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Attack Spans

GerdIsenberg — Thu, 04 Mar 2010 17:40:18 GMT

Home * Board Representation * Bitboards * Pawn Pattern and Properties * Attack Spans

Set-wise pattern, based on attackspans are for instance isolated pawns, passers and candidates.

The admittedly arbitrary definition of front attackspans includes the attacked squares itself, thus it is like a fill of attacked squares in the appropriate direction. The rear attackspan is the complement set on the same file, so that the union of both spans covers the whole file. As always, we keep disjoint east-west sets for separate applications, despite illustrated as union with one single pawn:

white attack        white attack     attack filefill with least one
frontspan           rearspan         square attacked by white
. . 1 . 1 . . .     . . . . . . . .     . . 1 . 1 . . .
. . 1 . 1 . . .     . . . . . . . .     . . 1 . 1 . . .
. . 1 . 1 . . .     . . . . . . . .     . . 1 . 1 . . .
. . 1 . 1 . . .     . . . . . . . .     . . 1 . 1 . . .
. . . w . . . .     . . 1 w 1 . . .     . . 1 w 1 . . .
. . . . . . . .     . . 1 . 1 . . .     . . 1 . 1 . . .
. . . . . . . .     . . 1 . 1 . . .     . . 1 . 1 . . .
. . . . . . . .     . . 1 . 1 . . .     . . 1 . 1 . . .
 
black attack        black attack     attack filefill with least one
frontspan           rearspan         square attacked by black
. . . . . . . .     . . 1 . 1 . . .     . . 1 . 1 . . .
. . . . . . . .     . . 1 . 1 . . .     . . 1 . 1 . . .
. . . . . . . .     . . 1 . 1 . . .     . . 1 . 1 . . .
. . . . . . . .     . . 1 . 1 . . .     . . 1 . 1 . . .
. . . b . . . .     . . 1 b 1 . . .     . . 1 b 1 . . .
. . 1 . 1 . . .     . . . . . . . .     . . 1 . 1 . . .
. . 1 . 1 . . .     . . . . . . . .     . . 1 . 1 . . .
. . 1 . 1 . . .     . . . . . . . .     . . 1 . 1 . . .

The routines based on one step only, vertical fills and pawn spans :

U64 wEastAttackFrontSpans (U64 wpawns) {return eastOne(wFrontSpans(wpawns));}
U64 wWestAttackFrontSpans (U64 wpawns) {return westOne(wFrontSpans(wpawns));}
U64 bEastAttackFrontSpans (U64 bpawns) {return eastOne(bFrontSpans(bpawns));}
U64 bWestAttackFrontSpans (U64 bpawns) {return westOne(bFrontSpans(bpawns));}
 
U64 wEastAttackRearSpans (U64 wpawns)  {return eastOne(wRearFill(wpawns));}
U64 wWestAttackRearSpans (U64 wpawns)  {return westOne(wRearFill(wpawns));}
U64 bEastAttackRearSpans (U64 bpawns)  {return eastOne(bRearFill(bpawns));}
U64 bWestAttackRearSpans (U64 bpawns)  {return westOne(bRearFill(bpawns));}

The filefills are independent on color

U64 eastAttackFileFill (U64 pawns) {return eastOne(fileFill(pawns));}
U64 westAttackFileFill (U64 pawns) {return westOne(fileFill(pawns));}

If a pawn is not member of own west or east attack filefills, the pawn is half-isolated.
If a pawn is not member of the union of own east and west attack filefills, the pawn is isolated.
If a pawn is not member of the union of all opponent front pawn- and attack-spans, it is a passed pawn.

What links here?

