   |   |   |   | 11  | 2 | 3 | 3 | 3 | 3 | 3 | 3 |   | 20
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22  | 2 | 3 | 3 |   |   |   |   |   |  8  |   | 3 | 3 | 3 | 3 | 3 |   |   | 15
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22  | 2 | 3 |   |   |   |   |   |   |  5  |   |   | 3 | 3 | 3 |   |   |   |  9
| 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 30  | 3 |   |   |   |   |   |   |   |  3  |   |   |   | 4 |   |   |   |   |  4
|   |   |   |   |   |   |   |   |     |   |   |   |   |   |   |   |   |     |   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+
 13  19  19  19  19  19  19  13  140   13  15  12   9   6   3           58    6  12  15  19  15  12   9   4   92
 
Knight                                                                      King
+---+---+---+---+---+---+---+---+                                           +---+---+---+---+---+---+---+---+
| 2 | 3 | 4 | 4 | 4 | 4 | 3 | 2 | 26                                        | 3 | 5 | 5 | 5 | 5 | 5 | 5 | 3 | 36
| 3 | 4 | 6 | 6 | 6 | 6 | 4 | 3 | 38                                        | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52                                        | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52                                        | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52                                        | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52                                        | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 3 | 4 | 6 | 6 | 6 | 6 | 4 | 3 | 38                                        | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 2 | 3 | 4 | 4 | 4 | 4 | 3 | 2 | 26                                        | 3 | 5 | 5 | 5 | 5 | 5 | 5 | 3 | 36
+---+---+---+---+---+---+---+---+                                           +---+---+---+---+---+---+---+---+
 26  38  52  52  52  52  38  26  336                                         36  58  58  58  58  58  58  36  420
 
Bishop                                Rook                                  Queen
+---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+
| 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 56  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |21 |21 |21 |21 |21 |21 |21 |168
| 7 | 9 | 9 | 9 | 9 | 9 | 9 | 7 | 68  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |23 |23 |23 |23 |23 |23 |21 |180
| 7 | 9 |11 |11 |11 |11 | 9 | 7 | 76  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |23 |25 |25 |25 |25 |23 |21 |188
| 7 | 9 |11 |13 |13 |11 | 9 | 7 | 80  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |23 |25 |27 |27 |25 |23 |21 |192
| 7 | 9 |11 |13 |13 |11 | 9 | 7 | 80  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |23 |25 |27 |27 |25 |23 |21 |192
| 7 | 9 |11 |11 |11 |11 | 9 | 7 | 76  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |23 |25 |25 |25 |25 |23 |21 |188
| 7 | 9 | 9 | 9 | 9 | 9 | 9 | 7 | 68  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |23 |23 |23 |23 |23 |23 |21 |180
| 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 56  |14 |14 |14 |14 |14 |14 |14 |14 |112  |21 |21 |21 |21 |21 |21 |21 |21 |168
+---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+
 56  68  76  80  80  76  68  56  560  112 112 112 112 112 112 112 112  896  168 180 188 192 192 188 180 168 1456

Board Circles

The concentric "circles" around the center with their respective influence sums of sliding pieces:

Bishop Circles                        Rook Circles                          Queen Circles
+---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+
|              196              |     |              392              |     |              588              |
+   +---+---+---+---+---+---+   +     +   +---+---+---+---+---+---+   +     +   +---+---+---+---+---+---+   +
|   |          180          |   |     |   |          280          |   |     |   |          460          |   |
+   +   +---+---+---+---+   +   +     +   +   +---+---+---+---+   +   +     +   +   +---+---+---+---+   +   +
|   |   |      132      |   |   |     |   |   |      168      |   |   |     |   |   |      300      |   |   |
+   +   +   +---+---+   +   +   +     +   +   +   +---+---+   +   +   +     +   +   +   +---+---+   +   +   +
|   |   |   |   52  |   |   |   |     |   |   |   |   56  |   |   |   |     |   |   |   |  108  |   |   |   |
+   +   +   +       +   +   +   +     +   +   +   +       +   +   +   +     +   +   +   +       +   +   +   +
|   |   |   | 4*13  |   |   |   |     |   |   |   | 4*14  |   |   |   |     |   |   |   | 4*27  |   |   |   |
+   +   +   +---+---+   +   +   +     +   +   +   +---+---+   +   +   +     +   +   +   +---+---+   +   +   +
|   |   |    12*11      |   |   |     |   |   |    12*14      |   |   |     |   |   |    12*25      |   |   |
+   +   +---+---+---+---+   +   +     +   +   +---+---+---+---+   +   +     +   +   +---+---+---+---+   +   +
|   |        20* 9          |   |     |   |        20*14          |   |     |   |        20*23          |   |
+   +---+---+---+---+---+---+   +     +   +---+---+---+---+---+---+   +     +   +---+---+---+---+---+---+   +
|            28* 7              |     |            28*14              |     |            28*21              |
+---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+     +---+---+---+---+---+---+---+---+

Quantities and Point Values

The mentioned move quantities of pawns and pieces only roughly correlate with their point values since the static enumeration of all moves with distinct coordinates does not take into account the reachability of all origin-squares. Only queen and rook can reach any square in at least two moves on the otherwise empty board. Bishop quantities cover all light and dark colored from-squares. While a single bishop is bounded to one square color, its individual influence quantity is therefor divided by two. Also, pawns can only move forward and can not reach each enumerated origin square, which decreases their individual influence accordantly. King and knights can reach every square on the otherwise empty board, but may take more time with respect to distance and knight-distance.

Divisibility by Seven

All influence quantities are divisible by four times seven, thanks to the double pushes. For a rook it is quite obvious, since each of the 64 from squares covers one rank and file each with seven squares left.

Piece	#	div 4	div 7	div 28
Pawn	140	35	20	5
Knight	336	84	48	12
King	420	105	60	15
Bishops	560	140	80	20
Bishop	280	70	40	10
Rook	896	224	128	32
Queen	1456	364	208	52
Q \| N	1792	448	256	64

Fibonacci Spiral

If we only consider pieces with disjoint moves (excluding pawns and king), and the queen as superset of bishop and rook, the influence quantities are even divisible by seven times sixteen, where the remaining quotients from knight to queen are Fibonacci numbers as shown by the Fibonacci spiral ^[3] ^[4] .


Fibonacci spiral ^[5]	Yupana, counting tool of the Incas

Piece	covers other pieces	#	div 112 (7*16)
Knight	-	336	3
Bishop	queen, king and pawn captures	560	5
Rook	queen, king and pawn pushes	896	8
possible queen move coordinates		1456	13
possible from-to move coordinates		1792	16

Analogy in Astronomy

In his esoteric and pseudo scientific touched Encyclopedia of Chess-Prehistory, Peter Orantek ^[6] mentions a possible connection to astronomy, related to the orbital period of Earth and Venus. The influence quantity of a queen is equivalent to about 4 years (4 x 364 days), while the influence quantity of a rook is equivalent to 224 days x 4 Venus rotations.


Moon		Venus 224		Earth 364

In his German text sample ^[7] , Orantek further elaborates that queen quantities of the four center squares (four times 27) represent four earth moon rotations, while the three concentric rings around the center might related to various synodic periods of the four terrestrial planets. He associates following prime numbers with planets or objects orbiting the Sun ^[8] :

Prime number	Piece	Engine	Planet or Objects	Orbital period in days	Synodic period in days
3	Knight	Black Knight White Knight	Mercury	87.9691	115.88
5	Bishop	BlackBishop The Crazy Bishop	Venus	224.70069	583.92 (579–589)
13	Queen	Queen Terra	Earth	365.256366
61			Mars	686.971	779.96 (764–811)
89		Anubis	Asteroids
127		Jupiter	Jupiter	4,331.572	398.88
167			Charon
181			Saturn	10,759.220	378.09
307		Chiron	Chiron	18,539.000
487			Uranus	30,799.095	369.66
499			Pholus	33,547.410
547		Neptune	Neptune	60,190.000	367.49
761			Pluto	90,613.305	366.73
1307			Transpluto

Publications

H. M. Taylor (1876). On the Relative Values of the Pieces in Chess. Philosophical Magazine, Series 5, Vol. 1, pp. 221-229
H. S. M. Coxeter (1940). Mathematical Recreations and Essays. from the original by W. W. Rouse Ball, Macmillan
Jack Good (1968). A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares. Machine Intelligence Vol. 2
Dan Heisman (1990, 1999, 2010, 2015).The Positional Elements of Chess. Russell Enterprises
Peter Orantek (2008). Encyclopedia of Chess-Prehistory - Programming Language Chess.

Forum Posts

Value of the pieces by Joost de Heer, rgc, February 01, 1995
Material/Mobility by kingliveson, OpenChess Forum, June 17, 2010

External Links

7 from Wikipedia
Seven-day week from Wikipedia
If - Fibonacci's Number (1971), YouTube Video
Frank Zappa and The Mothers of Invention, Inca Roads, 1974, (A Token of His Extreme), YouTube Video ^[9] ^[10] ^[11]
Frank Zappa, George Duke, Napoleon Murphy Brock, Chester Thompson, Tom Fowler, Ruth Underwood, Captain Beefheart

References

^ Dan Heisman (1990, 1999, 2010, 2015).The Positional Elements of Chess. Russell Enterprises
^ The Game of War from Samuel Bak - represented by Pucker Gallery since 1969
^ The Fibonacci Series - The Series - Fibonacci Spiral In Action
^ The relative piece values for {N, B, R, Q} of {3, 5, 8, 15} were mentioned by H. M. Taylor (1876). On the Relative Values of the Pieces in Chess. Philosophical Magazine, Series 5, Vol. 1, pp. 221-229 as reported in H. S. M. Coxeter (1940). Mathematical Recreations and Essays. pp. 162-165, from the original by W. W. Rouse Ball, Macmillan, as reported by Jack Good (1968). A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares. Machine Intelligence Vol. 2
^ Peter Orantek: Encyclopedia of Chess-Prehistory
^ Peter Orantek: Encyclopedia of Chess-Prehistory - Programming Language Chess
^ Peter 0rantek: Encyclopedia of Chess-Prehistory - Decoded prehistorical books of Chess (pdf text sample)
^ Peter 0rantek: Encyclopedia of Chess-Prehistory - Decoded prehistorical books of Chess - Contents (pdf)
^ Clay animation by Bruce Bickford
^ Kelly Fisher Lowe (2006). The Words and Music of Frank Zappa. Praeger Publishers, pp. 119
The lyrics to "Inca Roads" are absurdist in the extreme. They veer wildly from spacey - "Did a vehicle / Come from somewhere out there / Just to land in the Andes?," which both Watson and Courrier claim Zappa's satire on the popular-at-the-time book Chariots of the Gods? ...
^ Nazca Lines from Wikipedia

What links here?

Page	Date Edited
Butterfly Boards	Jan 27, 2015
Center	Jun 21, 2016
Dan Heisman	Jun 12, 2013
Distance	Sep 25, 2015
Encoding Moves	Mar 27, 2016
Evaluation of Pieces	Jan 8, 2018
Franklin Titus	Aug 20, 2013
Influence Quantity of Pieces	Jul 21, 2017
Jupiter	Sep 2, 2015
Material	Mar 31, 2018
Mobility	Jan 17, 2018
Moves	Feb 19, 2018
Pieces	Feb 19, 2018
Point Value	Mar 31, 2018
Pseudo-Legal Move	May 23, 2015
Ralph Betza	Mar 12, 2014
Scid	Apr 15, 2017
Table-driven Move Generation	Feb 19, 2017

Up one Level

King Safety

GerdIsenberg — Wed, 14 Feb 2018 19:18:53 GMT

Home * Evaluation * King Safety

		Good evaluation of the king safety is one of the most challenging tasks in writing an evaluation function, but also the most rewarding. The subjects are placed here in order of approximate (implementation) difficulty. If this page grows, it might be worthwhile to create a sub-page for each term.
Samuel Bak - King ^[1]

Pawn Shield

When the king has castled, it is important to preserve pawns next to it, in order to protect it against the assault. Generally speaking, it is best to keep the pawns unmoved or possibly moved up one square. The lack of a shielding pawn deserves a penalty, even more so if there is an open file next to the king.

Pawn Storm

If the enemy pawns are near to the king, there might be a threat of opening a file, even if the pawn shield is intact. Penalties for storming enemy pawns must be lower than penalties for (semi)open files, otherwise the pawn storm might backfire, resulting in a blockage.

King Tropism

King tropism is a simplified form of king safety evaluation. It takes into account the distance between the King and the attacking pieces, possibly weighted against piece value. For example, one may double the distance value for a queen, and halve it for bishops and rooks. This kind of evaluation acts in a probabilistic way - it is by no means certain that being close to the king helps in attacking it. For example, if white castles short, black rook on h8 gets a higher tropism value regardless whether it stands on an open file. Nevertheless, using this kind of crude evaluation term increases a probability of building up an attack.

This kind of algorithm is used by Crafty. Another, perhaps more basic example is the CPW-engine as implemented in CPW-Engine_eval, and the one demonstrated in the Evaluation function draft.

Scaling

Usually king safety value is scaled one way or the other. Even TSCP uses the pawn shield and pawn storm score, scaled by the opponent's material. This way, whenever the engine finds itself with a broken pawn shield, it tends to exchange pieces in order to alleviate the danger. Fruit uses a more elaborate scheme, counting the bonuses for attacking the squares near to the enemy king, and then multiplying their sum by the constant derived from the number of attackers. For an approximation of such approach, see CPW_King evaluation function.

Attacking King Zone

sample specification
King zone is usually defined as squares to which enemy King can move plus two or three additional squares facing enemy position. Basic King safety function, similar to the one described in Toga log user manual, can work as follows: we have two variables, attackingPiecesCount and valueOfAttacks, zeroed at startup. If a piece attacks enemy king zone, we increase attackingPiecesCount by one, and count how many squares within enemy King zone are attacked. We multpily the number of attacked squares by a constant: 20 for a knight, 20 for a bishop, 40 for a rook and 80 for a queen. The result of multiplication is added to valueOfAttacks. After finding all attacks, we look at attackingPiecesCount, use it as an index to the table given below, and our king attack score is (valueOfAttacks * attackWeight[attackingPiecesCount] ) / 100.

Nr of Attackers		Attack weight
1		0
2		50
3		75
4		88
5		94
6		97
7		99

Square Control

The most elaborate king safety evaluation schemes gather information about control of the squares near the enemy king. A good explanation of such an algorithm might be found on Ed Schröder's Programmer Corner ^[2] ^[3]. If a program, unlike Rebel, does not keep incrementally updated attack tables, this knowledge is likely to be uncovered while calculating mobility.

Attack Units

Rebel (as we know from its description) and Stockfish (as we know from its code) use attack counter as an index to a table holding king attack scores. Stockfish counts each minor piece attack on a king zone (defined as squares that enemy king can reach + three more forward squares facing enemy position) as 2 attack units, rook attack on king zone as 3 attack units and a queen attack as 5 attack units. The virtue of such approach is twofold. (1) other factors beside these attacks can be counted. For example, Stockfish adds 6 attack units for a safe queen contact check and a couple attack units for a safe rook contact check. (2) the values held in the table may reflect attitude that "the whole is greater than the sum of parts". Typical curve is S-shaped: it raises slowly at first, then it goes up faster, becoming almost flat at the end.

This is the table from Glaurung 1.2:

static const int SafetyTable[100] = {
   0,   0,   0,   1,   1,   2,   3,   4,   5,   6,
   8,  10,  13,  16,  20,  25,  30,  36,  42,  48,
  55,  62,  70,  80,  90, 100, 110, 120, 130, 140,
 150, 160, 170, 180, 190, 200, 210, 220, 230, 240,
 250, 260, 270, 280, 290, 300, 310, 320, 330, 340,
 350, 360, 370, 380, 390, 400, 410, 420, 430, 440,
 450, 460, 470, 480, 490, 500, 510, 520, 530, 540,
 550, 560, 570, 580, 590, 600, 610, 620, 630, 640,
 650, 650, 650, 650, 650, 650, 650, 650, 650, 650,
 650, 650, 650, 650, 650, 650, 650, 650, 650, 650
};

This is the table generated using a formula from Stockfish, rescaled to centipawns :

static const int SafetyTable[100] = {
    0,  0,   1,   2,   3,   5,   7,   9,  12,  15,
  18,  22,  26,  30,  35,  39,  44,  50,  56,  62,
  68,  75,  82,  85,  89,  97, 105, 113, 122, 131,
 140, 150, 169, 180, 191, 202, 213, 225, 237, 248,
 260, 272, 283, 295, 307, 319, 330, 342, 354, 366,
 377, 389, 401, 412, 424, 436, 448, 459, 471, 483,
 494, 500, 500, 500, 500, 500, 500, 500, 500, 500,
 500, 500, 500, 500, 500, 500, 500, 500, 500, 500,
 500, 500, 500, 500, 500, 500, 500, 500, 500, 500,
 500, 500, 500, 500, 500, 500, 500, 500, 500, 500
};

Using such tables, it is advisable not to evaluate king attack if only two pieces are attacking.

Patterns

There are positions that tend to be notoriously difficult for the chess programs. One of them is a sacrifice of a minor piece on g5/g4, when it is simultaneously attacked and protected by the "h" pawns. Another one occurs after a standard Bxh7 sacrifice: White knight stands unchallenged on g5, white queen on h5, black King on g8 (positions with Kg6 are best left to the search). Hard-coding such patterns raises program's tactical awareness.

Forums Posts

1998 ...

King Safety by Stuart Cracraft, CCC, April 22, 1998
King safety evaluation by Roberto Waldteufel, CCC, May 28, 1998
Asymetric king safety by Tom King, rgcc, March 13, 1999

2000 ...

What is Piece´s tropism? by carlos, CCC, October 08, 2001
Bishop tropism? by Pham Hong Nguyen, CCC, June 17, 2002

2005 ...

king safety by Charles Roberson, CCC, November 02, 2007

2010 ...

Distance to King by Adam Berent, CCC, January 08, 2010
value of king tropism in eval function by Tom King, CCC, May 17, 2011
Approaches to king safety? by Mike Robinson, CCC, January 19, 2012
For Ed Schroeder: Rebel's Pawn Shield and Pawn Storm Eval by Marcel Fournier, CCC, August 21, 2012
King shelter x-ray attacks by Lyudmil Tsvetkov, CCC, June 27, 2014 » X-ray Attacks (Bitboards)
Heavy piece shelter by Lyudmil Tsvetkov, CCC, June 27, 2014
King safety refinements by Lyudmil Tsvetkov, CCC, August 31, 2014

2015 ...

about king attack by Daniel Anulliero, CCC, August 27, 2015
king shelter - when and how? by Alexandru Mosoi, CCC, March 21, 2016
king safety: hard positions for zurichess by Alexandru Mosoi, CCC, March 27, 2016 » Zurichess
Castling Evaluation by Dennis Sceviour, CCC, August 02, 2016 » Castling
enemy edge pawn as part of own king shelter by Bram Mourik, CCC, September 30, 2017
Pawn Storm - Theory by Dennis Sceviour, CCC, February 14, 2018 » Pawn Storm

External Links

Programmer Corner by Ed Schröder, King Safety in REBEL ^[4]
Middle game - King safety from Chess Tutorial : Improve Your Middle Game by Mark Weeks
The Rolling Stones - Gimme Shelter (1998 promotion video), YouTube Video
Bridges to Babylon Tour feat. Lisa Fischer and Darryl Jones, et al., December 12 1997, Trans World Dome, St. Louis Missouri

References

^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ Programmer Corner by Ed Schröder, King Safety in REBEL
^ How Rebel Plays Chess is also available as pdf
^ For Ed Schroeder: Rebel's Pawn Shield and Pawn Storm Eval by Marcel Fournier, CCC, August 21, 2012

What links here?

Page	Date Edited
Abyss	Aug 5, 2017
Advances in Computer Chess 1	Oct 22, 2015
AI Chess	Jan 7, 2016
Alarm	Jun 7, 2017
Alexandru Mosoi	Jan 8, 2018
Amundsen	Sep 3, 2013
Amyan	Dec 10, 2013
Andscacs	Jan 16, 2018
Arasan	Apr 8, 2018
Aristarch	May 8, 2014
Asymmetric evaluation	Nov 17, 2016
Atlas (ESP)	Jan 28, 2018
Battery	Jan 29, 2017
Beaches	Jun 10, 2017
Belle	Jan 18, 2018
Belzebub	Oct 20, 2015
Betsabe	Jul 23, 2017
BigLion	Sep 28, 2016
Bismark	Apr 22, 2015
Bison	Sep 29, 2016
BlackBishop	Nov 7, 2014
Bobby	Jan 7, 2016
Bobcat	Jun 27, 2017
Bodo	Oct 6, 2016
Brainless	Jun 24, 2017
Brainstorm	Jun 24, 2017
Bruja	Feb 3, 2015
Bs6676	Jul 21, 2016
Carballo	Oct 2, 2016
Castling	May 5, 2017
Castling rights	Jan 7, 2017
Charles Roberson	Jan 7, 2016
Cheese	Feb 17, 2018
Cheiron	Jan 7, 2016
Chenard	Sep 5, 2015
Cheng	Jul 30, 2017
Cheops (Miller)	Jan 13, 2017
Chess 0.5	Nov 20, 2016
Chess Guru	Mar 4, 2017
Chess System Tal	Jan 13, 2017
chess22k	Apr 23, 2018
ChessBrainVB	Jun 24, 2017
ChessV	Jan 21, 2018
Chunking	Jun 12, 2017
Clarabit	Nov 3, 2011
Claudia	Jun 1, 2016
Coiled	Mar 12, 2017
Counter	Nov 13, 2017
CPW-Engine	Dec 31, 2014
Cumulus	Jan 7, 2016
Cupcake	May 19, 2016
DanaSah	Oct 9, 2017
Daniel Anulliero	Oct 3, 2017
Dartmouth CP	Jan 19, 2018
DayDreamer	Aug 22, 2016
Defenchess	Mar 18, 2018
Delicate Brute	Jun 7, 2016
Demolito	Mar 1, 2018
Dennis Sceviour	Feb 14, 2018
Design Principles	Jan 17, 2018
Diablo	May 17, 2016
Dimitri	Aug 22, 2017
Distance	Sep 25, 2015
Djinn	Feb 8, 2016
Dolphin	Nov 28, 2014
Donna	Aug 17, 2017
Dorpsgek	Apr 2, 2018
Dragon FR	Sep 9, 2016
Dreamer	Aug 5, 2015
Elephant	Sep 19, 2016
Enigma	Feb 9, 2015
Evaluation	Feb 1, 2018
Evaluation function draft	Jul 11, 2014
Evaluation of Pieces	Jan 8, 2018
Evaluation Overlap	Jul 19, 2016
Evaluation Patterns	Jun 24, 2013
Eveann	Apr 3, 2017
Exacto	Oct 3, 2015
Faile	May 27, 2014
Fencer	Jan 20, 2013
Fianchetto	Feb 18, 2015
Fidelity	Jan 7, 2016
Fischer-Schneider	Nov 23, 2016
Fischerle	Aug 21, 2017
Francesca	Jan 7, 2016
Freyr	Mar 6, 2014
Fridolin	Jun 27, 2017
Gambit Fruit	Mar 29, 2013
Garbochess	Sep 23, 2017
Gaviota	Jan 21, 2018
Gibbon	Dec 23, 2014
Ginkgo	Jul 13, 2016
Gk	Oct 9, 2017
Glass	May 24, 2017
Gogobello	Jul 30, 2017
GopherCheck	Feb 3, 2017
GullChess	Jun 27, 2017
Hagrid	Apr 12, 2016
Hakkapeliitta	Apr 26, 2016
HAL	Jun 14, 2016
HaQiKi D	Jul 26, 2017
Hash Table	Jan 1, 2018
Hossa	Jan 7, 2016
Houdini	Apr 14, 2018
Ifrit	Feb 7, 2016
ISA	Apr 2, 2018
IsiChess	Jan 7, 2016
Jabba	Sep 10, 2016
Joanna	Dec 9, 2014
Joker IT	Sep 16, 2017
Jonathan Warkentin	Jun 29, 2014
Kaissa	Apr 9, 2018
King	Feb 26, 2013
King Centralization	Oct 30, 2017
King of Kings	Sep 4, 2013
King Pattern	Nov 15, 2013
King Pawn Tropism	Sep 1, 2014
King Safety	Feb 14, 2018
KingSlayer	Oct 17, 2016
KnockOut	Sep 20, 2016
Komodo	Mar 6, 2018
Ktulu	May 16, 2015
Lachex	Jan 7, 2016
LarsenVB	Jun 24, 2017
Laser	Dec 27, 2017
Lyudmil Tsvetkov	Mar 28, 2018
Machiavelli	Jun 2, 2015
MadChess	Jul 4, 2017
Marvin	Feb 10, 2018
Master	Dec 28, 2017
Mate at a Glance	Sep 24, 2014
Mate Threat Extensions	Apr 14, 2012
MBChess	Sep 29, 2012
MChess	Feb 26, 2018
Meep	Sep 4, 2016
Mephisto Dallas	Sep 1, 2017
Middlegame	Sep 6, 2016
Minority Attack	Jun 6, 2012
Monsoon	Feb 8, 2015
Murka	Nov 11, 2016
Natwarlal	Aug 26, 2013
Nebula	Feb 7, 2015
Nemorino	Dec 21, 2017
Neurosis	Dec 23, 2017
NG-play	Feb 26, 2017
Nirvanachess	Sep 30, 2017
NoonianChess	Jan 7, 2016
NoraGrace	Nov 23, 2014
Obender	Apr 17, 2016
Oracle	Sep 4, 2016
Ostrich	Dec 28, 2017
Parrot	Dec 31, 2014
Pattern Recognition	Sep 8, 2017
Patzer	Apr 5, 2017
Pawn chain	Jan 17, 2018
Pawn Hash Table	Feb 1, 2018
Pawn Structure	Oct 2, 2017
Pawny	Jun 17, 2015
Pharaon	Sep 2, 2017
Plisk	Dec 31, 2014
Point Value by Regression Analysis	Aug 26, 2017
PolarChess	May 15, 2017
Prophet	Sep 30, 2017
Proscha	May 20, 2015
Protector	Oct 12, 2017
Quantifying Evaluation features	Jun 6, 2012
RattateChess	Dec 2, 2014
RDChess	May 3, 2013
Rebel	Feb 25, 2018
RedQueen	Nov 13, 2017
Rhetoric	Nov 15, 2017
Rival	Jul 30, 2017
Robocide	May 11, 2016
Rodent	Jan 11, 2018
Rodin	Feb 7, 2016
Ron Atkin	Oct 26, 2016
Rook on Open File	Apr 24, 2017
Rookie	Jan 7, 2016
RuyDos	Feb 17, 2018
Sacrifice	Aug 10, 2017
Sayuri	Oct 1, 2017
Schooner	Feb 2, 2018
Scidlet	May 31, 2014
Scorpio	Mar 28, 2018
SCP	Jun 16, 2016
Sharper	Jun 6, 2017
Shield	May 17, 2017
Shura-Bura's Program	Sep 29, 2013
Sierżant	Apr 15, 2014
Simplex	Mar 6, 2016
Sinobyl	Jul 3, 2014
Sjaak (Glebbeek)	Oct 4, 2017
Sloppy	Sep 17, 2016
Slow Chess	May 17, 2016
SmarThink	Feb 2, 2018
Smash	May 11, 2016
Snitch	Apr 7, 2016
Soldat	Aug 20, 2017
SOMA	Mar 25, 2015
Spector	Nov 11, 2016
Spike	Jan 7, 2016
Square Control	Sep 15, 2016
SSE2	Feb 27, 2018
Stockfish	Apr 7, 2018
Strategic Test Suite	Dec 19, 2016
Strategy	Jan 18, 2018
Sunsetter	Jun 1, 2017
SuperChess	Dec 7, 2016
Tactics	Jan 12, 2018
TCEC Season 9	Nov 6, 2017
Teki	Mar 29, 2018
Telepath	Jul 14, 2014
Tempo	Jan 17, 2018
Test-Positions	Feb 25, 2018
The Bernstein Chess Program	Jan 2, 2016
Thor's Hammer	Nov 23, 2013
Tigran	Aug 16, 2015
Toga Log	Apr 24, 2017
Tom King	Aug 19, 2017
TRACE	Feb 14, 2013
Tucano	Dec 16, 2017
Tunguska	Sep 16, 2017
Turochamp	Dec 14, 2017
Vajolet	Jan 25, 2018
Virtua Chess	Jul 3, 2018
Virtual Chess	Mar 25, 2017
Warrior	Feb 23, 2015
Wasp	Nov 24, 2017
WChess	Jan 7, 2016
Wing	Oct 26, 2017
Winglet	Apr 26, 2015
Witz	Nov 14, 2017
WyldChess	Mar 10, 2018
Xiphos	Apr 22, 2018
Xpdnt	Sep 13, 2015
ZChess	Jan 8, 2016
Zeus RU	Jun 6, 2015
Zurichess	Mar 12, 2018

Up one Level

Knight-Distance

GerdIsenberg — Sun, 20 Oct 2013 11:34:51 GMT

Home * Chess * Squares * Knight-Distance

		The Knight-Distance between two squares determines the minimal number of moves a Knight needs, to reach one square from the other on the otherwise empty board. Due to its move geometry, the knight changes its square-color, each times it moves. Thus, if squares have different color, the number of moves is odd, otherwise with same square color, even. Smaller distance does not generally imply smaller KnightDistance.
Samuel Bak - Across ^[1]

Knight Fill

Lookups

By 64 x 64 Lookup

By 0x88 Square Relations

By Absolute Rank-File Distance

References

What links here?

Knight Fill

With bitboards, one may use fill algorithms, to calculate the knight distance by counting the number of fill-cycles until a target set becomes subset of the consecutively expanded knight attacks.

U64 getKnightAttacks(U64 bb) {
   U64 l1 = (bb >> 1) & C64(0x7f7f7f7f7f7f7f7f);
   U64 l2 = (bb >> 2) & C64(0x3f3f3f3f3f3f3f3f);
   U64 r1 = (bb << 1) & C64(0xfefefefefefefefe);
   U64 r2 = (bb << 2) & C64(0xfcfcfcfcfcfcfcfc);
   U64 h1 = l1 | r1;
   U64 h2 = l2 | r2;
   return (h1<<16) | (h1>>16) | (h2<<8) | (h2>>8);
}
 
// no set should be empty -> assert (b1 != 0 && b2 != 0 )
int calcKnightDistance(U64 b1, U64 b2) {
   int d = 0;
   while ((b1 & b2) == 0) {
      b1 = getKnightAttacks(b1); // as long as sets are disjoint
      d++; // increment distance
   }
   return d;
}
 
int knightDistance(int a, int b) {
   return calcKnightDistance(C64(1) << a, C64(1) << b);
}

Lookups

One may use this fill-approach to initialize lookup-tables.

By 64 x 64 Lookup

The obvious and likely fastest solution is to go with a 64 times 64 array, which takes 4 KByte containing all possible knight-distances which are in the 0..6 range on a 8 times 8 board.

char arrKnightDistance[64][64]; // 4 KByte, requires some initialization code
 
int knightDistance(int a, int b) {
   return arrKnightDistance[a][b];
}

By 0x88 Square Relations

Similar to distance or Manhattan-distance, we may use the 0x88 square relation approach for a denser 240 sized array - but there is one minor issue to consider according to diagonal (or anti-diagonal) neighbored squares. Those squares have usually a knight distance of two, but a distance of four from (or to) the four corner squares. Those extra cases have to be considered by some extra conditions.

By Absolute Rank-File Distance

Another alternative is based on a lookup of two 64 element arrays, one is indexed by some absolute 8 x Rank-Distance plus absolute File-Distance, where diagonal neighbors have a unique distance of 9.

const int ndis[64] = { // char
   //  knight-distance
   0, 3, 2, 3, 2, 3, 4, 5,
   3, 2, 1, 2, 3, 4, 3, 4,
   2, 1, 4, 3, 2, 3, 4, 5,
   3, 2, 3, 2, 3, 4, 3, 4,
   2, 3, 2, 3, 4, 3, 4, 5,
   3, 4, 3, 4, 3, 4, 5, 4,
   4, 3, 4, 3, 4, 5, 4, 5,
   5, 4, 5, 4, 5, 4, 5, 6
};
 
const int corner[64] = { // char
   1, 0, 0, 0, 0, 0, 0, 1,
   0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0,
   1, 0, 0, 0, 0, 0, 0, 1
};
 
int absRankFileDiff(int a, int b) {
   int rd = (a|7) - (b|7);
   int fd = (a&7) - (b&7);
   return abs(rd) + abs(fd);
}
 
int knightDistance(int a, int b) {
   int c = absRankFileDiff(a,b);
   int d = ndis[c];
   if (c == 9) d += 2*(corner[a] ^ corner[b]);
   return d;
}

Or without a condition:

int knightDistance(int a, int b) {
   int c = absRankFileDiff(a,b);
   int d = ndis[c] + 2*((c == 9) & (corner[a] ^ corner[b]));
   return d;
}

To avoid further conditions, with the risk of branch miss-predictions up and then, abs as intrinsic is likely implemented based on following code snippet ...

int abs(int a) {
   int s = a >> 31; // cdq, signed shift, -1 if negative, else 0
   a ^= s;  // ones' complement if negative
   a -= s;  // plus one if negative -> two's complement if negative
   return a;
}

... by compilers, on x86 a sequence three instructions: {cdq, xor, sub} or {cdq, add, xor}.

References

^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota

What links here?

Page	Date Edited
Color of a Square	May 24, 2015
Connectivity	Mar 6, 2016
Direction	Oct 6, 2016
Distance	Sep 25, 2015
Double Attack	Oct 22, 2014
Fill Algorithms	Nov 6, 2013
Influence Quantity of Pieces	Jul 21, 2017
Knight Pattern	Feb 23, 2015
Knight-Distance	Oct 20, 2013
Manhattan-Distance	May 19, 2014
Nibble	Jan 25, 2015
Squares	Feb 15, 2015

Up one Level

Knowledge

GerdIsenberg — Sat, 22 Jul 2017 18:04:38 GMT

Home * Knowledge

		Knowledge is the possession of information, its acquisition involves complex cognitive processes: perception, learning, communication, association and reasoning. Inside a chess program, knowledge is manifested either as procedural or as declarative knowledge. The declarative a priori knowledge about the rules of chess is immanent inside the move generator in conjunction with check detection. Further declarative knowledge is coded as rules of thumb of the evaluation function, as well as persistent perfect knowledge from retrograde analysis, or as empirical knowledge mostly from human experience, to retrieve moves from an hand crafted opening book. Procedural knowledge is applied by Learning, as well to backup declarative knowledge by Search. However, the Search versus Knowledge trade-off in computer chess and games refers heuristic or perfect knowledge.
Samuel Bak - Knowledgeable ^[1]

Search versus Knowledge

The trade-offs of search versus knowledge ^[2]

Curves A and B represent a fixed performance level, say 2000 for B and 2200 for A. The curves indicate that there are many ways to archive that level of performance, either by little knowledge and lot of search, or vice versa. If a program has archived point P on curve B, it may improve between search only (point S) or knowledge only (point K).

In Practice

Andreas Junghanns and Jonathan Schaeffer in Search versus knowledge in game-playing programs revisited ^[3]:

The difficulty lies in quantifying the knowledge axis. Perfect knowledge assumes an oracle, which for most games we do not have. However, we can approximate an oracle by using a high-quality, game playing program that performs deep searches. Although not perfect, it is the best approximation available. Using this, how can we measure the quality of knowledge in the program?

A heuristic evaluation function, as judged by an oracle, can be viewed as a combination of two things: oracle knowledge and noise. The oracle knowledge is beneficial and improves the program' s play. The noise, on the other hand, represents the inaccuracies in the program' s knowledge. It can be introduced by several things, including knowledge that is missing, over- or under-valued, and/or irrelevant. As the noise level increase, the beneficial contribution of the knowledge is overshadowed.

By definition, an oracle has no noise. We can measure the quality of the heuristic evaluation in a program by the amount of noise that is added into it. To measure this, we add a random number to each leaf node evaluation ...

HiTech versus LoTech

At the Advances in Computer Chess 5 conference 1987, Hans Berliner et al. introduced an interesting experiment. HiTech with a sophisticated evaluation competed versus LoTech, almost the same program but a rudimentary evaluation, at different search depths ^[4]. According to Peter Kouwenhoven ^[5], Berliner's conclusion was that more was to be won by increasing HiTech's knowledge at constant speed rather than further increasing its speed while keeping knowledge constant. The abstract from the extended 1990 paper ^[6]:

Chess programs can differ in depth of search or in the evaluation function applied to leaf nodes or both. Over the past 10 years, the notion that the principal way to strengthen a chess program is to improve its depth of search has held sway. Improving depth of search undoubtedly does improve a program's strength. However, projections of potential gain have time and again been found to overestimate the actual gain.

We examine the notion that it is possible to project the playing strength of chess programs by having different versions of the same program (differing only in depth of search) play each other. Our data indicates that once a depth of “tactical sufficiency” is reached, a knowledgeable program can beat a significantly less knowledgeable one almost all of the time when both are searching to the same depth. This suggests that once a certain knowledge gap has been opened up, it cannot be overcome by small increments in searching depth. The conclusion from this work is that extending the depth of search without increasing the present level of knowledge will not in any foreseeable time lead to World Championship level chess. The approach of increasing knowledge has been taken in the HiTech chess machine.

Ed Schröder's Conclusion

Ed Schröder concluded HiTech's extra knowledge was just worth one ply in the computer-computer area ^[7]^[8], and further elaborated on tactical evaluation knowledge helpful in early Rebel searching 5-7 plies versus Rebel searching 13-15 plies on 2001 hardware ^[9] ^[10]:

Some specific chess knowledge through the years become out-dated due to the speed of nowadays computers. An example: In the early days of computer chess, say the period 1985-1989 I as hardware had a 6502 running at 5 Mhz. Rebel at that time could only search 5-7 plies on tournament time control. Such a low depth guarantees you one thing: horizon effects all over, thus losing the game.

To escape from the horizon effect all kind of tricks were invented, chess knowledge about dangerous pins, knight forks, double attacks, overloading of pieces and reward those aspects in eval. Complicated and processor time consuming software it was (15-20% less performance) but it did the trick escaping from the horizon effect in a reasonable way.

Today we run chess program on 1500 Mhz machines and instead of the 5-7 plies Rebel now gets 13-15 plies in the middle game and the horizon effect which was a major problem at 5 Mhz slowly was fading away.

So I wondered, what if I throw that complicated "anti-horizon" code out of Rebel, is it still needed? So I tried and found out that Rebel played as good with the "anti-horizon" code as without the code. In other words, the net gain was a "free" speed gain of 15-20%, thus an improvement.

One aspect of chess programming is that your program is in a constant state of change due to the state of art of nowadays available hardware. I am sure a Rebel at 10 Ghz several parts of Rebel need a face-lift to get the maximum out of the new speed monster.

Search versus Evaluation

Mark Uniacke in a reply to Ed Schröder, on Search or Evaluation, mentioning the 1st Computer Olympiad, Null Move Pruning, Hiarcs, Woodpusher, E6P, Rebel, Fritz ... ^[11]:

I am not saying search is the only reason but that search is more significant in the Elo jump than other factors. Thanks for the interesting history which in general I agree with but I should add for clarification... In 1989 I was exposed to the null move in HIARCS' first official computer tournament at the Olympiad in London. John Hamlen had written his program Woodpusher as part of his M.Sc project investigating the null move exclamation and although Woodpusher did not do well in that tournament I had the good fortune to discuss null move with John and reading his project which interested me very much. John and I had many discussions on computer chess over the following months. That Olympiad probably had an impact on you too and not only because Rebel won Gold above Mephisto X and Fidelity X for the first time but because there was a program there running quite fast (at that time in history) called E6P (so named because it could reach 6 ply full width!) running on an Acorn ARM based machine. Jan was operating Rebel at the tournament as you know and I noticed Jan take a keen interest in this new machine. Frans was using null move in Fritz 2 in Madrid 1992 (I am not sure about Fritz 1). I am sure you remember that tournament fondly. I remember at Madrid having a discussion with a few programmers including Richard about what on earth was Fritz 2 doing to reach the depths it was attaining, this seed of interest made me investigate search enhancements carefully after Madrid and it was then that I began re-investigating the null move. It was not long before HIARCS began using null moves too and by Christmas 1992 I had a working implementation which gave a big jump over Hiarcs 1 which had only been released shortly before. I had much fun playing my Hiarcs 1.n against Mephisto Risc 1 in late 1992, early 1993 and that sort of closes the circle on the E6P story. Even so, the null move idea still evolved and my implementation today is much better than it was initially and so it can be for other ideas. We can all profit from these techniques but some gain more than others if they find new ways to exploit it. Rebel 7/8/9 and Hiarcs 5/6/7 battled hard in those years and my big jump to the top of the rating lists happened partly because of a search change to Hiarcs 5/6 which led at one stage to a 71 Elo lead on the SSDF. I recall Rebel and Hiarcs exchanging the lead on the SSDF list a number of times in those years. So we agree the impact search has made on computer chess progress is clear. Now we diverge on what might be the reason for new progress in the field. Clearly we have good search enhancements on cut nodes and all nodes, but that does not mean they cannot be improved and enhanced or in fact that another technique might prove to be superior or complementary. Meanwhile there can be no doubt that progress is made positionally irrespective of search but I do not believe it can be the reason for a breakthrough jump in chess strength but rather a steady climb. But wait! Maybe there is a middle way, a third avenue of improvement which sort of falls between the two pillars of search and evaluation and that is search intelligence. Something both of us have practiced in our programs for years but maybe not properly exploited. The ability of the eval to have a more significant impact on the search than traditionally has been the case. I think this area has been relatively unexplored and offers interesting potential.

Knowing

Declarative Knowledge

A Priori

Heuristic Knowledge

Empirical Knowledge

Perfect Knowledge

Perfect Knowledge usually incorporates analysis or stored results from exhaustive search, which requires no further search at interior nodes except the root. An oracle might be considered as "perfect" evaluation.

Interior Node Recognizer

Interior Node Recognizer

Endgame Databases

as probed inside a Recognizer framework, if a certain material constellation is detected.

Procedural Knowledge

Publications

1970 ...

Marvin Minsky (1974). Framework for Representing Knowledge 1974. MIT-AI Laboratory Memo 306
Coen Zuidema (1974). Chess: How to Program the Exceptions? Technical Report IW21/74, Mathematical Center Amdsterdam. pdf

1975 ...

Donald Michie (1976). An Advice-Taking System for Computer Chess. Computer Bulletin, Ser. 2, Vol. 10, pp. 12-14. ISSN 0010-4531.
Jack Good (1977). Dynamic Probability, Computer Chess, and the Measurement of Knowledge. Machine Intelligence, Vol. 8 (eds. E. Elcock and Donald Michie), pp. 139-150. Ellis Horwood, Chichester.
Ivan Bratko, Danny Kopec, Donald Michie (1978). Pattern-Based Representation of Chess Endgame Knowledge. The Computer Journal, Vol. 21, No. 2, pp. 149-153. pdf
Donald Michie, Ivan Bratko (1978). Advice Table Representations of Chess End-Game Knowledge. Proceedings 3rd AISB/GI Conference, pp. 194-200.
David Wilkins (1979). Using Patterns and Plans to Solve Problems and Control Search. Ph.D. thesis, Computer Science Dept, Stanford University, AI Lab Memo AIM-329
Max Bramer, Mike Clarke (1979). A Model for the Representation of Pattern-Knowledge for the Endgame in Chess. International Journal of Man-Machine Studies, Vol. 11, No.5

1980 ...

Ivan Bratko, Donald Michie (1980). A Representation of Pattern-Knowledge in Chess Endgames. Advances in Computer Chess 2
David Wilkins (1980). Using patterns and plans in chess. Artificial Intelligence, vol. 14, pp. 165-203. Reprinted (1988) in Computer Chess Compendium
David Wilkins (1982). Using Knowledge to Control Tree Searching. Artificial Intelligence, vol. 18, pp. 1-51.
Alen Shapiro, Tim Niblett (1982). Automatic Induction of Classification Rules for Chess End game. Advances in Computer Chess 3
Hans Berliner (1982). Search vs. knowledge: an analysis from the domain of games. Technical Report Department of Computer Science, Carnegie Mellon University
Allen Newell (1982). The Knowledge Level. Artificial Intelligence, Vol. 18, No. 1
Raymond Smullyan (1982). An Epistemological Nightmare. MIT
David Wilkins (1983). Using chess knowledge to reduce search. In Chess Skill in Man and Machine (Peter W. Frey, ed.), Ch. 10, 2nd Edition, Springer-Verlag.
Danny Kopec (1983). Human and Machine Representations of Knowledge. Ph.D. thesis, University of Edinburgh, supervisor: Donald Michie
Alen Shapiro (1983). The Role of Structured Induction in Expert Systems. University of Edinburgh, Machine Intelligence Research Unit (Ph.D. thesis) ^[12]
Jonathan Schaeffer (1984). The Relative Importance of Knowledge. ICCA Journal, Vol. 7, No. 3
Albrecht Heeffer (1984). Automated Acquisition on Concepts for the Description of Middle-game Positions in Chess. Turing Institute, Glasgow, Scotland, TIRM-84-005

1985 ...