Page	Date Edited
Attack Spans	Mar 4, 2010
Backward Pawns (Bitboards)	May 5, 2017
Candidates (Bitboards)	Nov 11, 2017
Fill Algorithms	Nov 6, 2013
Holes	Oct 16, 2017
Isolated Pawns (Bitboards)	Nov 18, 2012
Passed Pawns (Bitboards)	Aug 23, 2010
Pawn Pattern and Properties	Nov 11, 2017
Pawn Spans	Jul 22, 2010
PawnKing	Sep 5, 2014
Pin	Mar 7, 2017

Up one Level

Backward Pawn

GerdIsenberg — Fri, 05 May 2017 10:30:24 GMT

Home * Evaluation * Pawn Structure * Backward Pawn

		A backward pawn is a pawn no longer defensible by own pawns and whose stop square lacks pawn protection but is controlled by a sentry. Thus, don't considering piece tactics, the backward pawn is not able to push forward without being lost, even establishing an opponent passer. If two opposing pawns on adjacent files in knight distance are mutually backward, the more advanced is not considered backward. A backward pawn is worse, or even a real Straggler, if on a half-open file as suitable target of opponent rooks. As pointed out by Sam Hamilton ^[1], considering stop squares might be insufficient for pawns which may actually push, but have a permanent weakened telestop. On the other hand, such a backward prospective pawn has a vital tempo, which is often decisive in certain pawn endings.
Behindhand Pawn ^[2]

Publications

Hans Kmoch (1959, 1990). Pawn Power in Chess. New York: Dover, 1990. Previous ed.: New York: McKay, 1959. ISBN 0-486-26486-6

Forum Posts

2000 ...

WHAT is the definition of a backward pawn? by Bas Hamstra, CCC, December 23, 2002
Backward Pawns by Mark Lefler, CCC, March 24, 2008
Doubled and Backward Pawn Engine "Definitions" by Brian Richardson, CCC, September 07, 2009
Re: Doubled and Backward Pawn Engine "Definitions" by Sam Hamilton, CCC, September 13, 2009

2010 ...

backward pawns in Stockfish by Marek Kwiatkowski, CCC, July 16, 2010
What is a backward pawn? by Lyudmil Tsvetkov, CCC, May 12, 2014
Pawn backwardness by Natale Galioto, CCC, October 06, 2015

External Links

Backward Pawn from Wikipedia

References

^ Re: Doubled and Backward Pawn Engine "Definitions" by Sam Hamilton, CCC, September 13, 2009
^ Chess painting in oil on canvas by Elke Rehder

What links here?

Page	Date Edited
Alarm	Jun 7, 2017
Backward Pawn	May 5, 2017
Backward Pawns (Bitboards)	May 5, 2017
Bas Hamstra	Feb 4, 2018
Blockage Detection	Oct 19, 2017
Cheese	Feb 17, 2018
Cheops (Miller)	Jan 13, 2017
ChessBrainVB	Jun 24, 2017
Clarabit	Nov 3, 2011
Coiled	Mar 12, 2017
Dartmouth CP	Jan 19, 2018
Defenchess	Mar 18, 2018
Diablo	May 17, 2016
Donna	Aug 17, 2017
Doubled Pawn	Mar 27, 2017
Evaluation function draft	Jul 11, 2014
Evaluation Overlap	Jul 19, 2016
Exacto	Oct 3, 2015
Faker	Nov 11, 2017
Garbochess	Sep 23, 2017
GopherCheck	Feb 3, 2017
Hakkapeliitta	Apr 26, 2016
Hans Kmoch	Nov 11, 2017
Hidden Passed Pawn	Nov 11, 2017
Holes	Oct 16, 2017
ISA	Apr 2, 2018
Isolated Pawn	Nov 18, 2012
Kaissa	Apr 9, 2018
King Pawn Tropism	Sep 1, 2014
Lyudmil Tsvetkov	Mar 28, 2018
Marek Kwiatkowski	Oct 22, 2017
Mark Lefler	Nov 23, 2017
Minority Attack	Jun 6, 2012
Nebula	Feb 7, 2015
NoonianChess	Jan 7, 2016
Open Pawns (Bitboards)	Aug 24, 2017
Pawn chain	Jan 17, 2018
Pawn Endgame	Oct 11, 2017
Pawn Majority	Jun 8, 2012
Pawn Rams (Bitboards)	Nov 11, 2017
Pawn Structure	Oct 2, 2017
Pawns and Files (Bitboards)	Jan 16, 2013
Prédateur	Nov 11, 2016
RattateChess	Dec 2, 2014
RuyDos	Feb 17, 2018
Sam Hamilton	Jan 28, 2015
Shield	May 17, 2017
Simplex	Mar 6, 2016
Sloppy	Sep 17, 2016
Stockfish	Apr 7, 2018
Tucano	Dec 16, 2017
Vajolet	Jan 25, 2018
Wasp	Nov 24, 2017
Weak Pawns	Dec 19, 2013
Wing	Oct 26, 2017
Winglet	Apr 26, 2015

Up one level

Backward Pawns (Bitboards)

GerdIsenberg — Fri, 05 May 2017 10:28:18 GMT

Home * Board Representation * Bitboards * Pawn Pattern and Properties * Backward Pawns

Stops with negative SEE

Kmoch's definition of a backward pawn or straggler: A half-free pawn on the second or third rank whose stop square lacks pawn protection but is controlled by a sentry. The definition of a backward pawn seems a bit ambiguous. May an isolated pawn also be a backward one? Or an pawn on a closed file? What about a backward ram or faked candidates or even levers?

Backward

We may use a more general definition of backwardness, to consider certain subsets independently. All pawns, which stop is not member of own front-attackspans but controlled by a sentry are backward:

U64 wBackward(U64 wpawns, U64 bpawns) {
   U64 stops = wpawns << 8;
   U64 wAttackSpans = wEastAttackFrontSpans(wpawns)
                    | wWestAttackFrontSpans(wpawns);
   U64 bAttacks     = bPawnEastAttacks(bpawns)
                    | bPawnWestAttacks(bpawns);
   return (stops & bAttacks & ~wAttackSpans) >> 8;
}

Straggler

Stragglers are the intersection of backward with open pawns and the second or third rank:

U64 wStraggler(U64 wpawns, U64 bpawns) {
   return wBackward (wpawns, bpawns)
        & wOpenPawns(wpawns, bpawns)
        & 0xffff00; // rank 2,3
}

In the strict sense, we still need to exclude levers. On the other hand, levers are subject of quiescence search anyway.

Telestop Weakness

As pointed out by Sam Hamilton ^[1] considering stop squares might be insufficient for pawns which may actually push, but have a permanent weakened telestop, f.i.:

8/5p2/6p1/p1p3P1/P1P5/7P/1P6/8 w - -

On the other hand, such a backward prospective pawn has a vital tempo, which is often decisive in certain pawn endings, so one should be careful to don't make the penalty too worse. Anyway, one may either apply the above wBackward algorithm with so far movable pawns shifted one rank up, or alternatively determine a backward square area, which is the black attack span of all black attacks which are outside the white front attack spans:

white pawns         black pawns
. . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . 1 . .
. . . . . . . .     . . . . . . 1 .
. . . . . . 1 .     1 . 1 . . . . .
1 . 1 . . . . .     . . . . . . . .
. . . . . . . 1     . . . . . . . .
. 1 . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .
 
~white front     &  black attacks    -> stop squares
attackspans                             dominated by black 
. . . . 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     . . . . . . . .     . . . . . . . .
stop squares
dominated by black
filled down
-> white         &  white pawns      -> backward pawns
backward area
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 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     . . . . . . . .     . . . . . . . .

Dynamic Backwardness

A further Pass

Another issue is that some pawns or their stop squares are statically member of their own attack spans, but those spans could not be realized, since their pawns are either backward or rammed (or both). Those pawns (f.i. white pawn c4, and mutually black pawn a4 in the diagram) may determined in a second pass, only considering attack spans of movable pawns.

8/8/1p6/8/p1P1p3/3pP3/1P1P4/8 w - -

Stops with negative SEE

A more sophisticated definition of backwardness was given by Vincent Diepeveen ^[2], even a member of a pawn duo may be backward, if its stop square has a negative SEE score, also considering pieces. Here b7 is considered backward, no matter whether the other friendly pawn is on c7 or c6, since it's stop square b6 has a negative SEE in both cases.