Albrecht Heeffer (1985). Validating Concepts from Automated Acquisition Systems. IJCAI 85, pdf
Reiner Seidel (1985). Grammatical Description of Chess Positions, Data-Base versus Human Knowledge. ICCA Journal, Vol. 8, No. 3
Jonathan Schaeffer, Tony Marsland (1985). The Utility of Expert Knowledge. Proceedings IJCAI 85, pp. 585-587. Los Angeles.
Alen Shapiro, Donald Michie (1986). A Self-commenting Facility for Inductively Synthesised Endgame Expertise. Advances in Computer Chess 4
Bernd Owsnicki, Kai von Luck (1986). N.N.: A Case Study in Chess Knowledge Representation. Advances in Computer Chess 4
Jonathan Schaeffer (1986). Experiments in Search and Knowledge. Ph.D. Thesis, University of Waterloo. Reprinted as Technical Report TR 86-12, Department of Computing Science, University of Alberta, Edmonton, Alberta.
Peter W. Frey (1986). Fuzzy Production Rules in Chess. ICCA Journal, Vol. 9, No. 4
Peter W. Frey (1986). A Bit-Mapped Classifier. BYTE, Vol. 11, No. 12, pp. 161-172.
Subhash Kak (1987). Patanjali and Cognitive Science. Vitasta Publishing ^[13]
Alen Shapiro (1987). Structured Induction in Expert Systems. Turing Institute Press in association with Addison-Wesley Publishing Company, Workingham, UK. ISBN 0-201-178133. amazon^[14]
Stephen Muggleton (1988). Inductive Acquisition of Chess Strategies. Machine Intelligence 11 (eds. Jean Hayes Michie, Donald Michie, and J. Richards), pp. 375-389. Clarendon Press, Oxford, U.K. ISBN 0-19-853718-2.
Reiner Seidel(1989). A Model of Chess Knowledge - Planning Structures and Constituent Analysis. Advances in Computer Chess 5
Hans Berliner, Carl Ebeling (1989). Pattern Knowledge and Search: The SUPREM Architecture. Artificial Intelligence, Vol. 38, No. 2, pp. 161-198. ISSN 0004-3702.
Revised as Hans Berliner, Carl Ebeling (1990). Hitech. Computers, Chess, and Cognition
Hans Berliner, Gordon Goetsch, Murray Campbell, Carl Ebeling (1989). Measuring the Performance Potential of Chess Programs, Advances in Computer Chess 5
Hermann Kaindl (1989). Towards a Theory of Knowledge. Advances in Computer Chess 5

1990 ...

Hans Berliner, Gordon Goetsch, Murray Campbell, Carl Ebeling (1990). Measuring the Performance Potential of Chess Programs. Artificial Intelligence, Vol. 43, No. 1
Kiyoshi Shirayanagi (1990). Knowledge Representation and its Refinement in Go Programs. Computers, Chess, and Cognition
Robert Levinson, Feng-hsiung Hsu, Tony Marsland, Jonathan Schaeffer, David Wilkins (1991). The Role of Chess in Artificial Intelligence Research. IJCAI 1991, pdf, also in ICCA Journal, Vol. 14, No. 3, pdf
Christian Posthoff, Michael Schlosser, Jens Zeidler (1993). Search vs. Knowledge? - Search and Knowledge! In: Proc. 3rd KADS Meeting, Munich, March 8-9 1993, Siemens AG, Corporate Research and Development, 305-326, 1993.
Steven Walczak, Douglas D. Dankel II (1993). Acquiring Tactical and Strategic Knowledge with a Generalized Method for Chunking of Game Pieces. International Journal of Intelligent Systems 8 (2), 249-270.
Christian Posthoff, Michael Schlosser, Rainer Staudte, Jens Zeidler (1994). Transformations of Knowledge. Advances in Computer Chess 7
Robert Levinson, Gil Fuchs (1994). A Pattern-Weight Formulation of Search Knowledge. UCSC-CRL-94-10, CiteSeerX

1995 ...

Richard Fikes (1996). Ontologies: What Are They, and Where's The Research? KR 1996
Andreas Junghanns, Jonathan Schaeffer (1997). Search versus knowledge in game-playing programs revisited. IJCAI-97, Vol 1, pdf
Johannes Fürnkranz (1997). Knowledge Discovery in Chess Databases: A Research Proposal. Technical Report OEFAI-TR-97-33, Austrian Research Institute for Artificial Intelligence, zipped ps, pdf ^[15]
Krzysztof Krawiec, Roman Slowinski, Irmina Szczesniak (1998). Pedagogical Method for Extraction of Symbolic Knowledge from Neural Networks. Rough Sets and Current Trends in Computing 1998
Edward J. Quigley, Anthony Debons (1999). Interrogative Theory of Information and Knowledge. SIGCPR '99, pdf

2000 ...

Michael Thielscher (2000). Representing the Knowledge of a Robot. KR 2000, CiteSeerX
Krzysztof Krawiec (2002). Genetic Programming-based Construction of Features for Machine Learning and Knowledge Discovery Tasks. Genetic Programming and Evolvable Machines, Vol. 3, No. 4
Stuart Russell, Peter Norvig (2003). Artificial Intelligence: A Modern Approach, 2nd edition, 3rd edition 2009
Stuart Russell (2003). Rationality and Intelligence. In Renee Elio (Ed.), Common sense, reasoning, and rationality, Oxford University Press, pdf
Aleksander Sadikov, Ivan Bratko, Igor Kononenko (2003). Search versus Knowledge: An Empirical Study of Minimax on KRK. Advances in Computer Games 10, pdf
Tristan Caulfield (2004). Acquiring and Using Knowledge in Computer Chess. BSc Computer Science, University of Bath, pdf
Elias M. Awad, Hassan M. Ghaziri (2004,2010). Knowledge Management Systems. Pearson Education India, Knowledge Management Systems - Lecture Notes, LaTeX2HTML by Nikos Drakos, Ross Moore
Nick Pelling (2004). The Network Is The Knowledge: Ideology & Strategy in Mintzberg's Ten Schools. MBA dissertation, Kingston University Business School, Surrey, UK

2005 ...

Christian Posthoff, Michael Schlosser (2005). Optimal strategies — Learning from examples — Boolean equations. in Klaus P. Jantke, Steffen Lange (eds.) (2005). Algorithmic Learning for Knowledge-Based Systems, Lecture Notes in Computer Science 961, Springer
Aleksander Sadikov, Ivan Bratko (2006). Search Versus Knowledge Revisited Again. CG 2006
David J. Stracuzzi (2006). Scalable Knowledge Acquisition through Cumulative Learning and Memory Organization. Ph.D. thesis, University of Massachusetts Amherst, advisor Paul E. Utgoff, pdf
Guillaume Chaslot, Louis Chatriot, Christophe Fiter, Sylvain Gelly, Jean-Baptiste Hoock, Julien Pérez, Arpad Rimmel, Olivier Teytaud (2008). Combining expert, offline, transient and online knowledge in Monte-Carlo exploration. pdf
Guillaume Chaslot, Christophe Fiter, Jean-Baptiste Hoock, Arpad Rimmel, Olivier Teytaud (2009). Adding Expert Knowledge and Exploration in Monte-Carlo Tree Search. Advances in Computer Games 12, pdf, pdf

2010 ...

Matej Guid (2010). Search and Knowledge for Human and Machine Problem Solving, Ph.D. thesis, University of Ljubljana, pdf ^[16]
Shi-Jim Yen, Jung-Kuei Yang, Kuo-Yuan Kao, Tai-Ning Yang (2012). Bitboard Knowledge Base System and Elegant Search Architectures for Connect6. Knowledge-Based Systems, Vol. 34
Bo-Nian Chen, Hung-Jui Chang, Shun-Chin Hsu, Jr-Chang Chen, Tsan-sheng Hsu (2013). Multilevel Inference in Chinese Chess Endgame Knowledge Bases. ICGA Journal, Vol. 36, No. 4 » Chinese Chess, Endgame Tablebases
Bo-Nian Chen, Hung-Jui Chang, Shun-Chin Hsu, Jr-Chang Chen, Tsan-sheng Hsu (2014). Advanced Meta-knowledge for Chinese Chess Endgame Knowledge Bases. ICGA Journal, Vol 37, No. 1

2015 ...

Tamal T. Biswas, Kenneth W. Regan (2015). Quantifying Depth and Complexity of Thinking and Knowledge. ICAART 2015, pdf

Forum Posts

1996 ...

Incoporating chess knowledge in chess programs by Valavan Manohararajah, rgcc, June 26, 1996
computer chess "oracle" ideas... by Robert Hyatt, rgcc, April 1, 1997 » Oracle
Knowledge is not elegant by Don Dailey, CCC, June 14, 1998
The end of computer chess progress? by Ed Schröder, rgcc, March 06, 1999
The Limits of Positional Knowledge by Michael Neish from CCC, November 11, 1999

2000 ...

suggestions for (a new generation of) chess knowledge using engines by Ingo Lindam, CCC, October 23, 2002
likelihood instead of pawnunits? + chess knowledge by Ingo Lindam, CCC, October 25, 2002
Knowledge by Sergei S. Markoff, CCC, September 26, 2004

2005 ...

The superior Rybka chess knowledge by Chrilly Donninger, CCC, January 18, 2006 » Rybka
knowledge and blitz; search and long games by Joseph Ciarrochi, CCC, February 15, 2006
Search or Evaluation? by Ed Schröder, Hiarcs Forum, October 05, 2007 » Search, Evaluation
Re: Search or Evaluation? by Mark Uniacke, Hiarcs Forum, October 14, 2007

2010 ...

hardware advances - a different perspective by Robert Hyatt, CCC, September 09, 2010
old crafty vs new crafty on new hardware by Robert Hyatt, CCC, September 11, 2010 » Crafty
Crafty tests show that Software has advanced more by Don Dailey, CCC, September 12, 2010
Final results - Crafty - hardware vs software by Robert Hyatt, CCC, September 13, 2010 » Crafty
Deep Blue vs Rybka by Don Dailey, CCC, September 13, 2010 » Deep Blue, Rybka
hardware doubling number for Crafty by Robert Hyatt, CCC, September 15, 2010 » Crafty
Ahhh... the holy grail of computer chess by Marcel van Kervinck, CCC, August 23, 2011
Is search irrelevant when computing ahead of very big trees? by Fermin Serrano, CCC, July 24, 2013 » Search
Improve the search or the evaluation? by Jens Bæk Nielsen, CCC, August 31, 2013 » Search versus Evaluation
Slow Searchers? by Michael Neish, CCC, November 02, 2013
Chessprogams with the most chessknowing by Joe Boden, CCC, December 19, 2014

2015 ...

An attempt to measure the knowledge of engines by Kai Laskos, CCC, March 23, 2015
Re: Chessprogams with the most chessknowing by Vincent Lejeune, CCC, February 18, 2017
Re: Chessprogams with the most chessknowing by Alvaro Cardoso, CCC, February 18, 2017
Re: Chessprogams with the most chessknowing by Mark Lefler, CCC, February 18, 2017 » Komodo
Re: Chessprogams with the most chessknowing by Marco Costalba, CCC, February 19, 2017 » Stockfish

External Links

Knowledge

Types of Knowledge

Musicvideo

Mahavishnu Orchestra - You Know You Know, August 17, 1972, more recent 3Sat broadcast ^[17], YouTube Video
John McLaughlin, Billy Cobham, Rick Laird, Jan Hammer, Jerry Goodman

References

^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ Jonathan Schaeffer (1997). One Jump Ahead Challenging Human Supremacy in Checkers, Springer, ISBN 0-387-94930-5, Prelude to Disaster, pp. 255-256 or pp. 249-250 in the Second Edition, 2009
^ Andreas Junghanns, Jonathan Schaeffer (1997). Search versus knowledge in game-playing programs revisited. IJCAI-97, Vol 1, pdf, 3 Search Versus Knowledge: Practise
^ Hans Berliner, Gordon Goetsch, Murray Campbell, Carl Ebeling (1989). Measuring the Performance Potential of Chess Programs, Advances in Computer Chess 5
^ Peter Kouwenhoven (1987). Advances in Computer Chess, The 5th Triennial Conference. ICCA Journal, Vol. 10, No. 2 (report)
^ Hans Berliner, Gordon Goetsch, Murray Campbell, Carl Ebeling (1990). Measuring the Performance Potential of Chess Programs. Artificial Intelligence, Vol. 43, No. 1
^ Chess in 2010 by Ed Schröder, The Berliner Experiment
^ The end of computer chess progress? by Ed Schröder, rgcc, March 06, 1999
^ Re: Intelligent software, please by Ed Schröder, CCC, November 26, 2001
^ Schröder, Ed (German) from Schachcomputer.info - Wiki also refers the post by Ed Schröder
^ Re: Search or Evaluation? by Mark Uniacke, Hiarcs Forum, October 14, 2007
^ UCI Machine Learning Repository: Chess (King-Rook vs. King-Pawn) Data Set
^ Patanjali from Wikipedia
^ Dap Hartmann (1988). Alen D. Shapiro: Structured Induction in Expert Systems. ICCA Journal, Vol. 11, No. 4
^ Knowledge discovery from Wikipedia
^ Dap Hartmann (2010). How can Humans learn from Computers? Review on Matej Guid's Ph.D. thesis, ICGA Journal, Vol. 33, No. 4
^ Original ZDF broadcast "Sonntagskonzert", September 17, 1972, recorded at Kongresshalle Deutschen Museum, Munich, "Jazz Now", August 17, 1972, curator Joachim-Ernst Berendt, see The Mahavishnu Orchestra On Film, MUENCHEN-72_KPL.pdf, Diese Woche im Fernsehen, Der Spiegel 38/1972 (German), 1972 Summer Olympics

What links here?

Page	Date Edited
1st Computer Olympiad	Jul 25, 2017
ABK	Feb 1, 2017
Alexander Szabo	Nov 10, 2012
Applied Concepts	Dec 25, 2017
Artificial Intelligence	Apr 9, 2018
Automated Tuning	Feb 27, 2018
Awit	Dec 22, 2017
Bart Selman	Dec 26, 2017
Bernd Owsnicki-Klewe	Jan 20, 2018
Bo-Nian Chen	Jul 17, 2017
Bookbuilder	Feb 4, 2018
Bookup	Feb 4, 2018
Bs6676	Jul 21, 2016
CAPS	Dec 23, 2017
Chess	Jan 21, 2018
Chess Psychology Booklist	Apr 11, 2013
CHREST	May 6, 2016
Chunker	Jul 12, 2016
Chunking	Jun 12, 2017
Coen Zuidema	Mar 25, 2016
Cognition	Dec 8, 2017
Comet	Jan 8, 2016
Constellation	Oct 2, 2016
CTG	Aug 22, 2016
Cyrus	Jul 22, 2014
Data	Nov 26, 2017
David Wilkins	Mar 2, 2016
Depth	Feb 25, 2018
Diep	Jan 28, 2018
Dietmar Lippold	Mar 22, 2014
Distance	Sep 25, 2015
E6P	Dec 17, 2016
ECO	Nov 2, 2017
Edwards' Tablebases	Sep 26, 2016
Endgame Bitbases	Apr 5, 2017
Endgame Tablebases	Mar 6, 2018
EPAM	Jul 15, 2017
Eric Postma	May 26, 2015
Ernst A. Heinz	Mar 6, 2017
Eval Tuning in Deep Thought	Jun 7, 2016
Evaluation	Feb 1, 2018
Evaluation Patterns	Jun 24, 2013
Evaluation Philosophy	Sep 29, 2014
Eye Movements	Jul 22, 2015
Fermin Serrano	Nov 27, 2015
FinalGen	Aug 14, 2016
Floyd	Sep 11, 2016
Fortress	Feb 1, 2018
Francesca	Jan 7, 2016
Freezer	Aug 14, 2016
Fritz	Feb 26, 2018
GAFS	Aug 14, 2016
Gandalf	Jan 21, 2018
Gaviota Tablebases	Apr 22, 2018
Gian Piero Favini	Jan 4, 2017
Gil Fuchs	Sep 22, 2015
Goliath	Apr 5, 2017
Grit Lachmann	Apr 26, 2014
Guard Heuristic	Nov 18, 2015
Hannibal	Oct 4, 2017
Hardware	Jan 20, 2018
Hartmut Tanke	Sep 7, 2014
Hash Table	Jan 1, 2018
Hiarcs	Feb 25, 2018
HiTech	Mar 31, 2018
Home	Jul 2, 2018
Interior Node Recognizer	Mar 12, 2018
Ivan Bratko	Aug 16, 2017
J. Howard Johnson	May 23, 2016
Jens Bæk Nielsen	Mar 3, 2015
Johannes Fürnkranz	Feb 26, 2018
Kai von Luck	Jan 20, 2018
Knowledge	Jul 22, 2017
Komodo	Mar 6, 2018
KRK	Nov 26, 2016
LCZero	Apr 18, 2018
Learning	Feb 20, 2018
Lomonosov Tablebases	May 20, 2016
MAPP	Jan 30, 2016
Marco Costalba	Feb 28, 2018
Mark Uniacke	Dec 12, 2016
Marko Maliković	Aug 10, 2013
Martin Možina	Jun 11, 2016
Matjaž Gams	May 23, 2016
Max Bramer	May 20, 2014
Memory	Dec 8, 2017
Mephisto Roma	Sep 1, 2017
Michael Borgstädt	Jan 24, 2016
Michèle Sebag	May 23, 2016
Mobility	Jan 17, 2018
N.N.	Jan 20, 2018
Nalimov Tablebases	Dec 23, 2016
Neurologic	Jan 7, 2016
NIC-Key	Jul 16, 2017
Nick Pelling	Dec 11, 2016
Nimzo	Dec 30, 2017
Nodes per second	Feb 28, 2018
Now	Jan 7, 2016
Null Move Pruning	Dec 2, 2017
Opening Book	Feb 26, 2018
Opponent Model Search	Aug 14, 2017
Oracle	Sep 4, 2016
Paradise	Nov 19, 2014
Pattern Recognition	Sep 8, 2017
PawnKing	Sep 5, 2014
Perceiver	Nov 21, 2017
Pieter Spronck	Jan 5, 2017
Planner	Sep 24, 2012
Planning	Feb 12, 2018
Playing Strength	Mar 31, 2018
PolyGlot	Jan 17, 2018
Prodigy	Jan 19, 2018
Psion	Mar 20, 2017
Psychology	Sep 20, 2016
Rebel	Feb 25, 2018
RetroChess	Feb 2, 2014
Retrograde Analysis	Mar 21, 2017
Richard Lang	Jan 7, 2016
Richard Snyder	Sep 20, 2015
Robert Levinson	Aug 25, 2016
Ross Hayward	May 23, 2016
Santos Gerardo Lazzeri	Mar 19, 2016
Scorpio Bitbases	Mar 12, 2018
Search	Feb 1, 2018
Search with Random Leaf Values	Apr 23, 2018
SmarThink	Feb 2, 2018
Soei Tan	Oct 27, 2012
SOS	Apr 5, 2017
Space-Time Tradeoff	Jun 17, 2015
space.menu	Oct 9, 2015
Stavros Vassos	May 25, 2015
Stephan Schiffel	Jul 8, 2016
Stephen B. Streater	Dec 17, 2016
Steven Walczak	May 23, 2016
Stockfish	Apr 7, 2018
Strategy	Jan 18, 2018
Super Constellation	Oct 1, 2016
Syzygy Bases	Apr 19, 2018
Tactics	Jan 12, 2018
TechMate	Aug 23, 2014
Texel's Tuning Method	Dec 2, 2017
The Baron	Jan 8, 2018
Thompson's Databases	Dec 24, 2014
Tristan Caulfield	Dec 1, 2017
WCCC 1992	Feb 26, 2018
WChess	Jan 7, 2016
Woodpusher	Dec 12, 2016
Yace	Dec 31, 2017
Zeus	Jan 3, 2018

Up one Level

Late Move Reductions

GerdIsenberg — Mon, 25 Sep 2017 21:12:31 GMT

Home * Search * Selectivity * Reductions * Late Move Reductions

		Late Move Reductions (LMR), or its version known as History Pruning and History Reductions ^[1] , save search by reducing moves that are ordered closer to the end of likely fail-low nodes. Typically, most schemes search the first few moves (say 3-4) at full depth, then if no move fails high, many of the remaining moves are reduced in search depth. The technique has been used for many years in various forms, but it became very popular in 2005 after Fruit and Glaurung ^[2] used open source implementations based on the History Heuristic. LMR can often reduce the effective branching factor to less than 2, depending on the reduction conditions.
Samuel Bak - Other Rules ^[3]

Common Conditions

Less Common Conditions

Common Conditions

Most programs do not reduce these types of moves:

Tactical moves (captures and promotions)
Moves while in check
Moves which give check
Moves that cause a search extension
Anytime in a PV-Node in a PVS search
Depth < 3 (sometimes depth < 2)

Less Common Conditions

Less common conditions on moves not to reduce:

Passed Pawn Moves
Killer Moves
Moves threatening the King area
Tactically threatening moves
Moves with good past relative history ^[4]
Any Pawn Moves
Allowing reductions of "bad" captures (SEE < 0)
Moves of a threatened piece to safety (often detected via a Null Move search)

Reduction Depth

Classical implementation reduces by one ply only. Yet modern programs, most notably Stockfish, allow reductions of more than one ply and increase them for later moves. Reduction depth changes according to expected node type (being typically smaller in pv nodes), depth and move number. Here some sample formulas can be viewed:

Senpai reduces by one ply for the first 6 moves and by depth / 3 for remaining moves.
Fruit Reloaded uses formula: uint8( sqrt(double(depth-1)) + sqrt(double(moves-1))); for non-PV nodes. In PV-nodes it reduces by 2/3 of this value.

Re-searches

Classical implementation assumes a re-search at full depth if the reduced depth search returns a score above alpha.

Test Results

Some test results related to LMR can be found on

Late Move Reduction Test Results

Publications

David Levy, David Broughton, Mark Taylor (1989). The SEX Algorithm in Computer Chess. ICCA Journal, Vol. 12, No. 1
Daniel S. Abdi (2013). Analysis of pruned minimax trees. pdf » Alpha-Beta, Null Move Pruning

Forum Posts

2004

Forward pruning and some related techniques by Sergei Markoff, CCC, March 02, 2004

2005 ...

Reductions and null move refutations by Tord Romstad, Winboard Forum, April 18, 2005 » Null Move Pruning
What is History Pruning? by David Dahlem, CCC, July 03, 2005
History based pruning question by Alvaro Jose Povoa Cardoso, CCC, August 26, 2005
About history pruning... by Svein Bjørnar Myrvang, CCC, October 26, 2005
What is "history pruning"? by Vladimir Medvedev, Winboard Forum, November 07, 2005

2006

History pruning by Frank Phillips, CCC, February 27, 2006
late move reductions by Robert Hyatt, CCC, March 01, 2006
Re: late move reductions by Alessandro Scotti, CCC, March 01, 2006 » Kiwi
PHR (Peak History Reduction) idea by Daniel Mehrmann, CCC, March 01, 2006 » Homer, Relative History Heuristic
history pruning/ late move pruning by Tom King, Winboard Programming Forum, March 02, 2006
LMR question by Uri Blass, Winboard Programming Forum, July 13, 2006

2007

LMR in micro-Max by Harm Geert Muller, CCC, April 07, 2007 » Micro-Max
Fruit and History Reductions by Ed Schröder, CCC, July 19, 2007 » Fruit
LMR other conditions by Mark Lefler, CCC, July 23, 2007
Improving history tables by Michael Sherwin, CCC, July 25, 2007
LMR: history or not? by Alessandro Scotti, CCC, December 13, 2007 » Hamsters

2008

Extreme late move reductions? by Gary, CCC, March 05, 2008
LMR? by Martin Giepmans, CCC, April 12, 2008 » Anatoli
Adaptative LMR and TT by Fermin Serrano, CCC, December 23, 2008

2009

About LMR & History reductions by Joona Kiiski, CCC, February 24, 2009
LMR by Robert Hyatt, CCC, March 05, 2009
LMR and 'tactically connected' moves by Harm Geert Muller, CCC, March 10, 2009
LMR revisited by Robert Hyatt, CCC, April 01, 2009
LMR and null move selectivity by Don Dailey, CCC, April 20, 2009
LMR by Bas Hamstra, CCC, September 30, 2009
May I Ask What You Think Of This? by Christopher Conkie, CCC, October 20, 2009
Did people try replacing LMR by pruning by Uri Blass, CCC, December 31, 2009

2010 ...

The problem with LMR in suprtactical positions by Oliver Brausch, CCC, January 05, 2010
Researching if LMR-affected search improves Alpha? by John Merlino, CCC, January 22, 2010
Problems with LMR in late endgames by Luca Hemmerich, CCC, March 01, 2010
LMR algorithm by kenny stanley, CCC, March 15, 2010
LMR Conditions by kenny stanley, CCC, March 23, 2010
LMR at root of search tree - worthwhile? by Tom King, CCC, May 21, 2010
EPR, even better than LMR! by Michael Sherwin, CCC, May 27, 2010
Re: "Automated Discovery of Search Extensions" by Ed Schröder, OpenChess Forum, June 26, 2010
lmr at PV nodes? by Tom King, CCC, July 23, 2010
move count based pruning by Tom King, CCC, September 02, 2010
LMR differences in long vs short games by Jacob Børs Lind, CCC, November 08, 2010
fulitiy + lmr; funny results by Volker Böhm, CCC, December 28, 2010

2011

lmr in PV by Larry Kaufman, CCC, January 03, 2011

2012

Should reduction depend on depth? by Larry Kaufman, CCC, January 14, 2012 » Komodo
Possible LMR improvement using AB_FOOL by Ed Schroder, CCC, April 24, 2012
LMR Research by Matthew R. Brades, CCC, July 02, 2012
Adjustable search pruning depending on time control by Jerry Donald, CCC, December 20, 2012 » Time Management

2013

ROC analysis of Late Move Reductions by Gerard van Ewijk, CCC, March 22, 2013 ^[5]
Is LMR Sound by Henk van den Belt, CCC, May 29, 2013
Is LMR safe within NULL move reduction by Henk van den Belt, CCC, May 30, 2013
LMR at CUT nodes can be arbitrarily bad! by Michel Van den Bergh, CCC, June 20, 2013 » Node Types, Python
How much to reduce ? by Henk van den Belt, CCC, October 03, 2013 » R

2014

Null move and LMR by Laurie Tunnicliffe, CCC, March 12, 2014 » Null Move Pruning
LMR & TT interaction by Natale Galioto, CCC, April 29, 2014 » Transposition Table
A question about Stockfish and LMR or other pruning... by Forrest Hoch, CCC, November 20, 2014

2015 ...

About LMR , again :-) by Daniel Anulliero, CCC, March 01, 2015
LMR tuning by Shawn Chidester, CCC, May 11, 2015
Interpretation of LMR by Alexandru Mosoi, CCC, May 29, 2015
What's Your Engine's Maximum LMR Reduction? by Steve Maughan, CCC, June 08, 2015
New "smoothing" issue by Robert Hyatt, CCC, July 20, 2015
On LMR, and statically predicting moves by Matthew Lai, CCC, August 25, 2015
LMR by another name by Steven Edwards, CCC, September 02, 2015 » Spector
Ratio reduction by Steven Edwards, CCC, September 20, 2015 » Symbolic

2016

late move reduction by Folkert van Heusden, CCC, January 21, 2016
Extensions in the days of LMR? by Martin Fierz, CCC, March 22, 2016 » Extensions
LMR problems by Alvaro Cardoso, CCC, May 16, 2016
Reductions by Harm Geert Muller, CCC, May 22, 2016 » R
Disappointing LMR Results by David Cimbalista, CCC, August 04, 2016
Null Move in LMR by Laurie Tunnicliffe, CCC, August 10, 2016 » Null Move Pruning

2017

LMR and PVS by thevinenator, OpenChess Forum, February 10, 2017 » Principal Variation Search
Late move reductions ? by Mahmoud Uthman, CCC, March 22, 2017
Check extension vs LMR by Harm Geert Muller, CCC, April 04, 2017 » Check Extensions
LMR - [for starters] - [Advance] and [Expert] by Ed Schroder, CCC, May 01, 2017
LMR and killer by Harm Geert Muller, CCC, September 14, 2017 » Killer Heuristic
LMR prescription by Evert Glebbeek, CCC, September 24, 2017

External Links

Late Move Reductions

Late Move Reductions from Wikipedia
An Introduction to Late Move Reductions by Tord Romstad (dead link)
Mediocre Chess: [Guide] Late move reduction (LMR) by Jonatan Pettersson, March 26, 2007 » Mediocre
History Reductions in Pro Deo by Ed Schröder » Pro Deo
LMR advanced from Rebel 13 by Ed Schroder ^[6] » Rebel

Misc

Wolfgang Schmid - The Latest Kick, Bix Jazzclub Stuttgart, Summer 2010, YouTube Video

References

^ History Reductions in Pro Deo by Ed Schröder
^ An Introduction to Late Move Reductions by Tord Romstad
^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ Mark Winands, Erik van der Werf, Jaap van den Herik, and Jos Uiterwijk (2006). The Relative History Heuristic. Computers and Games, Lecture Notes in Computer Science (LNCS 3846) (eds. Jaap van den Herik, Yngvi Björnsson, and Nathan S. Netanyahu), pp. 262-272. pdf
^ Receiver operating characteristic (ROC) from Wikipedia
^ LMR - [for starters] - [Advance] and [Expert] by Ed Schroder, CCC, May 01, 2017

What links here?

Page	Date Edited
Alessandro Scotti	Feb 27, 2014
AliBaba	Aug 17, 2014
Alpha-Beta	Jan 28, 2018
Alvaro Cardoso	Jan 12, 2018
Amoeba	Mar 19, 2018
Amundsen	Sep 3, 2013
Amyan	Dec 10, 2013
Anatoli	Oct 22, 2014
Andscacs	Jan 16, 2018
Artificial Intelligence	Apr 9, 2018
Atlas (ESP)	Jan 28, 2018
Bagatur	Sep 10, 2016
Bas Hamstra	Feb 4, 2018
Betsabe	Jul 23, 2017
Bison	Sep 29, 2016
Bobcat	Jun 27, 2017
Booot	Jan 22, 2018
Brainless	Jun 24, 2017
Branching Factor	Jun 28, 2017
Bright	Oct 25, 2016
Butterfly Boards	Jan 27, 2015
Butterfly Heuristic	May 6, 2016
Capture Extensions	Oct 26, 2012
Carballo	Oct 2, 2016
Check Extensions	Apr 19, 2018
Cheese	Feb 17, 2018
Cheng	Jul 30, 2017
Chepla	May 10, 2013
chess22k	Apr 23, 2018
ChessBrainVB	Jun 24, 2017
ChessV	Jan 21, 2018
Christopher Conkie	May 17, 2016
Cinnamon	Sep 23, 2017
Clarabit	Nov 3, 2011
Clubfoot	Sep 8, 2015
Coiled	Mar 12, 2017
Counter	Nov 13, 2017
CPW history	Jan 1, 2015
Crafty	Jan 28, 2018
CuckooChess	Jan 17, 2017
Cupcake	May 19, 2016
CXG Sphinx	Jun 23, 2017
Cyrus 68K	Jan 7, 2016
DanaSah	Oct 9, 2017
Daniel Anulliero	Oct 3, 2017
Daniel Mehrmann	Dec 13, 2015
Daniel Shawul	Jan 28, 2018
DayDreamer	Aug 22, 2016
Defenchess	Mar 18, 2018
Delfi	Jan 7, 2016
Demolito	Mar 1, 2018
Depth	Feb 25, 2018
Depth Reduction R	Oct 4, 2017
Deuterium	Jun 23, 2014
Dictionary	Aug 24, 2017
Dimitri	Aug 22, 2017
DisasterArea	Mar 27, 2017
DiscoCheck	Jun 23, 2017
Donna	Aug 17, 2017
Dorky	Oct 10, 2016
Dorpsgek	Apr 2, 2018
Encoding Moves	Mar 27, 2016
Engine Testing	Feb 1, 2018
Ethereal	Mar 20, 2018
Eveann	Apr 3, 2017
Evert Glebbeek	Sep 25, 2017
Exacto	Oct 3, 2015
Extensions	Apr 19, 2018
Fail-High Reductions	Mar 6, 2014
FCP	Jun 15, 2013
Fermin Serrano	Nov 27, 2015
Fischerle	Aug 21, 2017
Flux	Jan 12, 2016
Folkert van Heusden	Nov 24, 2017
Frank Phillips	Sep 26, 2016
Fridolin	Jun 27, 2017
Fruit	Sep 27, 2016
Futility Pruning	Aug 30, 2017
Galjoen	Mar 19, 2018
Garbochess	Sep 23, 2017
Garbochess-JS	Sep 23, 2017
Gary Linscott	Jan 16, 2018
Gaviota	Jan 21, 2018
Ghost	Feb 2, 2018
Gibbon	Dec 23, 2014
Ginkgo	Jul 13, 2016
Glass	May 24, 2017
Glaurung	Mar 14, 2017
Go	Jan 24, 2018
Gogobello	Jul 30, 2017
GopherCheck	Feb 3, 2017
Hakkapeliitta	Apr 26, 2016
Hamsters	Apr 11, 2014
HaQiKi D	Jul 26, 2017
Harm Geert Muller	Mar 31, 2018
History Heuristic	Jul 19, 2017
History Leaf Pruning	Apr 15, 2013
Home	Jul 2, 2018
Homer	Dec 23, 2013
Horizon	Mar 17, 2013
iCE	Jan 4, 2016
Ifrit	Feb 7, 2016
ISA	Apr 2, 2018
JFresh	Mar 2, 2016
JikChess	Nov 29, 2015
John Merlino	Feb 26, 2015
Killer Heuristic	Sep 14, 2017
KingSlayer	Oct 17, 2016
Kiwi	Sep 2, 2016
Komodo	Mar 6, 2018
Larry Kaufman	Jan 28, 2018
Laser	Dec 27, 2017
Late Move Reduction Test Results	Sep 25, 2017
Late Move Reductions	Sep 25, 2017
Laurie Tunnicliffe	Jun 13, 2017
Little Wing	Oct 26, 2017
LittleThought	Nov 7, 2016
Lozza	Apr 18, 2018
Luca Hemmerich	Jun 19, 2017
MadChess	Jul 4, 2017
Mark Lefler	Nov 23, 2017
Martin Fierz	Apr 26, 2018
Marvin	Feb 10, 2018
Matthew R. Brades	Jun 9, 2017
Mediocre	Feb 27, 2015
Micro-Max	Aug 7, 2017
Murka	Nov 11, 2016
Napoleon	Jun 25, 2017
Naum	Nov 23, 2017
Nebula	Feb 7, 2015
Nemorino	Dec 21, 2017
Nirvanachess	Sep 30, 2017
Node Types	Oct 22, 2017
NoraGrace	Nov 23, 2014
Null Move Pruning	Dec 2, 2017
Obender	Apr 17, 2016
Octochess	Aug 15, 2017
OliThink	May 19, 2017
Oliver Brausch	May 19, 2017
Orion	Oct 15, 2017
Paladin	Jan 29, 2017
Parity Pruning	Jan 14, 2013
Path-Dependency	Oct 16, 2017
Pawny	Jun 17, 2015
Phalanx	May 2, 2016
Philidor	Jan 7, 2016
Plisk	Dec 31, 2014
Prédateur	Nov 11, 2016
Principal Variation Search	Oct 22, 2017
ProbCut	Mar 25, 2016
Protector	Oct 12, 2017
Pruning	Jan 1, 2018
PV Extensions	May 4, 2013
Python	Jan 31, 2018
RattateChess	Dec 2, 2014
Reductions	Nov 1, 2017
Relative History Heuristic	Jun 8, 2015
Rhetoric	Nov 15, 2017
Robert Hyatt	Dec 25, 2017
Robocide	May 11, 2016
Rodent	Jan 11, 2018
RomiChess	Jan 2, 2018
RuyDos	Feb 17, 2018
Rybka	Mar 27, 2017
Sayuri	Oct 1, 2017
Schooner	Feb 2, 2018
Search Instability	May 5, 2017
Selectivity	Jan 12, 2018
Senpai	Nov 10, 2017
SEX Algorithm	Nov 25, 2014
Shawn Chidester	Aug 9, 2016
Shield	May 17, 2017
Simplex	Mar 6, 2016
Sjaak (Glebbeek)	Oct 4, 2017
Sloppy	Sep 17, 2016
Soldat	Aug 20, 2017
Spark	Oct 19, 2017
Spector	Nov 11, 2016
Spike	Jan 7, 2016
Stockfish	Apr 7, 2018
Symbolic	May 8, 2017
Tactics	Jan 12, 2018
Teki	Mar 29, 2018
Texel	Oct 9, 2017
The Baron	Jan 8, 2018
The Turk (TR)	Apr 1, 2017
Tigran	Aug 16, 2015
Time Management	Mar 20, 2018
Tom King	Aug 19, 2017
tomitankChess	Dec 8, 2017
Tord Romstad	Dec 9, 2017
Tornado	Dec 14, 2017
TRACE	Feb 14, 2013
Transposition Table	Apr 19, 2018
Tucano	Dec 16, 2017
Tunguska	Sep 16, 2017
UCT	Jan 22, 2018
Uncertainty Cut-Offs	Jul 21, 2015
Vadim Demichev	Jul 26, 2013
Vajolet	Jan 25, 2018
Vladimir Medvedev	Jul 22, 2016
Volker Böhm	Jan 7, 2016
Wasp	Nov 24, 2017
WildCat	Nov 11, 2016
Wing	Oct 26, 2017
Winter	Jan 23, 2018
WyldChess	Mar 10, 2018
Xiphos	Apr 22, 2018
Ziggy IS	Sep 6, 2015
Zochova	Nov 9, 2014
Zurichess	Mar 12, 2018

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Magic Bitboards

GerdIsenberg — Fri, 13 Apr 2018 13:09:31 GMT

Home * Board Representation * Bitboards * Sliding Piece Attacks * Magic Bitboards

		Magic bitboards, a multiply-right-shift perfect hashing algorithm to index an attack bitboard database - which leaves both line-attacks of bishop or rook in one run. Thanks to the fast 64-bit multiplication and fast and huge caches of recent processors, Magic Bitboards has become a de facto standard of modern bitboard engines, as used for instance in Crafty, Arasan, Stockfish and Houdini. While Robert Hyatt reported no immediate speed gain over Rotated Bitboards in Crafty ^[1] , Jon Dart mentioned a 20-25% speedup ^[2] in Arasan over rotated.
Samuel Bak - Auspicious Moon, 2001 ^[3]

History

The magic bitboard approach was motivated by Gerd Isenberg's multi-direction hashing technique kindergarten bitboards and probably by Gerd's and Tony van Roon-Werten's early trials to map line-wise occupancies by De Bruijn- or random number multiplication ^[4] . Lasse Hansen had the idea to hash the up to twelve relevant occupied bits of both directions of a rook- or bishop movement simultaneously ^[5] .

Pradu Kannan's improvements to Lasse Hansen's initial approach was to introduce a Java-like, two-dimensional array with individual size for each square and all it's relevant occupancies ^[6] . Big savings in table-size - since many squares on either orthogonal or diagonal lines require less bits than others, especially considering the inner six bits. While center squares are more dense for rooks, it is the opposite for bishops ^[7] .

Recently, Robert Purves coined the names Plain and Fancy Magics ^[8] , and found Hansen's initial Plain Magics with 2 MiB table for rooks and 256 KiB for bishops nearly indistinguishable from Fancy (about 800 KiB and 38 KiB) on his Intel i5 with huge L3 smart cache, see plain versus fancy source code. In the same CCC forum thread, Robert Houdart proposed a byte lookup per square for further table reductions.

How it works

A magic move-bitboard generation technique consists of four key steps:

Mask the relevant occupancy bits to form a key. For example if you had a rook on a1, the relevant occupancy bits will be from a2-a7 and b1-g1.
Multiply the key by a "magic number" to obtain an index mapping. This magic number can be generated by brute-force trial and error quite easily although it isn't 100% certain that the magic number is the best possible (see step 3).
Right shift the index mapping by 64-n bits to create an index, where n is the number of bits in the index. A better magic number will have less bits required in the index.
Use the index to reference a preinitialized move database.

The following illustration should give an impression, how magic bitboards work. All masked relevant occupied bits are perfectly hashed to the consecutive occupied state to index the pre-calculated attack-sets. Constructive collisions, where different occupancies map same attack-sets - since different bits are outer redundant bits "behind" the first blocker, are desired and even necessary to apply a perfect hashing with N bits.

                                        any consecutive
relevant occupancy                      combination of
bishop b1, 5 bits                       the masked bits
. . . . . . . .     . . . . . . . .     . . .[C D E F G]
. . . . . . . .     . 1 . . . . . .     . . . . . . . .
. . . . . . G .     . 1 . . . . . .     . . . . . . . .
. . . . . F . .     . 1 . . . . . .     . . . . . . . .
. . . . E . . .  *  . 1 . . . . . .  =  . . garbage . .    >> (64- 5)
. . . D . . . .     . 1 . . . . . .     . . . . . . . .
. . C . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
 
                                        any consecutive
relevant occupancy                      combination of
bishop d4, 9 bits                       the masked bits
. . . . . . . .     . . . . . . . .     2 4 5 B C E F G]
. . . . . . G .     . . .some . . .     . . . . . . .[1
. 5 . . . F . .     . . . . . . . .     . . . . . . . .
. . 4 . E . . .     . . .magic. . .     . . . . . . . .
. . . . . . . .  *  . . . . . . . .  =  . . garbage . .    >> (64- 9)
. . C . 2 . . .     . . .bits . . .     . . . . . . . .
. B . . . 1 . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
 
                                        any consecutive
relevant occupancy                      combination of
rook d4, 10 bits                        the masked bits
. . . . . . . .     . . . . . . . .     4 5 6 B C E F G]
. . . 6 . . . .     . . .some . . .     . . . . . .[1 2
. . . 5 . . . .     . . . . . . . .     . . . . . . . .
. . . 4 . . . .     . . .magic. . .     . . . . . . . .
. B C . E F G .  *  . . . . . . . .  =  . . garbage . .    >> (64-10)
. . . 2 . . . .     . . .bits . . .     . . . . . . . .
. . . 1 . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
 
                                        any consecutive
relevant occupancy                      combination of
rook a1, 12 bits                        the masked bits
. . . . . . . .     . . . . . . . .     5 6 B C D E F G]
6 . . . . . . .     . . .some . . .     . . . .[1 2 3 4
5 . . . . . . .     . . . . . . . .     . . . . . . . .
4 . . . . . . .     . . .magic. . .     . . . . . . . .
3 . . . . . . .  *  . . . . . . . .  =  . . garbage . .    >> (64-12)
2 . . . . . . .     . . .bits . . .     . . . . . . . .
1 . . . . . . .     . . . . . . . .     . . . . . . . .
. B C D E F G .     . . . . . . . .     . . . . . . . .

The above illustration is correct for the b1 bishop, since it has only one ray and one bit per file and works kindergarten like. In general a one to one mapping of N scattered occupied bits to N consecutive bits is not always possible due to overflows. A perfect mapping of N scattered bits to N consecutive bits is likely not minimal for most squares. It requires one or two gaps inside the consecutive N bits, to avoid collisions, blowing up the table size.

But the purpose is to perfectly hash attack-sets rather than consecutive occupied bits. The number of distinct attack-sets is much smaller than the relevant occupancies. Thus, with the help of constructive collisions, some initial guess how to map the bits, and/or trial and error, using exactly N bits is always possible. If one tries hard enough to maximize constructive collisions - even less. There are some N-1 ones reported at Best Magics so far, which will half the individual table size for some squares in the widespread Fancy Magic Bitboards approach.

Perfect Hashing

Magic bitboards applies perfect hashing. A surjective function, to map the vector of all relevant occupancies to a range of attack-sets per square. The less bits the attack-set - the closer the blockers, the more those attack-sets are shared by occupancies with different, but redundant outer squares.

The cardinality of all relevant occupancies is determined by the number of bits to map, varying from five to twelve - thus, the cardinality is the power of two the number of bits, varying from 32 to 4096.
The cardinality of distinct attack-sets is determined by the product of the length of each of the max four direction rays greater than zero (or one). The rook on d4 has 3*4*3*4 = 144 distinct attack-sets, a bishop on a8 has only 7.

The ratio of both cardinalities, that is all relevant occupancies versus the all distinct attack-sets is illustrated below: As a quarter of a board - due to the symmetry, the other squares may deduced by flipping and mirroring. Noticeable is the huge 4096/49 ratio of 2^12 occupied states versus 7 times 7 attack-sets of the edge rooks - 12 bits instead of 6. Those "expensive" squares make constructive collisions very desirable. To become more "minimal" by saving an index bit - to halve down the table for one square or the other.

	bishop on square				rook on square
	A	B	C	D		A	B	C	D
8	64/7	32/6	32/10	32/ 12	8	4096/49	2048/42	2048/ 70	2048/ 84
7	32/6	32/6	32/10	32/ 12	7	2048/42	1024/36	1024/ 60	1024/ 72
6	32/10	32/10	128/40	128/ 48	6	2048/70	1024/60	1024/100	1024/120
5	32/12	32/12	128/48	512/108	5	2048/84	1024/72	1024/120	1024/144

	bishop on square				rook on square
	A	B	C	D		A	B	C	D
8	9.14	5.33	3.20	2.67	8	83.59	48.76	29.26	24.38
7	5.33	5.33	3.20	2.67	7	48.76	28.44	17.07	14.22
6	3.20	3.20	3.20	2.67	6	29.26	17.07	10.24	8.53
5	2.67	2.67	2.67	4.74	5	24.38	14.22	8.53	7.11

The idea to implement minimal perfect hashing by an additional 16-bit indirection turned out to be slower (see conditional compiles in Pradu Kannan's source ^[9] ).

Recent table sizes were about 38 KiB for the bishop attacks, but still about 800 KiB for rook attacks (Fancy). That sounds huge, considering L1 and L2 (L3) cache-sizes and number of cachelines and pages needed - we likely fetch distinct cachelines for each different square or occupancy. On the other hand caches and pages become larger in future processors. And occupancy and squares of the lookups don't change that randomly inside a search that we can still expect a lot of L1-hits. Unfortunately changes in occupancy outside the blockers and therefor not affecting the attack-set will introduce some more cache misses.

Wishing Dreams

Since there are 1428/4900 distinct attack sets for the bishop/rook attacks, we can use 11(2048 > 1428)/13(8196 > 4900) index bits for all bishop/rook attack bitboards. The table size will be 16KB for the bishop attacks and 64KB for rook attacks. To make it possible, we must find a group of magics (one per square and dependent each other). All the magics in the group must hash its all relevant occupancies into the same 11/13 bit index without any collision with others (anyhow for each square, different occupancies can hash to the same attack sets).

U64 bishopAttacks[2048]; // 16KB
U64 rookAttacks[8196]; // 64KB
 
struct GMagic {
   U64 mask;  // to mask relevant squares of both lines (no outer squares) and include sliding piece itself
   U64 magic; // magic 64-bit factor
};
 
GMagic mBishopTbl[64]; //1KB
GMagic mRookTbl[64]; //1KB
 
U64 bishopAttacks(U64 occ, enumSquare sq) {
   occ &= mBishopTbl[sq].mask;
   occ *= mBishopTbl[sq].magic;
   occ >>= 64-11;  //fixed shift
   return bishopAttacks[occ]; //no offset
}
 
U64 rookAttacks(U64 occ, enumSquare sq) {
   occ &= mRookTbl[sq].mask;
   occ *= mRookTbl[sq].magic;
   occ >>= 64-13;
   return rookAttacks[occ];
}

But the idea seems like a wishing dream. Can we find ONE of the magic group of magics? Does it exist in theory? If not, can we use more bits to reach the condition? If yes, can we find a good magic group? A good magic group means that all the hash value <=n, so we can reduce the table size to n, until it reach to 1428/4900. Enough? If all hash values are grouped by square, can we think about using the Sharing Attacks method?