8/1pp5/8/2P5/8/8/8/1R6 w - -

Publications

Hans Kmoch (1959, 1990). Pawn Power in Chess. New York: Dover, 1990. Previous ed.: New York: McKay, 1959. ISBN 0-486-26486-6

Forum Posts

WHAT is the definition of a backward pawn? by Bas Hamstra, CCC, December 23, 2002
Backward Pawns by Mark Lefler, CCC, March 24, 2008
Doubled and Backward Pawn Engine "Definitions" by Brian Richardson, CCC, September 07, 2009
What is a backward pawn? by Lyudmil Tsvetkov, CCC, May 12, 2014

External Links

Backward pawn from Wikipedia

References

^ Re: Doubled and Backward Pawn Engine "Definitions" by Sam Hamilton, CCC, September 13, 2009
^ Re: WHAT is the definition of a backward pawn? by Vincent Diepeveen, CCC, December 24, 2002

What links here?

Page	Date Edited
Backward Pawn	May 5, 2017
Backward Pawns (Bitboards)	May 5, 2017
Bas Hamstra	Feb 4, 2018
Dartmouth CP	Jan 19, 2018
Design Principles	Jan 17, 2018
Hans Kmoch	Nov 11, 2017
Lyudmil Tsvetkov	Mar 28, 2018
Murka	Nov 11, 2016
Open Pawns (Bitboards)	Aug 24, 2017
Pawn Attacks (Bitboards)	Mar 4, 2010
Pawn chain	Jan 17, 2018
Pawn Pattern and Properties	Nov 11, 2017
PawnKing	Sep 5, 2014
Weak Pawns	Dec 19, 2013

Up one Level

Butterfly Boards

GerdIsenberg — Tue, 27 Jan 2015 19:02:19 GMT

Home * Programming * Data * Butterfly Boards

		Butterfly Boards are two-dimensional arrays (typically of various history counters for each color), indexed by the from- and to-square coordinates of (valid and likely quiet) moves, which appear inside the search. Those counters can then be used for move ordering as mentioned in the history heuristic, or to decide about late move reductions and history leaf pruning. Another application is a kind of killer- or refutation table, to store a refutation of a specific move ^[1], also base of the countermove heuristic ^[2] ^[3].
M. C. Escher, Symmetry ^[4]

Layout

The size of the array is 4K (64 x 64 = 4096) elements for each color, but the density is poor, since most from- and to-square combinations are illegal moves by the rules of chess. Thus, most entries inside the Butterfly boards are not used. Also, as an additional drawback, from-to coordinates, specially those with distance one, are ambiguous and may be legal for several pieces. For instance e2-e3 might be a rook-, queen-, king- or white pawn-move. However, knight-, rook- and bishop moves are disjoint, queen moves are the superset from rook- and bishop-moves, king-moves the one-distance subset of queen moves, and pawn pushes are subset of rook-moves, while pawn captures and en passant (if stored at all) are subset of bishop-moves.

Therefor some programmers omit the origin from-square, but use piece-type instead for denser 12 x 64 tables with only 3/4K entries - or exclude not only captures, but also pawn pushes and/or king moves. Other programmers have abandoned hashing moves for History Heuristic and LMR, and say that given enough search depth, History counters produce just some random noise ^[5] .

This is how butterfly boards may be declared in C or C++:

counterType arrWhiteButterfly[64][64]; // from, to -> 4K
counterType arrBlackButterfly[64][64]; // from, to -> 4K

counterType arrButterfly[2][64][64]; // color, from, to -> 8K

Valid Entries

As mentioned in Influence Quantity of Pieces, there are only 1792 (7/16 of 4K) possible valid moves coordinates, 9/16 of the space in the Butterfly boards is "wasted".

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

The Eponym

The name Butterfly Boards was proposed by Dap Hartmann in 1988, when he introduced the Butterfly Heuristic in the ICCA Journal ^[6], and the application of a Butterfly refutation table at the Advances in Computer Chess 6 conference in 1990 ^[7]. Plotting the illegal move coordinates as black cells # inside a 64*64 sheet, seven butterfly shaped pattern appear along the impossible move diagonal (where squares are equal).