Implementations

Despite its huge table size, register usage and code size are important issues as well - and here Magic Bitboards are unbeatable. There are enough variations of space-time tradeoff and implementation details of that theme for all who like to play the optimization game. C-source code with various precompiler options is available from Pradu Kannan's site. MINIMIZE_MAGIC is about Plain versus Fancy ^[10] , while PERFECT_MAGIC_HASH enables an additional indirection via 16-bit indices. As always, with space-time tradeoffs - it depends on the individual cache- and memory footprint inside a particular chess program and the hardware architecture, which solution is preferable.

Fancy

Fancy Magic Bitboards is the main stream implementation as proposed by Pradu Kannan with individual table sizes for each square. It requires an individual shift, to leave that many index bits remaining as determined by the population of relevant occupancies. As mentioned, if one tries hard enough to maximize constructive collisions while looking for magics, one may half the size for several individual squares, see Best Magics so far.

U64 attack_table[...]; // ~840 KiB all rook and bishop attacks, less with constructive collisions optimization
 
struct SMagic {
   U64* ptr;  // pointer to attack_table for each particular square
   U64 mask;  // to mask relevant squares of both lines (no outer squares)
   U64 magic; // magic 64-bit factor
   int shift; // shift right
};
 
SMagic mBishopTbl[64];
SMagic mRookTbl[64];
 
U64 bishopAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mBishopTbl[sq].ptr;
   occ      &= mBishopTbl[sq].mask;
   occ      *= mBishopTbl[sq].magic;
   occ     >>= mBishopTbl[sq].shift;
   return aptr[occ];
}
 
U64 rookAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mRookTbl[sq].ptr;
   occ      &= mRookTbl[sq].mask;
   occ      *= mRookTbl[sq].magic;
   occ     >>= mRookTbl[sq].shift;
   return aptr[occ];
}

Plain

Plain Magic Bitboards, Lasse Hansen's initial approach, takes much more memory for homogeneous two-dimensional attack arrays. 32 KiB per rook square, 4 KiB for each bishop square. It does not need a variable shift and therefor needs one processor register less to further reduce register pressure, despite shorter code. Unfortunately, so far, there are two rook corner squares (0 and 7), which prohibit dividing the rook table size by two.

U64 mBishopAttacks[64] [512]; // 256 K
U64 mRookAttacks  [64][4096]; // 2048K
 
struct SMagic {
   U64 mask;  // to mask relevant squares of both lines (no outer squares)
   U64 magic; // magic 64-bit factor
};
 
SMagic mBishopTbl[64];
SMagic mRookTbl  [64];
 
U64 bishopAttacks(U64 occ, enumSquare sq) {
   occ &= mBishopTbl[sq].mask;
   occ *= mBishopTbl[sq].magic;
   occ >>= 64-9;
   return mBishopAttacks[sq][occ];
}

Fixed shift Fancy

A fancy fixed shift variation was introduced by Onno Garms, looking for magics producing factors with appropriate reduced value ranges. That is, leave 12 bit rook indices for all squares, but with upper bit(s) clear for all possible occupancies for all the squares with less than 12 relevant bits, so that it efficiently becomes a less 12 bit index. Onno believes that it is possible to find magic factors with that property for most of those squares, to come close to the fancy table size with the advantage of a fixed shift ^[11] . Even an "overlapping" of square arrays is feasible, if they contain accordant unused slot gaps on both ends. Volker Annuss came up with a fixed shift solution of only 800 KiB and below ^[12] ^[13], and more recently even innovated with Black Magic Bitboards.

U64 attack_table[...]; // > 800 KiB  - 1.x MiB  - depending on the effort on looking for magics
 
struct SMagic {
   U64* ptr;  // pointer to attack_table for each particular square
   U64 mask;  // to mask relevant squares of both lines (no outer squares)
   U64 magic; // magic 64-bit factor
};
 
SMagic mBishopTbl[64];
SMagic mRookTbl[64];
 
U64 rookAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mRookTbl[sq].ptr;
   occ      &= mRookTbl[sq].mask;
   occ      *= mRookTbl[sq].magic;
   occ     >>= 64-12;
   return aptr[occ];
}

Black Magic Bitboards

Volker Annuss' most recent innovation and further improvement of his already dense 700 KiB fixed shift fancy reference implementation is called Black Magic Bitboards, introduced in CCC in August 2017 ^[14]. Instead of intersection with a mask to clear the not relevant occupancy bits, he used the union with the complement of mask to set all not relevant occupancy bits.

  and mask[d4]  vs.   or ~mask[d4]
. . . . . . . .     1 1 1 1 1 1 1 1
. . . 1 . . . .     1 1 1 . 1 1 1 1
. . . 1 . . . .     1 1 1 . 1 1 1 1
. . . 1 . . . .     1 1 1 . 1 1 1 1
. 1 1 . 1 1 1 .     1 . . 1 . . . 1
. . . 1 . . . .     1 1 1 . 1 1 1 1
. . . 1 . . . .     1 1 1 . 1 1 1 1
. . . . . . . .     1 1 1 1 1 1 1 1

This trick, which basically adds a huge constant to the occupancy factor, enables to find Black Magics yielding in even smaller array sizes per square, determined by maximum and minimum index - the latter no longer zero for the empty occupancy! Unfortunately so far, the individual savings with denser square arrays don't completely advance to the size of the combined overlapping table, since overlapping became harder due to smaller gaps ^[15] . However, 692 KiB for the complete rook and bishop attack table is the new fixed shift reference. Black Magic Bitboards are now used in Volker's engine Arminius ^[16] ^[17]:

U64 attack_table[88507]; // 692 KiB for published black magics by Volker Annuss (new size 88316 aka 690 KiB) 
 
struct SBlackMagic {
   U64* ptr;  // pointer to attack_table for each particular square
   U64 notmask;  // to mask relevant squares of both lines (no outer squares)
   U64 blackmagic; // black magic 64-bit factor
};
 
SBlackMagic mBishopTbl[64];
SBlackMagic mRookTbl[64];
 
U64 rookAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mRookTbl[sq].ptr;
   occ      |= mRookTbl[sq].notmask;
   occ      *= mRookTbl[sq].blackmagic;
   occ     >>= 64-12;
   return aptr[occ];
}

Byte Lookup

Since there are only up to 144 different attack sets per square, Robert Houdart proposed to lookup bytes by square and hashed occupancy for a minimal perfect hashing with an additional indirection via an offset per square, which is successfully used in his engine Houdini ^[18] . Following sample code uses the Plain fixed shift method, while it may also applied for the dense Fancy one.

byte mBishopAttacks[64] [512]; // 32 K
byte mRookAttacks  [64][4096]; // 256 K
 
U64 mRookLookup[4900];  // 39 K
U64 mBishopLookup[1428];  // 11 K
 
struct SMagic {
   U64 mask;  // to mask relevant squares of both lines (no outer squares)
   U64 magic; // magic 64-bit factor
   int offset;   // offset into lookup table
};
 
SMagic mBishopTbl[64];
SMagic mRookTbl  [64];
 
U64 bishopAttacks(U64 occ, enumSquare sq) {
   occ &= mBishopTbl[sq].mask;
   occ *= mBishopTbl[sq].magic;
   occ >>= 64-9;
   return mBishopLookup[mBishopTbl[sq].offset + mBishopAttack[sq][occ]];
}

32-bit Magics

Optimizations are possible for 32-bit systems, as proposed by Grant Osborne ^[19] . Instead of letting the compiler split up a 64-bit multiply, two 32-bit multiplications can be manually implemented. Multiply the low bits of the magic with the low bits of the key and add it with the product of the high bits of the magic and the high bits of the key and use the upper bits of the sum to index the move database. For the bishops one may try only one 32-bit multiplication after xoring the masked high and low half.

struct {
  unsigned int rookMaskLo;
  unsigned int rookMaskHi;
  unsigned int rookMagicLo;
  unsigned int rookMagicHi;
  unsigned int rookShift;
  U64 *pRookAttacks;
} sm[64];
 
U64 rookAttacks(U64 occ, enumSquare sq) {
   unsigned int lo = (int) occ;
   unsigned int hi = (int)(occ >> 32);
   lo &= sm[sq].rookMaskLo;
   hi &= sm[sq].rookMaskHi;
   lo *= sm[sq].rookMagicLo;
   hi *= sm[sq].rookMagicHi;
   lo  = (lo ^ hi) >> sm[sq].rookShift;
   return sm[sq].pRookAttacks[lo];
}

Sharing Attacks

The development has not finished. Lasse Hansen came up with another stunning idea ^[20] , to use a final intersection by attacks on an empty board, to share tables by two (rooks) or even four (bishops) squares. Bishop sharing is simple to understand, since there are light and dark colored bishops with disjoint attacks-sets, able to share the pre-calculated union of two square-attacks.

The trick is to share even equal colored bishops and rooks where both attack-sets are not disjoint - but all members of the intersection are always set, since they are direct neighbors of both sliders. This is how rooks and bishops may share union-attack-sets by two resp. four squares:

int rookSharing[64] = {
   0,  1,  2,  3,  4,  5,  6,  7,
   1,  0,  3,  2,  5,  4,  7,  6,
   8,  9, 10, 11, 12, 13, 14, 15,
   9,  8, 11, 10, 13, 12, 15, 14,
  16, 17, 18, 19, 20, 21, 22, 23,
  17, 16, 19, 18, 21, 20, 23, 22,
  24, 25, 26, 27, 28, 29, 30, 31,
  25, 24, 27, 26, 29, 28, 31, 30,
};
 
int bishopSharing[64] = {
   0,  2,  4,  4,  4,  4, 12, 14,
   0,  2,  5,  5,  5,  5, 12, 14,
   0,  2,  6,  6,  6,  6, 12, 14,
   0,  2,  7,  7,  7,  7, 12, 14,
   1,  3,  8,  8,  8,  8, 13, 15,
   1,  3,  9,  9,  9,  9, 13, 15,
   1,  3, 10, 10, 10, 10, 13, 15,
   1,  3, 11, 11, 11, 11, 13, 15,
};

On the cost of one additional and-instruction, post-masking has the potential to almost halve the rook tables - and even better for the already small bishop tables. Additionally, four union attack bitboards can be shared by eight rook- and six bishop-squares.

R 1 1 1 1 1 1 1    1 R 1 1 1 1 1 1    1 1 R 1 1 1 1 1    1 1 1 R 1 1 1 1
B R 1 1 1 1 1 1    R B 1 1 1 1 1 1    1 1 B R 1 1 1 1    1 1 R B 1 1 1 1
1 1 1 . . . . .    1 1 1 . . . . .    . 1 1 1 1 . . .    . . 1 1 1 . . .
1 1 1 1 . . . 1    1 1 . 1 . . . .    1 . 1 1 1 1 . .    . 1 1 1 . 1 . .
1 1 . 1 1 . 1 .    1 1 . . 1 . . .    . . 1 1 . 1 1 .    1 . 1 1 . . 1 .
1 1 . . 1 B . .    1 1 . . . 1 . .    . . 1 1 . . 1 B    . . 1 1 . . . 1
1 1 . . 1 1 1 .    1 1 . . . . 1 .    . . 1 1 . . 1 1    . . 1 1 . . . .
1 1 . 1 . . 1 1    1 1 . . . . . 1    . . 1 1 . 1 . .    . . 1 1 . . . .

If the additional post-mask becomes member of a structure, it exceeds 32 byte in 64-bit mode. A structure of arrays may be preferable than an array of structures.

U64 attack_table[...]; // ~400K Byte for all rook and (shared) bishop attacks
 
struct SMagic {
   U64* ptr;      // pointer to attack_table for each particular square
   U64 magic;     // magic 64-bit factor
   U64 premask;   // to mask relevant squares of both lines (no outer squares)
   U64 postmask;  // attacks on the otherwise empty board
   int shift;     // shift right
};
 
SMagic mBishopTbl[64];
SMagic mRookTbl[64];
 
U64 bishopAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mBishopTbl[sq].ptr;
   occ      &= mBishopTbl[sq].premask;
   occ      *= mBishopTbl[sq].magic;
   occ     >>= mBishopTbl[sq].shift;
   return      mBishopTbl[sq].postmask & aptr[occ];
}
 
U64 rookAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mRookTbl[sq].ptr;
   occ      &= mRookTbl[sq].premask;
   occ      *= mRookTbl[sq].magic;
   occ     >>= mRookTbl[sq].shift;
   return      mRookTbl[sq].postmask & aptr[occ];
}

Incorporating the Shift

Another possible improvement was introduced by Grant Osborne ^[21] - to don't store the variable right shift inside an own array or structure element, but to use the almost redundant upper six bit of the magic factor instead - incorporating the shift into the magic number. While using a structure for pre-, postmask, magic and pointer, it's size is 4*8 = 32-byte or - if properly aligned - the half of one cache line. The additional effort for the right shift 58 to extract the variable shift is likely hidden by the latency of the independent multiplication, improving ipc.

U64 attack_table[...]; // ~400K Byte for all rook and (shared) bishop attacks
 
struct SMagic {
   U64* ptr;      // pointer to attack_table for each particular square
   U64 magic;     // magic 64-bit factor, including upper six bits as shift amount
   U64 premask;   // to mask relevant squares of both lines (no outer squares)
   U64 postmask;  // attacks on the otherwise empty board
}; // 32 Byte with 64-bit pointer!
 
SMagic mBishopTbl[64];
SMagic mRookTbl[64];
 
U64 bishopAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mBishopTbl[sq].ptr;
   int shift = mBishopTbl[sq].magic >> 58;
   occ      &= mBishopTbl[sq].premask;
   occ      *= mBishopTbl[sq].magic;
   return      mBishopTbl[sq].postmask & aptr[occ >> shift];
}
 
U64 rookAttacks(U64 occ, enumSquare sq) {
   U64* aptr = mRookTbl[sq].ptr;
   int shift = mRookTbl[sq].magic >> 58;
   occ      &= mRookTbl[sq].premask;
   occ      *= mRookTbl[sq].magic;
   return      mRookTbl[sq].postmask & aptr[occ >> shift];
}

Incorporating Offset

A similar idea as in Incorporating the Shift in the domain fixed shift magics was proposed by Eugene Kotlov concerning the indirection to the stored attack array, using the 16 lower bits of the magic factor as offset ^[22].

Initalization

Looking for Magics

The main issue is to find 64 magic factors for each rook and bishop square, to ensure they are free of collisions.

Looking for Magics

Magic Records

You may try to find your own magics - to possibly contribute to the record table for most dense fancy or plain tables. So far, there were no magics found for the expensive rook squares a1 and h1 (0, 7) with less than 12 bits, which would allow to half the plain table size. Is there any prove they don't exist - even with Black Magic?

Best Magics so far

Publications

Pradu Kannan (2007). Magic Move-Bitboard Generation in Computer Chess, as pdf
Fritz Reul (2009). New Architectures in Computer Chess, Ph.D. Thesis, Chapter 3, Magic Hash Functions for Bitboards, pdf
Maurizio Monge (2011). On perfect hashing of numbers with sparse digit representation via multiplication by a constant. Discrete Applied Mathematics, Vol. 159, No. 11

Forum Posts

2006

Fast(er) bitboard move generator by Lasse Hansen, Winboard Forum, June 14, 2006
List of magics for bitboard move generation by Pradu Kannan, Winboard Forum, August 23, 2006
Fastest Magic Move Bitboard Generator ready to use by Pradu Kannan, Winboard Forum, August 25, 2006
A Faster Magic Move Bitboard Generator? by Grant Osborne, Winboard Forum, December 15, 2006

2007

SEE with magic bitboards by Pradu Kannan, Winboard Forum, January 24, 2007 » Static Exchange Evaluation
Magic bitboards, Java by Sargon, CCC, August 19, 2007 » Java
BitBoard Tests Magic v Non-Rotated 32 Bits v 64 Bits by Brian Richardson, CCC, August 24, 2007 ^[23]
Magic and precomputation by Onno Garms, Winboard Forum, September 23, 2007

2008

Magic Move Generation by Colin, CCC, February 18, 2008
How to reduce the "bits" used in a magic number by Charlie Brune, CCC, May 24, 2008
magic move - bitboard orientation by Frank Phillips, CCC, June 01, 2008
Incorporating the shift into the magic number by Grant Osborne, CCC, June 18, 2008

2009

Magics revisited by Richard Pijl, CCC, January 04, 2009
Magic with fixed shift by Onno Garms, Winboard Forum, March 18, 2009
Paradigm shifts by Gian-Carlo Pascutto, CCC, November 14, 2009
32-bit Magic experiments by Andrew Fan, Winboard Forum, December 03, 2009 » Kindergarten Bitboards

2010 ...

Plain and fancy magic on modern hardware by Robert Purves, CCC, August 22, 2010
Fixed shift magics with 800KB lookup table by Volker Annuss, Winboard Forum, September, 05, 2010
Build magics on the fly by Marco Costalba, CCC, June 07, 2011
Magic Multiplier Fundamentals by Cheney Nattress, CCC, January 03, 2013
Occupancy Variations by CDaley11, OpenChess Forum, January 25, 2013
Magic bitboards: Cache issues and state of the art? by Samuel Siltanen, CCC, March 22, 2013
Understanding Magic Bitboards by Jaco van Niekerk, Winboard Forum, April 03, 2013

2015 ...

question about magic keys generation time by Fermin Serrano, CCC, March 19, 2015 » Looking for Magics
Fancy magic bitboards question by Eric VanderHelm, CCC, September 22, 2015
M42 - A C++ library for Bitboard attack mask generation by Syed Fahad, CCC, April 30, 2016 ^[24]
understanding fixed shift fancy magic bitboard generation by Kalyankumar Ramaseshan, CCC, May 05, 2016
Re: understanding fixed shift fancy magic bitboard generation by Volker Annuss, CCC, May 06, 2016
Why should magic bitboards be sparse? by Alessandro Power, CCC, December 21, 2016
Looking for dense magics by Lucas Braesch, CCC, July 11, 2017
Black magic bitboards by Volker Annuss, CCC, August 03, 2017 » Black Magic Bitboards
Disproving the existence of some magics by Niklas Fiekas, CCC, September 16, 2017 » Looking for Magics
magic number comprising offset by Eugene Kotlov, CCC, February 07, 2018
No bishop magics with fixed shift 8 by Niklas Fiekas, CCC, April 09, 2018 » Looking for Magics

External Links

Buzz - A Winboard Chess Playing Program by Pradu Kannan - Source of Pradu Kannan's magic Move Generator
Rival Chess Engine - Magic Bitboards by Russell Newman and Chris Moreton » Rival
Chess Programming | Generating Magic Multipliers by Steve Maughan » Looking for Magics
chess - Sliding move generation using magic bitboard - Stack Overflow, June 4, 2013
M42 by Syed Fahad ^[25]
GitHub - goutham/magic-bits: Magic-bitboards for Chess by Goutham Bhat

Other Magic Stuff

Magic from Wikipedia
Magic (illusion) from Wikipedia
Magic (paranormal) from Wikipedia
Magic (cryptography) from Wikipedia
Magic number from Wikipedia
Magic constant from Wikipedia
Magic square from Wikipedia
Magic hypercube from Wikipedia
Five Senses - Magic Constant, Christmas Jazz Festival, Tallinn, December 10, 2011, YouTube Video
line-up: Nguyên Lê, Claudio Puntin, Steffen Schorn, Kristjan Randalu, Bodek Janke
Youn Sun Nah - Momento Magico (2013), YouTube Video
Youn Sun Nah, Ulf Wakenius, Lars Danielsson, Vincent Peirani

References

^ Re: BitBoard Tests Magic v Non-Rotated 32 Bits v 64 Bits by Robert Hyatt, CCC, August 25, 2007
^ Arasan Blog - Aug 26, 2008 by Jon Dart
^ Major Works from Samuel Bak - represented by Pucker Gallery since 1969
^ rotated bitboards obsolete? by Gerd Isenberg, CCC, February 26, 2006
^ Fast(er) bitboard move generator by Lasse Hansen, Winboard Forum, June 14, 2006, Initial idea
^ Pradu Kannan (2007). Magic Move-Bitboard Generation in Computer Chess, as pdf
^ List of magics for bitboard move generation by Pradu Kannan, Winboard Forum, August 23, 2006
^ Plain and fancy magic on modern hardware by Robert Purves, CCC, August 22, 2010
^ Buzz - A Winboard Chess Playing Program by Pradu Kannan - Source of Pradu Kannan's magic Move Generator, PERFECT_MAGIC_HASH
^ Buzz - A Winboard Chess Playing Program by Pradu Kannan - Source of Pradu Kannan's magic Move Generator, MINIMIZE_MAGIC
^ Magic with fixed shift by Onno Garms, Winboard Forum, March 18, 2009
^ Fixed shift magics with 800KB lookup table by Volker Annuss, Winboard Forum, September, 05, 2010
^ Re: understanding fixed shift fancy magic bitboard generation by Volker Annuss, CCC, May 06, 2016
^ Black magic bitboards by Volker Annuss, CCC, August 03, 2017
^ Re: Black magic bitboards by Volker Annuss, CCC, August 04, 2017
^ Re: Black magic bitboards by Volker Annuss, CCC, August 04, 2017
^ source code according to the fixed shift fancy sample - array size from Volker's posting, also containing black magics and arrayoffsets, see Black magic bitboards by Volker Annuss, CCC, August 03, 2017
^ Re: Plain and fancy magic on modern hardware by Robert Houdart, CCC, August 26, 2010
^ A Faster Magic Move Bitboard Generator? by Grant Osborne, Winboard Forum, December 15, 2006
^ Lasse Hansen's postmask trick, Winboard Forum, May 09, 2008
^ Incorporating the shift into the magic number by Grant Osborne, CCC, June 18, 2008
^ magic number comprising offset by Eugene Kotlov, CCC, February 07, 2018
^ Movegen Re: Bitmap Type Re: Tinker 81 secs Re: Testing speed by Brian Richardson, CCC, April 24, 2000
^ M42 by Syed Fahad
^ M42 - A C++ library for Bitboard attack mask generation by Syed Fahad, CCC, April 30, 2016

What links here?

Page	Date Edited
Abbess	Jun 10, 2017
Abulafia	Oct 4, 2017
Alberto Sanjuan	Nov 3, 2014
AMD	Mar 9, 2018
Andreas Guettinger	Aug 14, 2013
Andrew Fan	Jul 30, 2017
Andscacs	Jan 16, 2018
Arasan	Apr 8, 2018
Arminius	Aug 5, 2017
Array	Dec 1, 2016
Atlas (ESP)	Jan 28, 2018
Backtracking	Dec 16, 2017
Barbarossa	Dec 20, 2016
BBChess (SI)	Jan 12, 2015
Best Magics so far	Apr 13, 2018
Bitboard Serialization	Dec 24, 2014
Bitboards	Nov 14, 2017
BMI2	Mar 6, 2018
Bobcat	Jun 27, 2017
Brutus NL	Aug 22, 2016
Buzz	Jun 22, 2016
Carballo	Oct 2, 2016
Cheese	Feb 17, 2018
Cheng	Jul 30, 2017
chess22k	Apr 23, 2018
chess4j	Jan 1, 2018
Chiron	Sep 24, 2017
Clarabit	Nov 3, 2011
Congruent Modulo Bitboards	Jun 26, 2013
Counter	Nov 13, 2017
Crafty	Jan 28, 2018
CuckooChess	Jan 17, 2017
Defenchess	Mar 18, 2018
Demolito	Mar 1, 2018
DiscoCheck	Jun 23, 2017
Djinn	Feb 8, 2016
Don Dailey	Dec 7, 2016
Donna	Aug 17, 2017
Edsel Apostol	Nov 2, 2016
Efficient Generation of Sliding Piece Attacks	Nov 5, 2016
Eric Marathée	Dec 27, 2014
Ethereal	Mar 20, 2018
Exacto	Oct 3, 2015
Fire	Oct 12, 2017
Firefly	Oct 23, 2017
Fridolin	Jun 27, 2017
Galjoen	Mar 19, 2018
Garbochess	Sep 23, 2017
General Setwise Operations	Feb 25, 2018
Gerd Isenberg	Apr 4, 2016
Gibbon	Dec 23, 2014
Ginkgo	Jul 13, 2016
Giraffe	Jan 8, 2018
Glaurung	Mar 14, 2017
Godot	Apr 28, 2015
Gogobello	Jul 30, 2017
GopherCheck	Feb 3, 2017
Grant Osborne	Dec 2, 2011
Greko	Feb 27, 2018
GullChess	Jun 27, 2017
Hakkapeliitta	Apr 26, 2016
Hash Table	Jan 1, 2018
Hashing Dictionaries	Mar 1, 2014
Hedgehog	Feb 18, 2018
Hermann	Dec 7, 2017
Hiding the Implementation	Feb 3, 2011
Home	Jul 2, 2018
Houdini	Apr 14, 2018
iCE	Jan 4, 2016
Ifrit	Feb 7, 2016
Java	Feb 25, 2018
JFresh	Mar 2, 2016
Kholin	Jan 3, 2018
Kindergarten Bitboards	Aug 1, 2017
Laser	Dec 27, 2017
Lasse Hansen	Sep 1, 2015
Looking for Magics	Apr 13, 2018
Loop (Program)	Mar 14, 2017
Magic Bitboards	Apr 13, 2018
Marco Costalba	Feb 28, 2018
Mark Levene	Jun 2, 2015
Marvin	Feb 10, 2018
Maurizio Monge	Nov 27, 2015
Maverick	Jan 7, 2016
MinkoChess	Sep 5, 2013
Move Generation	Jan 29, 2018
Murka	Nov 11, 2016
Napoleon	Jun 25, 2017
Nemorino	Dec 21, 2017
NoraGrace	Nov 23, 2014
Occupancy	Sep 19, 2016
Octochess	Aug 15, 2017
Onno	Jul 19, 2013
Onno Garms	Jul 19, 2013
Orion	Oct 15, 2017
Paladin	Jan 29, 2017
Pawn Hash Table	Feb 1, 2018
Pawny	Jun 17, 2015
Pedone	Jan 16, 2018
Pradu Kannan	Aug 3, 2015
Prophet	Sep 30, 2017
Protector	Oct 12, 2017
RedQueen	Nov 13, 2017
Rhetoric	Nov 15, 2017
Rival	Jul 30, 2017
Robert Houdart	Dec 8, 2017
Robert Hyatt	Dec 25, 2017
Robert Pope	Jun 10, 2017
Robocide	May 11, 2016
Rodent	Jan 11, 2018
Rodin	Feb 7, 2016
RuyDos	Feb 17, 2018
Rybka	Mar 27, 2017
Schooner	Feb 2, 2018
Scorpio	Mar 28, 2018
Searcher	Sep 26, 2016
SEE - The Swap Algorithm	Jun 5, 2017
Senpai	Nov 10, 2017
Shield	May 17, 2017
Sliding Piece Attacks	May 27, 2016
Sloppy	Sep 17, 2016
SmarThink	Feb 2, 2018
SnailChess	Nov 26, 2014
Space-Time Tradeoff	Jun 17, 2015
Static Exchange Evaluation	Dec 14, 2017
Stockfish	Apr 7, 2018
Syed Fahad	Jan 1, 2017
Takuya Obata	Jan 7, 2017
Texel	Oct 9, 2017
Tim Kosse	May 23, 2013
Tinker	Aug 29, 2015
Titboards	Feb 20, 2013
Tornado	Dec 14, 2017
Traversing Subsets of a Set	Oct 14, 2016
Trevor Fenner	Jun 2, 2015
Trial and Error	Feb 11, 2018
Tucano	Dec 16, 2017
Tunguska	Sep 16, 2017
Vadim Demichev	Jul 26, 2013
Vajolet	Jan 25, 2018
Volker Annuss	Aug 3, 2017
Wing	Oct 26, 2017
Winglet	Apr 26, 2015
Winter	Jan 23, 2018
WyldChess	Mar 10, 2018
Xiphos	Apr 22, 2018
Zevra	Mar 12, 2018
Ziggurat	Oct 9, 2017
Zurichess	Mar 12, 2018

Up one Level

Middlegame

GerdIsenberg — Tue, 06 Sep 2016 13:43:09 GMT

Home * Evaluation * Game Phases * Middlegame

		The Middlegame is the game phase which happens after the opening, where the game of chess literally starts after developing most minor pieces and to prepare or already achieve castling. Quite often due to (double) pushes of the center pawns, the basic pawn structure is often already determined during the first moves, sometimes with center rams involved, already defining which bishop is good or bad.
Samuel Bak - Study for Middle Game, 1990 ^[1]

Opening versus Middlegame

Opening versus Middlegame

The early middlegame does not necessarily imply a reduction of material by trading pawns or pieces. On the other hand, early pawn trades or other captures don't necessarily imply the beginning of middlegame as long as other aims of the opening are not achieved. Tapered eval for a smooth transition between game phases by multiple piece-square tables does usually not distinguish between opening and early middlegame with all or most material still on the board. Therefor some programmers apply special opening knowledge inside their evaluation to avoid too early queen activity or moving developed pieces multiple times while other minor pieces are still on their home square and have not moved yet (considering returning bishop). Other programs purely rely on the opening book and don't care to differentiate between these early phases.

Evaluation

Beside material, mobility and pawn structure considerations, king safety is the most important evaluation term in the middlegame.

Publications

Albrecht Heeffer (1984). Automated Acquisition on Concepts for the Description of Middle-game Positions in Chess. Turing Institute, Glasgow, Scotland, TIRM-84-005
Alex van Tiggelen (1991). Neural Networks as a Guide to Optimization - The Chess Middle Game Explored. ICCA Journal, Vol. 14, No. 3
Miroslav Kubat, Jan Žižka (2000). Learning Middle Game Patterns in Chess: A Case Study. Lecture Notes in Computer Science, Vol. 1821, Springer

External Links

References

^ The Game of War from Samuel Bak - represented by Pucker Gallery since 1969

What links here?

Page	Date Edited
Albrecht Heeffer	Sep 6, 2016
Alexs	Dec 7, 2017
Andscacs	Jan 16, 2018
Attack and Defend Maps	Nov 5, 2016
Battery	Jan 29, 2017
Bismark	Apr 22, 2015
Bison	Sep 29, 2016
CHEKMO-II	Jan 3, 2018
chess22k	Apr 23, 2018
Dartmouth CP	Jan 19, 2018
DayDreamer	Aug 22, 2016
Deep Learning	Feb 12, 2018
Diep	Jan 28, 2018
Djinn	Feb 8, 2016
Double Null Move	May 8, 2015
Endgame	Sep 18, 2017
Eval Tuning in Deep Thought	Jun 7, 2016
Evaluation	Feb 1, 2018
Evaluation of Pieces	Jan 8, 2018
Fortress	Feb 1, 2018
Game Phases	May 22, 2017
Genie	Feb 7, 2016
Gibbon	Dec 23, 2014
Grok	Aug 14, 2011
J. Biit	Jan 17, 2017
King Centralization	Oct 30, 2017
King Pattern	Nov 15, 2013
MadChess	Jul 4, 2017
MChess	Feb 26, 2018
Mephisto Roma	Sep 1, 2017
Middlegame	Sep 6, 2016
Morphy	Dec 25, 2017
Mr. Turk	Feb 21, 2015
Much	Jun 7, 2016
Myopic	Nov 11, 2016
N.N.	Jan 20, 2018
Neural Networks	Mar 12, 2018
NG-play	Feb 26, 2017
Nullmover	Jul 21, 2013
Opening	Jun 25, 2017
Oracle	Sep 4, 2016
Paradise	Nov 19, 2014
Pawn chain	Jan 17, 2018
Phalanx	May 2, 2016
Pin	Mar 7, 2017
ProbCut	Mar 25, 2016
Rachelle Heller	Jun 26, 2017
RedQueen	Nov 13, 2017
Samiel	Oct 6, 2014
Santos Gerardo Lazzeri	Mar 19, 2016
Schach	Jan 7, 2016
Scidlet	May 31, 2014
Sierżant	Apr 15, 2014
Simona Tancig	Nov 7, 2012
Soldat	Aug 20, 2017
Square Control	Sep 15, 2016
Steinitz	Nov 10, 2014
Stockfish	Apr 7, 2018
SuperChess	Dec 7, 2016
Superpawn	Mar 9, 2015
Tactics	Jan 12, 2018
Tarrasch Rule	Jun 2, 2014
The King	Jan 21, 2018
Thor's Hammer	Nov 23, 2013
Transposition	Jun 8, 2015
Tunguska	Sep 16, 2017
Turning Point	Apr 6, 2012
Wing	Oct 26, 2017
Winglet	Apr 26, 2015
Zugzwang	Dec 8, 2017
Zurichess	Mar 12, 2018

Up one level

Mobility

GerdIsenberg — Wed, 17 Jan 2018 18:54:07 GMT

Home * Evaluation * Mobility

		Mobility, a measure of the number of choices (legal moves) a player has in a given position. It is often used as a term in the evaluation function of chess programs. It is based on the idea that the more choices you have at your disposal, the stronger your position. A study by Eliot Slater of 350 tournament games in which the material balance was still even after the 20th move showed a definite correlation between a player's mobility and the number of games won ^[1] .
Samual Bak, Quite Clear ^[2] ^[3]

Calculating Mobility

In computer programs, mobility is sometimes calculated differently than simply by summing up the number of legal or pseudo-legal moves. Often, it is done piece-by-piece, and the mobility bonus per possible move is not always the same for each type of piece (e.g., in the opening, the mobility of the bishops and knights is more important than that of the rooks). Sometimes forward mobility is scored higher than backward mobility, sometimes (in case of rooks) vertical mobility gets priority over horizontal mobility. Also, if a piece can move to the square of another friendly piece, sometimes that move is also counted - although it would not be a legal move, it is protecting the friendly piece, and therefore still serves a useful role.

Safe Mobility

A couple of programs evaluates so-called safe mobility - counting only squares where a piece can move without being En prise. This might be quite expensive, unless a program already keeps incrementally updated attack tables. In some cases, most notably in case of a knight, a middle-of-the-ground approach, not counting squares controlled by enemy pawns, seems best.

Papa's Entropy

Notes by Tony Marsland on The World Computer-Chess Championship by Hayes and Levy ^[4] ^[5] ^[6] :

Freedom and Papa both use mobility as their primary term in their evaluation functions. As with Wita, both use the ratio of computer's moves / opponent moves. Papa and Wita also multiply by the ratio of the squares controlled and Papa goes one step further and takes the logarithm of this product to form the "entropy" of the position. The true merit of this entropy over the product ratio was not made clear, but it does ensure that in extreme situations the evaluation remains more closely bounded.

The Value of Reaching a Square

Dan Heisman ^[7] represents an attempt at mathematical abstraction applied to chess, introducing seven concepts as fundamental in analyzing a chess position: mobility, flexibility, vulnerability, center control, piece coordination, time and speed. Heisman applies two dichotomies: actual versus potential and local versus global:

	*local*	*global*
*actual*	Single moves from this position	All reachable squares from this position
*potential*	Single moves on an empty board	All reachable squares on an empty board

Distance as generalization of mobility and unification of Heisman's notions was introduced by Robert Levinson and Richard Snyder in the famous 1993 ICCA Journal, Vol. 16, No. 3 ^[8] . Abstract and excerpt:

This article suggests a new approach to computer chess. A graph-theoretic representation of chess knowledge, uniformly based on a single mathematical abstraction, DISTANCE, is described. Most of the traditional forms of chess knowledge, it is shown, can be formalized in this new representation. In addition to comparing this approach to others, the article gives some experimental results and suggests how the new representation may be unified with existing approaches.

The DISTANCE idea is based on exploring a piece's mobility graph to determine what is close to and what is close to it. From a DISTANCE standpoint, moves on the chess-board are only considered good if they result in improved movement graphs for the mover's pieces and/or inferior ones for the opponent's pieces. Often, a good chess-player will move a piece, not to improve the attacking chances of that piece but rather the attacking chances of the piece behind it.

Mobility with Bitboards

For programs using Bitboards, piece mobility can be calculated very quickly either by Population Count or a SIMD-wise kind of weighted population count. Similar to Attacks by Occupancy Lookup to determine attack sets of sliding pieces, one may use pre-calculated population count or even center-weighted population count as a rough estimate on piece mobility. However it does not consider subsets of let say safe target squares. Most strong chess programs use a mobility calculation as part of the positional evaluation in some way. This approach is taken to the extremes in case of OliThink - a chess engine whose evaluation consists entirely of material balance and mobility.

Progressive Mobility

Fill approaches, like Dumb7Fill or Kogge-Stone algorithm are great to determine target sets one may reach in two or more moves, which population or weighted population might be considered as progressive mobility in some kind of positions ^[9] . Another application in late endings is to determine whether a piece may control a decisive stop or telestop of a passed pawn in time. Path finding algorithms for various pieces may be applied to find so called Trajectories ^[10] ^[11] .

Quotes

Alan Turing

Quote by Alan Turing on Slater's 1950 paper Statistics for the Chess Computer and the Factor of Mobility. ^[12]:

I wish to make two points concerning Dr. Slater's paper. I was greatly interested by the statistics provided, but fear that some people might draw invalid conclusions from them. It might for instance be thought that a good way of playing is to maximize one's mobility at one's next move, or perhaps to minimize that of one's opponent at his next move but one. It is evidently not feasible to foresee mobilities many moves ahead. Although the immediate mobility is a useful measure of the relative advantage of the players in normal play it by no means follows that it is wise to direct one's play to maximizing such a measure. To do so would be like taking a statistical analysis of the laundry of men in various positions and deciding, from the data collected, that an infallible method of getting ahead in life was to send a large number of shirts to the wash each week.

Eliot Slater

Eliot Slater in reply ^[13] :

Dr. Turing's argument by analogy what a naive laundry worker might conclude about ways of becoming rich really amounts to the suggestion that strategic advantage is the cause rather than the product of an advantage in mobility. I do not think that this can be accepted. An advantage in mobility usually appears in a game a number of moves before strategic advantage is detectable in other ways; it seems to be an essential aspect of what chess-players understand by "development"; and it supplies the decisive criterion of winning or losing.

Publications

1949 ...

Claude Shannon (1949). Programming a Computer for Playing Chess. pdf from The Computer History Museum
Eliot Slater (1950). Statistics for the Chess Computer and the Factor of Mobility. Proceedings of the Symposium on Information Theory, London. Reprinted (1988) in Computer Chess Compendium, pp. 113-117. Including the transcript of a discussion with Alan Turing and Jack Good
Adriaan de Groot (1965, 1978). Thought and Choice in Chess. Mouton & Co Publishers, The Hague, The Netherlands. amazon, google ^[14]

1980 ...

Dap Hartmann (1987). How to Extract Relevant Knowledge from Grandmaster Games. Part 2: the Notion of Mobility, and the Work of De Groot and Slater. ICCA Journal, Vol. 10, No. 2
Jan Eric Larsson (1987). Challenging that Mobility is Fundamental. ICCA Journal, Vol. 10, No. 3

1990 ...

Dan Heisman (1990, 1999, 2010, 2015).The Positional Elements of Chess. Russell Enterprises
Chrilly Donninger (1992). The Relation of Mobility, Strategy and the Mean Dead Rabbit in Chess. Heuristic Programming in AI 3
Robert Levinson, Richard Snyder (1993). Distance: Toward the Unification of Chess Knowledge. ICCA Journal, Vol. 16, No. 3
Jonathan Allen, Edward Hamilton, Robert Levinson (1997). New Advances in Adaptive Pattern-Oriented Chess. Advances in Computer Chess 8

2000 ...

Mark Levene, Trevor Fenner (2001). The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values. Artificial Intelligence, Vol. 130, No. 1, Review in ICGA Journal, Vol. 24, No. 4, pdf
John L. Jerz (2008, 2013). A Proposed Heuristic for a Computer Chess Program.

Forum Posts

1993 ...

deriving piece values from mobility by Barney Pell, rgc, August 09, 1993
Mobility Measure: Proposed Algorithm by Dietrich Kappe, rgc, September 23, 1993

1995 ...

Playing for position (mobility) by S.Read, rgcc, September 29, 1995
Re: Playing for position (mobility) by Peter Mysliwietz, rgcc, October 02, 1995 » Mobility in Zugzwang
Re: Incoporating chess knowledge in chess programs by Bruce Moreland, rgcc, June 28, 1996 » Search with Random Leaf Values
Mobility in evaluation functions- how much is it worth? by Tom King, rgcc, June 07, 1997
Mobility in eval by Willie Wood, CCC, November 24, 1997

2000 ...

Mobility in chess engines by Jean-François Gazet, rgcc, May 11, 2003
piece mobility? by Daniel Shawul, CCC, January 08, 2004
An idea: Offensive and defensive mobility by Tord Romstad, CCC, February 06, 2004

2005 ...

Mobility by David B. Weller, CCC, January 06, 2005
Mobility in Chess Evaluation Function at terminal-nodes by Stuart Cracraft, CCC, December 28, 2005
Re: CCC Retirement, Robert Hyatt on Mobility, CCC, January 16, 2006
Magic and precomputation by Onno Garms, Winboard Programming Forum, September 23, 2007
The limits of "Just-mobility-evaluation" by Oliver Brausch, CCC, January 29, 2008
Random number mobility scores by Guest, rgcc, September 20, 2008 » Search with Random Leaf Values
future mobility evaluation term by Stuart Cracraft, CCC, December 01, 2008

2010 ...

mobility evaluation of stockfish by Uri Blass, CCC, October 09, 2010
Attack and mobility evaluation in chess variants by Evert Glebbeek, CCC, February 15, 2011
Mobility eval by Harm Geert Muller, CCC, May 01, 2012
static mobility(Q&D) by Harm Geert Muller, CCC, March 13, 2013
Safe spatial mobility by Lyudmil Tsvetkov, CCC, August 04, 2013
Re: Engine results: a surprise! by Harm Geert Muller, CCC, October 18, 2013

2015 ...

mobility score by Colin Jenkins, CCC, May 15, 2015
Bishop Mobility ? by Henk van den Belt, CCC, August 31, 2016
Mobility Evaluation ? by Mahmoud Uthman, CCC, October 12, 2016
Safe mobility? by J. Wesley Cleveland, CCC, July, 18, 2017

External Links

Mobility from Wikipedia
Chess Strategy/Mobility - Wikibooks

References

^ Eliot Slater (1950). Statistics for the Chess Computer and the Factor of Mobility. Proceedings of the Symposium on Information Theory, London. Reprinted (1988) in Computer Chess Compendium, pp. 113-117. Including the transcript of a discussion with Alan Turing and Jack Good
^ The Game of War from Samuel Bak - represented by Pucker Gallery since 1969
^ The mountain in the background looks like Torghatten near Brønnøysund
^ Jean E. Hayes, David Levy (1976). The world computer chess championship, Stockholm 1974. University Press (Edinburgh) ISBN 0852242859
^ wita-awit#19-box2.pdf from Wita Notes by Tony Marsland
^ Entropy in thermodynamics and information theory from Wikipedia
^ Dan Heisman (1990, 1999, 2010, 2015).The Positional Elements of Chess. Russell Enterprises
^ Robert Levinson, Richard Snyder (1993). DISTANCE: Toward the Unification of Chess Knowledge. ICCA Journal, Vol. 16, No. 3
^ John L. Jerz (2008, 2013). A Proposed Heuristic for a Computer Chess Program.
^ Boris Stilman (1994). A Linguistic Geometry of the Chess Model. Advances in Computer Chess 7, pdf draft
^ Boris Stilman (2000). Linguistic Geometry - From Search to Construction (Operations Research/Computer Science Interfaces Series). amazon.com
^ Eliot Slater (1950). Statistics for the Chess Computer and the Factor of Mobility. Proceedings of the Symposium on Information Theory, London. Reprinted (1988) in Computer Chess Compendium, pp. 113-117. Including the transcript of a discussion with Alan Turing and Jack Good
^ Computer Chess Compendium, pp. 115-117. Discussion on Dr. E. Slater's paper
^ Quotes by Adriaan de Groot: "... one of the important characteristics of a chess position is the number of possibilities available, i.e., the player's freedom of choice", as mentioned in Dap Hartmann (1987). How to Extract Relevant Knowledge from Grandmaster Games. Part 2: the Notion of Mobility, and the Work of De Groot and Slater. ICCA Journal, Vol. 10, No. 2: "De Groot did not consider in-check positions, so imposing De Groot Mobility as a distinct norm"

What links here?