The Butterfly

Single Shape

The thorax of the Butterfly is centered by the wraps from one rank (or dependent on the Square Mapping Considerations, one file) to the next one. With 'a1' as square null mapping, and 'd1' as square 3, 'e2' is square 12, the shape indexed by square coordinates looks as follows, covering two wrapped rank "halfs" including their center files, e.g. d1 - e2:

d e f g h a b c d e        d e f g h a b c d e
1 1 1 1 1 2 2 2 2 2        1 1 1 1 1 2 2 2 2 2
#         #           d1   # - - - - # ~ \ | /
  #       # #         e1   - # - - - # # ~ \ |
    #     # # #       f1   - - # - - # # # ~ \
      #   # # # #     g1   - - - # - # # # # ~
        # # # # # #   h1   - - - - # # # # # #
# # # # # #           a2   # # # # # # - - - -
  # # # #   #         b2   ~ # # # # - # - - -
    # # #     #       c2   \ ~ # # # - - # - -
      # #       #     d2   | \ ~ # # - - - # -
        #         #   e2   / | \ ~ # - - - - #

That is why Dap Hartmann called it Butterfly Boards.

Connected Shapes

one butterfly spans a 10 square range
n butterflies span an 8*n + 2 square range
seven butterflies span 58 square range, from 3 (d1) to 60 (e8)

d e f g h a b c d e f g h a b c d e       d e f g h a b c d e f g h a b c d e
1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3       1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3
#         #                          d1   # - - - - # ~ \ | / ~ # # # \ ~ | ~
  #       # #                        e1   - # - - - # # ~ \ | / ~ # # # \ ~ |
    #     # # #                      f1   - - # - - # # # ~ \ | / ~ # # # \ ~
      #   # # # #                    g1   - - - # - # # # # ~ \ | / # # # # \
        # # # # # #                  h1   - - - - # # # # # # ~ \ | # # # # #
# # # # # #                          a2   # # # # # # - - - - - - - | / ~ # #
  # # # #   #                        b2   ~ # # # # - # - - - - - - \ | / ~ #
    # # #     #                      c2   \ ~ # # # - - # - - - - - ~ \ | / ~
      # #       #         #          d2   | \ ~ # # - - - # - - - - # ~ \ | /
        #         #       # #        e2   / | \ ~ # - - - - # - - - # # ~ \ |
                    #     # # #      f2   ~ / | \ ~ - - - - - # - - # # # ~ \
                      #   # # # #    g2   # ~ / | \ - - - - - - # - # # # # ~
                        # # # # # #  h2   # # ~ / | - - - - - - - # # # # # #
                # # # # # #          a3   # # # # # | \ ~ # # # # # # - - - -
                  # # # #   #        b3   \ # # # # / | \ ~ # # # # - # - - -
                    # # #     #      c3   ~ \ # # # ~ / | \ ~ # # # - - # - -
                      # #       #    d3   | ~ \ # # # ~ / | \ ~ # # - - - # -
                        #         #  e3   ~ | ~ \ # # # ~ / | \ ~ # - - - - #

C-Code

Some arbitrary C-code, to produce the plot:

#include "stdafx.h"
#include <math.h>
 
void butterflyBoard(int from, int to) {
   int sq1, sq2, f1, f2, r1, r2, df, dr;
   int nr = 0, nb = 0, nn = 0;
   for (sq2 = from; sq2 <= to; sq2++)
      printf("%c", (sq2 % 10) ? ' ' : '0' + (sq2/10) );
   printf("\n");
   for (sq2 = from; sq2 <= to; sq2++)
      printf("%1d", sq2 % 10 );
   printf("\n");
   for (sq1 = from; sq1 <= to; sq1++) {
      for (sq2 = from; sq2 <= to; sq2++) {
         if ( sq1 != sq2 ) {
            r1 = sq1 >> 3;
            r2 = sq2 >> 3;
            if (r1 == r2) { // same rank
               nr++;
               printf("-");
               continue;
            }
            f1 = sq1 & 7;
            f2 = sq2 & 7;
            if ( f1 == f2 ) { // same file
               nr++;
               printf("|");
               continue;
            }
            if  (f1 - r1 == f2 - r2) { // same diagonal
               nb++;
               printf("/");
               continue;
            }
            if  (f1 + r1 == f2 + r2) { // same anti-diagonal
               nb++;
               printf("\\");
               continue;
            }
            df = abs (f2 - f1);
            dr = abs (r2 - r1);
            if ( df + dr == 3 )    { // knight distance
               nn++;
               printf("~");
               continue;
            }
         }
         printf("#"); // invalid
      }
      printf(" %2d\n", sq1);
   }
   printf("rook   moves %4d\n", nr);
   printf("bishop moves %4d\n", nb);
   printf("knight moves %4d\n", nn);
   printf("total  moves %4d\n", nr + nb + nn);
}
 
int main(int argc, char* argv[])
{
   butterflyBoard(3, 20); // 0, 63
   return 0;
}