Page	Date Edited
Advances in Computer Chess 1	Oct 22, 2015
AI Chess	Jan 7, 2016
Amoeba	Mar 19, 2018
Amundsen	Sep 3, 2013
Amyan	Dec 10, 2013
Anaconda	Jul 4, 2015
Analog Evaluation	Oct 27, 2017
Andrea Zinno	May 19, 2017
Andscacs	Jan 16, 2018
Arasan	Apr 8, 2018
Assembly	Sep 3, 2017
Asymmetric evaluation	Nov 17, 2016
Atlas	Nov 5, 2017
Atlas (ESP)	Jan 28, 2018
Attack and Defend Maps	Nov 5, 2016
Bad bishop	Jun 22, 2015
Bebe	Dec 23, 2017
Belle	Jan 18, 2018
Berkeley Chess Microprocessor	May 22, 2013
Betsabe	Jul 23, 2017
BigLion	Sep 28, 2016
Bison	Sep 29, 2016
Blockade	Oct 19, 2017
Blockade of Stop	Oct 11, 2016
Bobcat	Jun 27, 2017
Bodo	Oct 6, 2016
Brainless	Jun 24, 2017
Brute Force (Program)	Sep 7, 2017
Capture (program)	Jan 8, 2016
Carballo	Oct 2, 2016
CDC Cyber	Dec 22, 2017
Center	Jun 21, 2016
Center Control	Jan 17, 2018
Charly	Jan 10, 2013
Cheese	Feb 17, 2018
Cheng	Jul 30, 2017
Cheops (Miller)	Jan 13, 2017
Chess 0.5	Nov 20, 2016
Chess Guru	Mar 4, 2017
chess22k	Apr 23, 2018
ChessBrainVB	Jun 24, 2017
ChessV	Jan 21, 2018
Chester	Feb 15, 2014
ChipTest	Jun 19, 2016
Chiron	Sep 24, 2017
Clarabit	Nov 3, 2011
Claudia	Jun 1, 2016
Coiled	Mar 12, 2017
Connectivity	Mar 6, 2016
CookieCat	Nov 15, 2016
Cumulus	Jan 7, 2016
Cupcake	May 19, 2016
Dan Heisman	Jun 12, 2013
DanaSah	Oct 9, 2017
Daniel Anulliero	Oct 3, 2017
Darmenios	Jan 7, 2016
Dartmouth CP	Jan 19, 2018
David B. Weller	Sep 13, 2015
DayDreamer	Aug 22, 2016
Defenchess	Mar 18, 2018
Demolito	Mar 1, 2018
Development	Jan 17, 2018
Diablo	May 17, 2016
Distance	Sep 25, 2015
Dolphin	Nov 28, 2014
Donna	Aug 17, 2017
Dorpsgek	Apr 2, 2018
Dumb7Fill	May 27, 2016
Échec	Jan 7, 2016
Edward Hamilton	Aug 25, 2016
Elephant	Sep 19, 2016
Eliot Slater	Aug 6, 2016
Ethereal	Mar 20, 2018
Evaluation	Feb 1, 2018
Evaluation of Pieces	Jan 8, 2018
Evaluation Overlap	Jul 19, 2016
Eveann	Apr 3, 2017
Evert Glebbeek	Sep 25, 2017
Fencer	Jan 20, 2013
Fill Algorithms	Nov 6, 2013
Fischer-Schneider	Nov 23, 2016
Freedom	Dec 28, 2017
Fridolin	Jun 27, 2017
Galjoen	Mar 19, 2018
Garbochess	Sep 23, 2017
Garbochess-JS	Sep 23, 2017
Gaviota	Jan 21, 2018
Genie	Feb 7, 2016
Gibbon	Dec 23, 2014
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Gk	Oct 9, 2017
Glass	May 24, 2017
GopherCheck	Feb 3, 2017
Greko	Feb 27, 2018
Gunnar Andersson	Jun 23, 2011
Hakkapeliitta	Apr 26, 2016
HAL	Jun 14, 2016
Half-open file	Mar 11, 2014
Harm Geert Muller	Mar 31, 2018
Houdini	Apr 14, 2018
Hydra 97	Jan 1, 2017
Ian Kennedy	Nov 7, 2016
Influence Quantity of Pieces	Jul 21, 2017
ISA	Apr 2, 2018
Isolated Pawn	Nov 18, 2012
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John L. Jerz	Jul 15, 2013
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Up one level

Null Move Pruning

GerdIsenberg — Sat, 02 Dec 2017 22:13:31 GMT

Home * Search * Selectivity * Pruning * Null Move Pruning

		Null Move Pruning, also called Null Move Heuristic (NMH), is a method based on the Null Move Observation to reduce the search space by trying a "null" or "passing" move, then seeing if the score of the subtree search is still high enough to cause a beta cutoff. Nodes are saved by reducing the depth of the subtree under the null move. The value of this depth reduction is known as R.
Samuel Bak - Signals ^[1]

History

Mater II

In computer chess, Null Move was already used in threatening mate in one detection, as elaborated by George Baylor and Herbert Simon in A chess mating combinations program, 1966, the description of Mater II ^[2] .

Routine G17 asks if a proposed move threatens mate in one move. It determines the answer by assuming Black does nothing on his turn, that is, by playing a "No Move" and then seeing if White can enforce an immediate checkmate.

Kaissa

Null Move pruning was already used in Kaissa, as described by their authors 1975 in Some Methods of Controlling the Tree Search in Chess Programs ^[3] , at the end of chapter 2:

2. The Order of Move Considerations:
A less trivial idea was that sometimes an extension of the game tree by introducing of dummy move can lead to a reduction of the search tree. In positions with material advantage (with respect to limits) it was permitted to try a so-called "blank" move in which ones own pieces are not moved. Certainly in positions with "Zugzwang" (the side to move must weaken his position) this may lead to errors.

However, the standard of the program's play is still such that such errors do not essentially lower it. (We plan to develop in the future a procedure for recognizing "Zugzwang" positions, and to forbid a blank move in them.) The reduction of search takes place in this case, because the blank move proves to be a closing one and furthermore does not generate complex forcing variations.

Beal's NMQS

Null move was further examined by Don Beal, as already elaborated in his Advances in Computer Chess 5 lecture. He proposed a so called Null Move Quiescence Search (NMQS) as a selective layer between a regular full width search and quiescence search, later dubbed Generalized Quiescence Search ^[4]. The full width search was called with two depth parameters, both considered inside the transposition table, full-depth and q-depth. Full-depth was recursively decremented as usual, but instead of calling quiescence at the full-depth horizon, NMQS with q-depth was called - q-depth recursively decremented in this layer as well. As long as q-depth is greater than zero, the hash move, if any, is searched first regularly. Next, NMQS calls quiescence for the other side to move, to check for a possible null move beta-cutoff, before proceeding the remaining moves in usual manner. As pointed out by Chun Ye in his 1992 thesis ^[5], NMQS permits more flexible iterative deepening concerning full-depth in an outer and q-depth in an inner loop.

Schaeffer

In his 1987 ICCA Journal paper Speculative Computing, Jonathan Schaeffer mentioned The Null-Move Algorithm or Don Beal's null-move, and used it non-recursively up to once per search path in his tactical scout solver Minix (Mini-Phoenix), which up and then gave the parallel running Phoenix, which was a less deep searcher than Minix, some tactical hints ^[6].

Goetsch and Campbell

Gordon Goetsch and Murray Campbell published the results of some experiments with Null move pruning in 1988 and 1990 ^[7] ^[8], already considering recursive NMP with depth reduction of 1, also mentioned in Chun Ye's 1992 thesis with source code as implemented inside the Chinese Chess program Abyss ^[9] .

Morsch and Donninger

Null move pruning was used recursively to possibly occur multiple times inside a path of the search by Frans Morsch ^[10] inside his chess engines Quest and Fritz. Frans exchanged his ideas with Chrilly Donninger, who popularized null move by his Null Move and Deep Search paper in the ICCA Journal 1993 ^[11] .

Schemes

Most typical engines use recursive null move with an R value of 2 or 3. Recursive null move pruning is simply allowing more than one null move in one branch of the search. Fruit uses a depth reduction factor R=3, with no null move pruning when down to king and pawns for the side to move, or when in check. The default for Fruit is to try a null search if the static evaluation is greater than beta, or the depth less than four. Newer versions of Fruit as well as Toga default to always doing a null search, as long as there is at least one piece of value greater than a pawn for that side.

Adaptive Null Move Pruning

Ernst A. Heinz proposed refinements with Adaptive Null Move Pruning ^[12] . Some programs vary R with depth, or based on evaluation features, such as being in or near the endgame.

Restrictions on use

Obviously, the null move cannot be used when the side to move is in check, because that would result in an illegal position. But there are more less obvious restrictions on using null move safely. The theoretical basis of null move pruning, as coined by Christophe Théron, is the null move observation. The null move observation is the fact that in chess, in almost every position, the side to move will have a move to play that is better than doing nothing.

There are a few situations in which this assumption does not hold. The null move will produce very bad results in zugzwang positions - positions in which not moving would be the best move, if it were legal. For this reason, some conditions must be used for when the null move is tried in search. Most engines do not try the null move in the endgame, because that is where zugzwang positions are most likely to occur, because there are fewer pieces to move. It is debatable whether a programmer should allow the null move search descend directly to the quiescence search. Most probably it is worthwile only with more tactically aware versions of quiescence.

Some other ways to combat the negative effect of the null move observation are listed here:

Zugzwang Verification

Concerning null move failures in zugzwang ^[13] , there were proposals by Stefan Plenkner 1995, ^[14] ^[15] and later the Verified Null-Move Pruning approach by Omid David and Nathan S. Netanyahu ^[16] . Recently Robert Hyatt tested Verified Null-Move Pruning extensively with a lot of variations and depth reductions for the verified search, and concluded it does not help at all in Crafty ^[17] similar with extended null-move reductions ^[18] ^[19] . However, Marco Costalba states that verification search has almost nothing to do with zugzwang ^[20] .

Double Null Move

Widely discussed in computer chess forums was the Double Null Move idea by Vincent Diepeveen to perform two consecutive null moves to detect zugzwang ^[21] .

Variable NM Bound

The idea to permit a null move cutoff not only if the null move search returns a value greater than or equal to beta, but also if the value is slightly less - that is using a bound of beta minus some tempo bonus, was already proposed by Gordon Goetsch and Murray Campbell in 1988 as future research idea ^[22] . Yngvi Björnsson and Tony Marsland substantiated the idea as implemeted in The Turk, where the number of potentially good alternative moves (numPGAM) per side in the path from the root to the current node as estimated by positive scores of generated moves from the history heuristic, was used to determine a tempo bonus of 10 or 20 centipawns - the higher numPGAM, the lower the probability that an erroneous forward pruning decision will propagate up the tree ^[23] .

if ( nullMoveAllowed &&  ...) {
   int bound = beta;
   if ( inNullMoveSearch == 0 ) {
      tempo = 10*(numPGAM > 0) + 10* numPGAM > 15);
      bound -= tempo; // variable bound
   }
   makeNullMove(); ++inNullMoveSearch;
   score = -zwSearch(1-bound, depth-R-1)
   unmakeNullMove(); --inNullMoveSearch;
   if ( score >= bound ) {
      return beta; // null move pruning
   }
}

For zwSearch, see Zero Window Search inside the Principal Variation Search.

Threat Detection

Mate Threats

As suggested in Donninger's paper, concerning the deep search, null move is not only about pruning, but also about detecting threat moves by the opponent to improve further move ordering and to possibly trigger mate threat extensions ^[24] ^[25] ^[26] ^[27] . However, some kind of fail-soft framework is necessary to recognize "I get mated, if I do nothing", otherwise the hard bound of a null window null-move search around beta will limit the upper bound to beta-1 ^[28] . Another, possibly too expensive solution with a fail-hard framework, is to play a bit with the search window, if the null move doesn't fail high:

if ( nullMoveAllowed && depth >= X && ...) {
   makeNullMove()
   score = -zwSearch(1-beta, depth-R-1) // -AlphaBeta (0-beta, 1-beta, depth-R-1)
   if (score >= beta ) {
      // fail high on null move
      unmakeNullMove();
      return beta; // null move pruning
   } else {
      if ( zwSearch( VALUE_MATE/2, depth-R-1) > VALUE_MATE/2 )
         extend; // mate threat extension inside a fail hard framework
      unmakeNullMove();
   }
}

Botvinnik-Markoff Extension

Null move is also the base of the Botvinnik-Markoff Extension, as proposed by Sergei Markoff - as a tribute to the computer chess pioneer and former World Chess Champion Mikhail Botvinnik, who addressed related issues in his publications ^[29] .

Influence on Move Ordering

Most of the time, null move is refuted by a capture. Therefore it makes sense to extract a move that refuted null move from the transposition table, record the target square of such a move, to give a move ordering boost for escaping from that square. Also, there is a strong conjecture that in programs using history move ordering, even a failed null move search helps by filling the history tables faster.

Test Results

Null Move Pruning Test Results - various experimental test results of null move pruning
Null Move Test-Positions, where Null Move may fail due to zugzwang

Publications

1966

George W. Baylor, Herbert A. Simon (1966). A chess mating combinations program. AFIPS Joint Computer Conferences, reprinted 1988 in Computer Chess Compendium

1975

Georgy Adelson-Velsky, Vladimir Arlazarov, Mikhail Donskoy (1975). Some Methods of Controlling the Tree Search in Chess Programs. Artificial Intelligence, Vol. 6, No. 4, pp. 361-371. ISSN 0004-3702. Reprinted (1988) in Computer Chess Compendium

1980 ...

Gordon Goetsch, Murray Campbell (1988). Experimenting with the Null Move Heuristic in Chess. AAAI Spring Symposium Proceedings, pp. 14-18.
Don Beal (1989). Experiments with the Null Move. Advances in Computer Chess 5, a revised version is published (1990) under the title A Generalized Quiescence Search Algorithm. Artificial Intelligence, Vol. 43, No. 1, pp. 85-98. ISSN 0004-3702, edited version in (1999). The Nature of MINIMAX Search. Ph.D. thesis, IKAT, ISBN 90-62-16-6348. Chapter 10, pp. 101-116

1990 ...

Don Beal (1990). A Generalized Quiescence Search Algorithm. Artificial Intelligence, Vol. 43, No. 1, pp. 85-98. ISSN 0004-3702
Gordon Goetsch, Murray Campbell (1990). Experiments with the Null-Move Heuristic. Computers, Chess, and Cognition, pp. 159-168
Chun Ye (1992). Experiments in Selective Search Extensions. M.Sc. thesis, Department of Computing Science, University of Alberta, pdf
Chrilly Donninger (1993). Null Move and Deep Search: Selective-Search Heuristics for Obtuse Chess Programs. ICCA Journal, Vol. 16, No. 3
Stefan Plenkner (1995). A Null-Move Technique Impervious to Zugzwang. ICCA Journal, Vol. 18, No. 2
Ernst A. Heinz. (1999). Adaptive null-move pruning. ICCA Journal, Vol. 22, No. 3, ps

2000 ...

Yngvi Björnsson, Tony Marsland (2000). Selective Depth-First Search Methods. in Jaap van den Herik, Hiroyuki Iida (eds.) (2000). Games in AI Research. Universiteit Maastricht, pdf preprint
Omid David, Nathan S. Netanyahu (2002). Verified null-move pruning. ICGA Journal, Vol. 25 No. 3 ^[30] ^[31]
Don Beal (2006). Review of a nullmove-quiescence search mechanism from 1986. (Draft) ^[32]
Omid David, Nathan S. Netanyahu (2008). Extended Null-Move Reductions. CG 2008, pdf
Daniel S. Abdi (2013). Analysis of pruned minimax trees. pdf » Alpha-Beta, Late Move Reductions

Forum Posts

1995 ...

Null Move heuristic by Valavan Manohararajah, rec.games.chess, July 28, 1995

1997

Null move depth reductions by Tom King, rgcc, February 02, 1997 » Depth Reduction R
Null move? by MLC, rgcc, October 07, 1997
Searching correctly with the Nullmove ==> no zugzwang problems anymore by Vincent Diepeveen, rgcc, October 23, 1997

1998

During Null Move search by Peter Fendrich, CCC, June 02, 1998
Extend or not extend in a nullmove tree by Roland Pfister, CCC, June 08, 1998 » Extensions
Zero-width Window Null Move Search by Dezhi Zhao, CCC, June 15, 1998 » Null Window
search extension by Werner Inmann, CCC, July 08, 1998
Null move reductions by Roberto Waldteufel, CCC, October 04, 1998

1999

Singular Extensions, Nullmove deepsearch by Frank Schneider, CCC, February 16, 1999 » Singular Extensions
NULL MOVE by Sylvain Lacombe, CCC, February 24, 1999
To skin a cat (was Re: NULL MOVE) by Don Dailey, CCC, February 24, 1999
Null move around (beta-1, beta) by Tom King, rgcc, March 05, 1999
Null move mate extension by James Robertson, CCC, June 25, 1999

2000 ...

Pseudo C code for double nullmove + PVS by Vincent Diepeveen, CCC, August 06, 2000
is this nullmove? problems in pulsar algorithm by Mike Adams, CCC, September 20, 2000 » Pulsar

2001

Can nullmoves behave like this? by Severi Salminen, CCC, January 08, 2001
Nullmove: when to avoid it? by Leen Ammeraal, CCC, February 28, 2001
An idea for all you chess programmers. by Paul, Winboard Forum, March 16, 2001
Double Nullmove by David Rasmussen, CCC, March 30, 2001
Double Null move? by Steve Maughan, CCC, July 13, 2001
Null move R=2 vs Null move R=2/3 by Tom King, CCC, August 09, 2001 » Depth Reduction R

2002

Crafty-IsiChess,CCT4,r11 ==> A move to avoid? by José Antônio Fabiano Mendes, CCC, January 29, 2002
Double Nullmove by Andreas Herrmann, CCC, April 25, 2002
Null-Move: Difference between R = 2 and R = 3 in action by Omid David, CCC, July 11, 2002
Verified Null-Move Pruning, ICGA 25(3) by Omid David, CCC, November 20, 2002
new thoughts on verified null move by Scott Farrell, CCC, November 23, 2002

2003

An interesting forward pruning experiment - with pseudo description by Vincent Diepeveen, rgcc, February 08, 2003
The "same threat extension" as effective way to resolve horizon problem by Sergei Markoff, CCC, October 01, 2003 » Botvinnik-Markoff Extension
a question to Tord about detecting threats in null move by Uri Blass, CCC, October 03, 2003

2004

Re: not using nullmove? by Tord Romstad, CCC, February 13, 2004
mtd(f) and null move by Peter Alloysius, CCC, March 11, 2004 » MTD(f)
double null move help by Daniel Shawul, CCC, July 04, 2004
An MTD(f) question about NULL MOVE searching by Dann Corbit, CCC, July 16, 2004 » MTD(f)
null move question(Fruit) by Jan K., CCC, July 22, 2004
mate threat extension/null move by Rick Bischoff, CCC, September 25, 2004

2005 ...

recusive null move in iterative search by Daniel Shawul, Winboard Forum, March 25, 2005 » Iterative Search
Reductions and null move refutations by Tord Romstad, Winboard Forum, April 18, 2005 » Reductions, Late Move Reductions
depthnull by Pedro Castro, Winboard Programming Forum, July 04, 2005

2006

Verified null-move pruning by Tom King, Winboard Programming Forum, March 09, 2006
Simple NULL move enhancement, checks in qsearch by Mark Lefler, Winboard Programming Forum, April 14, 2006

2007

NMP on ALL nodes by Onno Garms, Winboard Programming Forum, April 15, 2007 » All Nodes
Re: Search or Evaluation? by Mark Uniacke, Hiarcs Forum, October 14, 2007
Null Move by Stuart Cracraft, CCC, November 23, 2007
fractal null move by Pawel Koziol, CCC, November 28, 2007

2008

null move threat extension by Andrew Short, CCC, October 23, 2008

2009

Null move in quiescence search idea from Don Beal, 1986 by Eelco de Groot, CCC, Aug 17, 2009 » Quiescence Search, Don Beal
verified null move by Robert Hyatt, CCC, June 21, 2009
Null-moves and zugzwang by Luca Hemmerich, CCC, September 25, 2009 » Zugzwang

2010 ...

Using Heinz in 2010 is not optimal by Milos Stanisavljevic, CCC, January 01, 2010
Null-move pruning and the hash table by Robert Purves, CCC, March 28, 2010 » Transposition Table
nullmove and repetitive draw detection by Edward Yu, CCC, June 20, 2010 » Repetitions
Stockfish null move pre-condition by Rein Halbersma, CCC, July 22, 2010 » Stockfish
Extended Null-Move Reductions by Alvaro Cardoso, CCC, August 20, 2010

2011

Less null move pruning by trans map by Onno Garms, CCC, March 13, 2011 » Onno
Null Move Pruning by Alex Farley, CCC, April 03, 2011
Null move alternative in endgames by Aleks Peshkov, CCC, November 16, 2011

2012

TT avoid nullmove flag by Matthew R. Brades, CCC, August 02, 2012 » Transposition Table
Nullmove vs classic selective search by Ed Schröder, CCC, August 04, 2012 ^[33]

2013

Null Move Fail by CDaley11, OpenChess Forum, January 10, 2013
Two questions by Jerry Donald, CCC, February 11, 2013
nullmove verification vs avoid null by Martin Sedlak, CCC, September 14, 2013
Null move, razoring and mate threats by Jon Dart, CCC, October 28, 2013 » Razoring
Is SF DD greater efficiency would be null move pruning? by Jonathan Lee, CCC, December 22, 2013 » Stockfish

2014

fixing the null move search "bug" by Uri Blass, CCC, February 01, 2014 » Stockfish
Disabling Null Move Pruning in Stockfish by Louis Zulli, CCC, February 15, 2014 » Stockfish
Null move and LMR by Laurie Tunnicliffe, CCC, March 12, 2014 » Late Move Reductions
Null move pruning on PV nodes by Eric Oldre, CCC, July 22, 2014 » PV-Nodes

2015 ...

Why not two consecutive null moves ? by Henk van den Belt, CCC, May 07, 2015
thoughts on null-move reduction by Youri Matiounine, CCC, June 14, 2015 » Null Move Reductions
Null move: minimum depth by Henk van den Belt, CCC, September 14, 2015
Null Move in Quiescent search by Laurie Tunnicliffe, CCC, December 09, 2015 » Quiescence Search, Search Pathology

2016

When to do null move by J. Wesley Cleveland, CCC, June 05, 2016
Calculating R value for Null Move by Andrew Grant, CCC, June 23, 2016 » Depth Reduction R
Null Move recommendations by kickstone, OpenChess Forum, July 29, 2016
Null Move in LMR by Laurie Tunnicliffe, CCC, August 10, 2016 » Late Move Reductions
Nullmove bugs by Matthew R. Brades, CCC, August 28, 2016

2017

What is wrong with doing Nulls & ttcuts in a pv node ? by Mahmoud Uthman, CCC, January 21, 2017 » PV-Nodes, Transposition Table
NULL Move code question by thevinenator, OpenChess Forum, January 27, 2017 » CPW-Engine_search
null move by Folkert van Heusden, CCC, April 14, 2017
tt move vs null move by Erin Dame, CCC, May 27, 2017 » Hash Move, Null Move
End game and Null move by Laurie Tunnicliffe, CCC, June 12, 2017
Fifty move counter and Null move by Tamás Kuzmics, CCC, August 09, 2017 » Fifty-move Rule, Halfmove Clock
Rethinking r in null move by Michael Sherwin, CCC, August 18, 2017 » Depth Reduction R
Question on Null Move Pruning by Jason Fernandez, CCC, August 29, 2017
Threat detection by Harm Geert Muller, CCC, September 09, 2017 » Threat Detection, Threat Move

External Links

Selective Search Techniques in REBEL (null-move) from Programmer Corner by Ed Schröder ^[34] ^[35] » Rebel
A presentation describing the power and flaws in null move pruning: Null Move pruning (pdf) Slides by Lucas Bradstreet
Null-move heuristic from Wikipedia

References

^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ George W. Baylor, Herbert A. Simon (1966). A chess mating combinations program. AFIPS Joint Computer Conferences, reprinted 1988 in Computer Chess Compendium
^ Georgy Adelson-Velsky, Vladimir Arlazarov, Mikhail Donskoy (1975). Some Methods of Controlling the Tree Search in Chess Programs. Artificial Intelligence, Vol. 6, No. 4, pp. 361-371. ISSN 0004-3702. Reprinted (1988) in Computer Chess Compendium
^ Don Beal (1989). Experiments with the Null Move. Advances in Computer Chess 5, A revised version is published (1990) under the title A Generalized Quiescence Search Algorithm. Artificial Intelligence, Vol. 43, No. 1, pp. 85-98. ISSN 0004-3702.
^ Chun Ye (1992). Experiments in Selective Search Extensions. M.Sc. thesis, Department of Computing Science, University of Alberta, pdf, pp. 57
^ Jonathan Schaeffer (1987). Speculative Computing. ICCA Journal, Vol. 10, No. 3
^ Gordon Goetsch, Murray Campbell (1988). Experimenting with the Null Move Heuristic in Chess. AAAI Spring Symposium Proceedings, pp. 14-18
^ Gordon Goetsch, Murray Campbell (1990). Experiments with the Null-Move Heuristic. Computers, Chess, and Cognition, pp. 159-168
^ Chun Ye (1992). Experiments in Selective Search Extensions. M.Sc. thesis, Department of Computing Science, University of Alberta, pdf, pp. 27-29
^ Re: SOMA by Ed Schröder, CCC, August 26, 2009
^ Chrilly Donninger (1993). Null Move and Deep Search: Selective-Search Heuristics for Obtuse Chess Programs. ICCA Journal, Vol. 16, No. 3
^ Ernst A. Heinz. (1999). Adaptive null-move pruning. ICCA Journal, Vol. 22, No. 3, ps
^ Position from local chess club by Bernhard Bauer, CCC, November 05, 1999
^ Stefan Plenkner (1995). A Null-Move Technique Impervious to Zugzwang. ICCA Journal, Vol. 18, No. 2
^ Null-move zugzwang avoidance, Jun '95 ICCAJ by Bruce Moreland in rgcc, December 6, 1996
^ Omid David, Nathan S. Netanyahu (2002). Verified null-move pruning. ICGA Journal, Vol. 25 No. 3
^ verified null move by Robert Hyatt, CCC, June 21, 2009
^ Omid David, Nathan S. Netanyahu (2008). Extended Null-Move Reductions. CG 2008, pdf
^ Re: Extended Null-Move Reductions by Robert Hyatt, CCC, August 20, 2010
^ Re: Extended Null-Move Reductions by Marco Costalba, CCC, August 20, 2010
^ Re: Null move? by Vincent Diepeveen, rgcc, October 11, 1997
^ Gordon Goetsch, Murray Campbell (1988). Experimenting with the Null Move Heuristic in Chess. AAAI Spring Symposium Proceedings, pp. 14-18
^ Yngvi Björnsson, Tony Marsland (2000). Selective Depth-First Search Methods. in Jaap van den Herik, Hiroyuki Iida (eds.) (2000). Games in AI Research. Universiteit Maastricht, pdf preprint
^ Deep Search Extension by Stuart Cracraft, CCC, January 18, 1998
^ Null move mate extension by James Robertson, CCC, June 25, 1999
^ mate threat extension/null move by Rick Bischoff, CCC, September 25, 2004
^ Re: mate threat extension/null move by Don Beal, CCC, October 04, 2004 » Mate Threat Extensions and WAC booster
^ null move threat extension by Andrew Short, CCC, October 23, 2008
^ The "same threat extension" as effective way to resolve horizon problem by Sergei Markoff, CCC, October 01, 2003
^ Verified Null-Move Pruning, ICGA 25(3) by Omid David, CCC, November 20, 2002
^ Proving something is better by Bruce Moreland, CCC, December 17, 2002
^ courtesy of Don Beal and Carey Bloodworth, Re: Antique chess programs by Carey, CCC, December 16, 2015
^ Selective Search Techniques in REBEL (introduction) from Programmer Corner by Ed Schröder
^ How Rebel Plays Chess is also available as pdf
^ Nullmove vs classic selective search by Ed Schröder, CCC, August 04, 2012

What links here?

Page	Date Edited
Abyss	Aug 5, 2017
Advances in Computer Chess 5	Dec 2, 2017
AEL-Pruning	Jun 22, 2013
AICE	Nov 29, 2017
Alaric	Mar 4, 2014
Alarm	Jun 7, 2017
Aleks Peshkov	Jan 13, 2016
Alpha-Beta	Jan 28, 2018
Alvaro Cardoso	Jan 12, 2018
Amateur	Feb 25, 2012
Amoeba	Mar 19, 2018
Amy	May 9, 2017
Amyan	Dec 10, 2013
Andrew Grant	Jan 13, 2018
Andscacs	Jan 16, 2018
AnMon	Nov 17, 2017
Arion	Nov 28, 2014
Atlas (ESP)	Jan 28, 2018
Atomystica	Oct 2, 2014
Axon	Jul 14, 2013
Bagatur	Sep 10, 2016
BBchess	Oct 30, 2011
Beaches	Jun 10, 2017
Belzebub	Oct 20, 2015
Beowulf	May 5, 2017
Best Move	May 15, 2017
Betsabe	Jul 23, 2017
Betsy	Jul 28, 2014
BigLion	Sep 28, 2016
BikJump	Aug 11, 2014
Bismark	Apr 22, 2015
Bison	Sep 29, 2016
BlackBishop	Nov 7, 2014
Bobcat	Jun 27, 2017
Bodo	Oct 6, 2016
Booot	Jan 22, 2018
Botvinnik-Markoff Extension	Nov 27, 2015
Brainless	Jun 24, 2017
Branching Factor	Jun 28, 2017
Bruja	Feb 3, 2015
Brutus NL	Aug 22, 2016
Capture (program)	Jan 8, 2016
Carballo	Oct 2, 2016
Celes	May 23, 2014
Cheese	Feb 17, 2018
Cheiron	Jan 7, 2016
Cheng	Jul 30, 2017
Chess Guru	Mar 4, 2017
Chess Wizard	Dec 22, 2014
chess22k	Apr 23, 2018
ChessBrainVB	Jun 24, 2017
Chessterfield	Sep 29, 2016
ChessV	Jan 21, 2018
Chezzz	Jan 20, 2013
Chispa	Feb 13, 2014
Chompster	Jul 27, 2013
Chrilly Donninger	Dec 19, 2016
Cilkchess	Jan 21, 2016
Cinnamon	Sep 23, 2017
Clarabit	Nov 3, 2011
Claudia	Jun 1, 2016
Clubfoot	Sep 8, 2015
Coiled	Mar 12, 2017
Comet	Jan 8, 2016
Counter	Nov 13, 2017
CPW-Engine	Dec 31, 2014
CPW-Engine_search	Feb 4, 2017
Crafty	Jan 28, 2018
Critter	Jan 25, 2014
Crux	Jan 30, 2017
CuckooChess	Jan 17, 2017
Cupcake	May 19, 2016
Cyclone	Nov 24, 2013
Czolgista	Apr 20, 2013
DanaSah	Oct 9, 2017
Daniel Shawul	Jan 28, 2018
DarkThought	Jul 3, 2018
Darmenios	Jan 7, 2016
DayDreamer	Aug 22, 2016
Deep Blue	Aug 1, 2017
Defenchess	Mar 18, 2018
Delfi	Jan 7, 2016
Delphil	Sep 17, 2016
DelphiMax	Apr 3, 2013
Demolito	Mar 1, 2018
Depth	Feb 25, 2018
Depth Reduction R	Oct 4, 2017
Desperado	May 19, 2017
Deuterium	Jun 23, 2014
Diablo	May 17, 2016
Dictionary	Aug 24, 2017
Dimitri	Aug 22, 2017
Diogenes	Jan 8, 2016
DisasterArea	Mar 27, 2017
DiscoCheck	Jun 23, 2017
Djinn	Feb 8, 2016
DOCCC 1993	Dec 12, 2016
Dolphin	Nov 28, 2014
Don Beal	Jul 27, 2017
Don Dailey	Dec 7, 2016
Donna	Aug 17, 2017
Dorky	Oct 10, 2016
Dorpsgek	Apr 2, 2018
Double Null Move	May 8, 2015
Dragon FR	Sep 9, 2016
DrunkenMaster	Nov 1, 2016
Dumb	Mar 10, 2018
E.T.Chess	Jan 28, 2013
Elephant	Sep 19, 2016
Engine Testing	Feb 1, 2018
Enhanced Forward Pruning	Oct 21, 2014
Ernst A. Heinz	Mar 6, 2017
ESC	Aug 14, 2013
Ethereal	Mar 20, 2018
Eugen	Jan 7, 2016
Eugenio Castillo Jiménez	Jul 23, 2017
Eveann	Apr 3, 2017
Exacto	Oct 3, 2015
EXchess	Jan 21, 2018
Extensions	Apr 19, 2018
Fail-High Reductions	Mar 6, 2014
Fail-Soft	Jun 2, 2017
Faile	May 27, 2014
Falcon	Sep 2, 2016
FCP	Jun 15, 2013
Ferret	Jan 7, 2016
Fifty-move Rule	Aug 9, 2017
Fischerle	Aug 21, 2017
Floyd	Sep 11, 2016
Flux	Jan 12, 2016
Fortress (Engine)	Oct 19, 2017
Frank Schneider	Jan 7, 2016
Frenzee	Feb 24, 2013
Freyr	Mar 6, 2014
Fridolin	Jun 27, 2017
Fritz	Feb 26, 2018
Fruit	Sep 27, 2016
Futility Pruning	Aug 30, 2017
Gaia	Nov 3, 2015
Galjoen	Mar 19, 2018
Gandalf	Jan 21, 2018
Garbochess	Sep 23, 2017
Garbochess-JS	Sep 23, 2017
Gaviota	Jan 21, 2018
Gazebo	May 21, 2017
Genesis IL	Feb 15, 2014
Gerbil	Feb 3, 2017
GES	Sep 13, 2015
Ghost	Feb 2, 2018
Gian-Carlo Pascutto	Jan 16, 2018
Gibbon	Dec 23, 2014
Ginkgo	Jul 13, 2016
Gk	Oct 9, 2017
Glass	May 24, 2017
Glaurung	Mar 14, 2017
Godot	Apr 28, 2015
Gogobello	Jul 30, 2017
GopherCheck	Feb 3, 2017
Gordon Goetsch	Jan 7, 2016
Greko	Feb 27, 2018
Gromit	Apr 5, 2017
Guidance for Creating New Pages	Dec 15, 2014
Gullydeckel	Oct 28, 2015
Hagrid	Apr 12, 2016
Hakkapeliitta	Apr 26, 2016
Halfmove Clock	Aug 9, 2017
HaQiKi D	Jul 26, 2017
Harm Geert Muller	Mar 31, 2018
Hash Move	Oct 4, 2017
HeavyChess	Feb 14, 2014
History	Jan 2, 2018
Holmes	Apr 24, 2014
Horizon	Mar 17, 2013
ICGA Journal	Dec 21, 2017
Ifrit	Feb 7, 2016
Ikarus	Jul 5, 2016
InmiChess	Mar 6, 2014
Insomniac	Jan 27, 2016
ISA	Apr 2, 2018
IsiChess	Jan 7, 2016
Iterative Search	Oct 20, 2016
Jabba	Sep 10, 2016
Jan Kaan	Feb 4, 2018
Jazz	Oct 4, 2017
JFresh	Mar 2, 2016
JikChess	Nov 29, 2015
Joker IT	Sep 16, 2017
Jon Dart	Dec 17, 2017
Jumbo	Dec 19, 2017
Kaissa	Apr 9, 2018
Kallisto	Oct 28, 2017
Karlo Bala Jr.	Feb 19, 2017
Kholin	Jan 3, 2018
Killer Move	Feb 16, 2017
King of Kings	Sep 4, 2013
KingSlayer	Oct 17, 2016
Kiwi	Sep 2, 2016
KnightCap	Nov 6, 2016
KnockOut	Sep 20, 2016
Knowledge	Jul 22, 2017
Komodo	Mar 6, 2018
Kurt	Apr 20, 2014
Lachex	Jan 7, 2016
LambChop	Nov 24, 2017
LarsenVB	Jun 24, 2017
Laser	Dec 27, 2017
Lasker-Reichhelm Position	Oct 24, 2017
Late Move Reductions	Sep 25, 2017
Laurie Tunnicliffe	Jun 13, 2017
LChess	Jan 7, 2016
Leen Ammeraal	Nov 3, 2014
Lime	May 17, 2015
Little Wing	Oct 26, 2017
LittleThought	Nov 7, 2016
Lozza	Apr 18, 2018
MadChess	Jul 4, 2017
Madeleine	May 18, 2017
Marco Costalba	Feb 28, 2018
Mark Lefler	Nov 23, 2017
Mark Winands	Sep 19, 2017
Martin Sedlak	Dec 25, 2017
Marvin	Feb 10, 2018
Matador	Oct 30, 2015
Matant	Aug 14, 2013
Mate at a Glance	Sep 24, 2014
Mate Threat Extensions	Apr 14, 2012
Mathematician	Apr 9, 2018
Matthew R. Brades	Jun 9, 2017
Maverick	Jan 7, 2016
MBChess	Sep 29, 2012
Merlin	Jan 20, 2018
Monarch	Nov 19, 2014
Monsoon	Feb 8, 2015
Move Ordering	Feb 27, 2018
Movei	Jan 7, 2016
Moves	Feb 19, 2018
Multi-Cut	Jul 4, 2016
Murka	Nov 11, 2016
Murray Campbell	Jun 2, 2017
Muse	May 17, 2016
Napoleon	Jun 25, 2017
Natwarlal	Aug 26, 2013
Naum	Nov 23, 2017
Nebula	Feb 7, 2015
Nemorino	Dec 21, 2017
Nesik	Jan 24, 2014
NG-play	Feb 26, 2017
Nightmare GER	Dec 12, 2016
Nirvanachess	Sep 30, 2017
Node Types	Oct 22, 2017
NoraGrace	Nov 23, 2014
Null Move	Aug 9, 2017
Null Move Observation	Dec 30, 2015
Null Move Pruning	Dec 2, 2017
Null Move Pruning Test Results	May 16, 2015
Null Move Reductions	Jun 22, 2015
Null Move Test-Positions	Nov 22, 2015
Null Window	Nov 8, 2016
Nullmover	Jul 21, 2013
Obender	Apr 17, 2016
Octochess	Aug 15, 2017
OliThink	May 19, 2017
Omid David	Jan 2, 2017
Onno	Jul 19, 2013
Onno Garms	Jul 19, 2013
Open Source Engines	Jul 14, 2015
Orion	Oct 15, 2017
Othello	Jan 4, 2018
Paladin	Jan 29, 2017
Parity Pruning	Jan 14, 2013
Patzer	Apr 5, 2017
Pawel Koziol	Dec 17, 2017
Pawn Endgame	Oct 11, 2017
Pawny	Jun 17, 2015
Pedro Castro	Apr 19, 2016
Peter Aloysius Harjanto	Jul 21, 2015
Peter Fendrich	May 19, 2017
Phalanx	May 2, 2016
Pharaon	Sep 2, 2017
Phoenix	May 8, 2017
Plisk	Dec 31, 2014
PolarChess	May 15, 2017
Popochin	Feb 5, 2016
PostModernist	Jan 7, 2016
Prédateur	Nov 11, 2016
Principal variation	Dec 4, 2017
ProbCut	Mar 25, 2016
ProChess IT	Sep 30, 2015
Prophet	Sep 30, 2017
Protector	Oct 12, 2017
Protej	Jul 27, 2014
Pruning	Jan 1, 2018
Pulsar	May 4, 2017
Purple Haze	Oct 26, 2017
PV-Move	Jan 16, 2013
Quest	Mar 26, 2017
Quiescence Search	Aug 19, 2017
Rajah	Sep 12, 2012
Ramjet	Sep 27, 2017
RattateChess	Dec 2, 2014
Razoring	Oct 5, 2015
Recursion	Nov 18, 2017
RedQueen	Nov 13, 2017
Reductions	Nov 1, 2017
Refutation Move	May 13, 2013
Rein Halbersma	Dec 22, 2015
Repetitions	Jan 16, 2018
Requiem	Feb 5, 2018
Reverse Futility Pruning	Jun 2, 2017
Rhetoric	Nov 15, 2017
Robocide	May 11, 2016
ROCE	Jun 6, 2017
Rodent	Jan 11, 2018
Rodin	Feb 7, 2016
Roland Pfister	Apr 5, 2017
RomiChess	Jan 2, 2018
Ronald de Man	Nov 20, 2017
Rookie	Jan 7, 2016
Ruffian	Jun 6, 2017
RuyDos	Feb 17, 2018
Scidlet	May 31, 2014
Scott Farrell	Jun 16, 2013
Search Instability	May 5, 2017
Search Pathology	Nov 26, 2017
SEE	Jan 14, 2013
Selectivity	Jan 12, 2018
Senpai	Nov 10, 2017
Severi Salminen	May 7, 2015
SharpChess	Jun 6, 2017
Sharper	Jun 6, 2017
Shield	May 17, 2017
Sierżant	Apr 15, 2014
Simplex	Mar 6, 2016
Singular Extensions	Jan 9, 2018
Sinobyl	Jul 3, 2014
Sjaak (Glebbeek)	Oct 4, 2017
Sjeng	Aug 17, 2017
Sloppy	Sep 17, 2016
Slow Chess	May 17, 2016
Small Potato	Feb 14, 2014
Smash	May 11, 2016
SnailChess	Nov 26, 2014
Snitch	Apr 7, 2016
Socrates	Jul 3, 2018
Soldat	Aug 20, 2017
SOS	Apr 5, 2017
Spector	Nov 11, 2016
Spike	Jan 7, 2016
StarTech	Oct 20, 2016
Stefan Plenkner	Dec 31, 2015
Stockfish	Apr 7, 2018
Stuart Cracraft	May 19, 2017
Sungorus	Apr 11, 2014
Sunsetter	Jun 1, 2017
Tactics	Jan 12, 2018
Tao	Jan 8, 2016
Teki	Mar 29, 2018
Tempo	Jan 17, 2018
Terra	Feb 11, 2015
Texel	Oct 9, 2017
The Baron	Jan 8, 2018
The Turk (TR)	Apr 1, 2017
Thor's Hammer	Nov 23, 2013
Thorsten Greiner	May 9, 2017
Threat Move	Sep 10, 2017
Tigran	Aug 16, 2015
Tom King	Aug 19, 2017
tomitankChess	Dec 8, 2017
Tord Romstad	Dec 9, 2017
Tornado	Dec 14, 2017
TRACE	Feb 14, 2013
Transposition Table	Apr 19, 2018
Triangulation	Apr 4, 2013
TSCP	Feb 5, 2016
Tucano	Dec 16, 2017
Tunguska	Sep 16, 2017
Turning Point	Apr 6, 2012
Tytan	Nov 3, 2015
Uri Blass	Feb 26, 2018
Vadim Demichev	Jul 26, 2013
Vajolet	Jan 25, 2018
Vice	Mar 8, 2016
Virtua Chess	Jul 3, 2018
Virtual Chess	Mar 25, 2017
Voyager	Aug 12, 2012
Walter Faxon	Mar 6, 2015
Wasp	Nov 24, 2017
Waxman	Aug 18, 2014
WChess	Jan 7, 2016
WildCat	Nov 11, 2016
Will Singleton	Mar 6, 2015
Win at Chess	Sep 25, 2017
Wing	Oct 26, 2017
Winglet	Apr 26, 2015
Winglet to include	Apr 25, 2015
Witz	Nov 14, 2017
Woodpusher	Dec 12, 2016
WyldChess	Mar 10, 2018
XiniX	Jan 7, 2016
Xiphos	Apr 22, 2018
Xpdnt	Sep 13, 2015
XXXX	Jan 7, 2016
ZChess	Jan 8, 2016
Zeus	Jan 3, 2018
Zeus RU	Jun 6, 2015
Ziggy IS	Sep 6, 2015
Zochova	Nov 9, 2014
Zugzwang	Dec 8, 2017
Zugzwang (Program)	Dec 19, 2016
Zurichess	Mar 12, 2018
Zzzzzz	May 14, 2016

Up one level

Null Window

GerdIsenberg — Tue, 08 Nov 2016 22:09:14 GMT

Home * Dictionary * Null Window

		A Null Window, also called Zero Window, Scout Window or Narrow Window, is a way to reduce the search space in alpha-beta like search algorithms, to perform a boolean test, whether a move produces a worse or better score than a passed value. Null window searches are the base of Scout, NegaScout or Principal Variation Search, and MTD(f).
Samuel Bak - Above and Below ^[1]

History

Applications

History

Null windows were first described by Judea Pearl, when introducing his Scout algorithm in April 1980 ^[2]. Independently, null window searches were further elaborated by John Philip Fishburn in the SIGART Bulletin, Issue 72, July 1980 ^[3], who was already trying to get this published starting in August 1979. Fishburn was somewhat disappointed in the speedup (or lack thereof) that he measured on checkers lookahead trees. However when he went to work at Bell Labs in 1981, Ken Thompson told him that he had read the SIGART paper, and had sped up Belle by 1.5x with null windows ^[4].

Applications

Null window searches are performed in

MTD(f)
Multi-Cut to prove no singularity
NegaC*
NegaScout
Null Move Pruning to prove a null move fails high
Principal Variation Search
ProbCut for the reduced search
Scout
SSS* and Dual* as MT

A null window search can never return an exact score with alpha < score < beta and therefor a principal variation, but either an upper bound with score < beta (score <= alpha) or a lower bound with score >= beta (score > alpha).

With integers a null-window is defined as alpha == beta - 1.

Forum Posts

Zero-width Window Null Move Search by Dezhi Zhao, CCC, June 15, 1998
when to try zero window search by Andrew Short, CCC, November 14, 2008
Zero window TT entry by Vlad Stamate, CCC, March 05, 2010 » Transposition Table

External Links

Negascout from Wikipedia

References

^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
^ Judea Pearl (1980). Scout: A Simple Game-Searching Algorithm with Proven Optimal Properties. Proceedings of the First Annual National Conference on Artificial Intelligence. Stanford. pdf
^ John Philip Fishburn (1980). An optimization of alpha-beta search, SIGART Bulletin, Issue 72
^ John Philip Fishburn, personal communication

What links here?

Page	Date Edited
Alexander Reinefeld	Jul 4, 2016
Aspiration Windows	Nov 1, 2017
B*	Nov 27, 2017
Belle	Jan 18, 2018
Capture (program)	Jan 8, 2016
Crafty	Jan 28, 2018
Dictionary	Aug 24, 2017
Duck	Dec 12, 2016
Exact Score	Dec 28, 2012
Fail-High	Oct 22, 2017
Fail-Low	Jun 23, 2017
Fail-Soft	Jun 2, 2017
Fidelity	Jan 7, 2016
Jamboree	Jun 15, 2015
Judea Pearl	Jan 18, 2018
Kevin Coplan	Dec 17, 2016
Lachex	Jan 7, 2016
Move Ordering	Feb 27, 2018
MTD(f)	Jul 17, 2017
Multi-Cut	Jul 4, 2016
NegaC*	Dec 17, 2016
NegaScout	Jul 6, 2016
Node Types	Oct 22, 2017
Null Move Pruning	Dec 2, 2017
Null Window	Nov 8, 2016
Parabelle	Jul 28, 2017
Patzer	Apr 5, 2017
Phoenix	May 8, 2017
Principal Variation Search	Oct 22, 2017
Razoring	Oct 5, 2015
Scout	Jan 28, 2018
Singular Extensions	Jan 9, 2018
SSS* and Dual*	Jan 22, 2018
Sunsetter	Jun 1, 2017
Touch	Dec 12, 2016
Transposition Table	Apr 19, 2018
Triangular PV-Table	Jun 12, 2017
Vlad Stamate	Dec 31, 2014
Window	Jun 7, 2017
Young Brothers Wait Concept	Apr 22, 2018

Up one level

Wikispaces : chessprogramming - items matching description

Attack and Defend Maps

Table of Contents

Maintaining Attacks

Incremental Update

On the Fly

Implementations

Classical Approach

Alternatives

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Bitboards

Table of Contents

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1994

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Candidates (Bitboards)

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Candidate and Faker

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The Sneaker

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Check

Table of Contents

Kind of Checks

Single Check

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By last Move

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