Analogy in Astronomy

Dap Hartmann found a nice analogy in astronomy. Edward Maunders was the first astronomer (1904) to plot the distribution in heliographic latitude of the centers of sunspot groups as a functions of time:

A modern version of the Mauders' sunspot "butterfly diagram" ^[8] .

Publications

Jonathan Schaeffer (1983). The History Heuristic. ICCA Journal, Vol. 6, No. 3
Dap Hartmann (1988). Butterfly Boards. ICCA Journal, Vol. 11, Nos. 2/3
Dap Hartmann, Peter Kouwenhoven (1991). Sundry Computer Chess Topics. Advances in Computer Chess 6
Jos Uiterwijk (1992). The Countermove Heuristic. ICCA Journal, Vol. 15, No. 1

External links

AVR Butterfly Board from Asuro Wiki (German)

Wikipedia

Butterflies from Wikipedia ^[9]

Butterfly insect of the order Lepidoptera
Butterfly Game a two-player abstract strategy game from Mozambique
BBN Butterfly a massively parallel computer from the 1980s
Butterfly diagram in the context of fast Fourier transform ^[10] algorithms
Butterfly or Zassenhaus lemma
Schmetterlingsgraph (German)
Butterfly knot
Butterfly theorem in elementary geometry
Butterfly curve (algebraic)
Butterfly curve (transcendental)
Butterfly catastrophe Catastrophe theory
Butterfly options a combination option trade strategy
Iron Butterfly spread
Iron Butterfly (band)
Butterfly ballot
Butterfly effect in the context of Chaos theory
The Butterfly Effect (Film)
The Butterfly Effect (band)

Musicvideo

Herbie Hancock & The Headhunters, Butterfly, 1974, YouTube Video

References

^ Dap Hartmann, Peter Kouwenhoven (1991). Sundry Computer Chess Topics. Advances in Computer Chess 6
^ Jos Uiterwijk (1992). The Countermove Heuristic. ICCA Journal, Vol. 15, No. 1
^ Re: History pruning / move ordering question by Don Dailey, CCC, May 10, 2013
^ Picture gallery "Symmetry" from The Official M.C. Escher Website
^ Re: LMR: history or not? by Robert Hyatt from CCC, December 13, 2007
^ Dap Hartmann (1988). Butterfly Boards. ICCA Journal, Vol. 11, Nos. 2/3
^ Dap Hartmann, Peter Kouwenhoven (1991). Sundry Computer Chess Topics. Advances in Computer Chess 6
^ Edward Walter Maunder, Solar observations A modern version of the Mauders' sunspot "butterfly diagram". (This version from the solar group at NASA Marshall Space Flight Center.)
^ Butterfly (disambiguation) from Wikipedia
^ Fast Fourier Transform (FFT) from Reliable Software

What links here?

Page	Date Edited
Array	Dec 1, 2016
Bobby	Jan 7, 2016
Butterfly Boards	Jan 27, 2015
Butterfly Heuristic	May 6, 2016
Countermove Heuristic	Oct 1, 2017
Dap Hartmann	Jun 10, 2017
Dappet	Dec 12, 2016
Data	Nov 26, 2017
Dictionary	Aug 24, 2017
Direction	Oct 6, 2016
Encoding Moves	Mar 27, 2016
History Heuristic	Jul 19, 2017
History Leaf Pruning	Apr 15, 2013
ICGA Journal	Dec 21, 2017
Influence Quantity of Pieces	Jul 21, 2017
Last Best Reply	Jul 6, 2013
Mathematician	Apr 9, 2018
Moves	Feb 19, 2018
Neural MoveMap Heuristic	Sep 24, 2015
Relative History Heuristic	Jun 8, 2015
Squares	Feb 15, 2015
Table-driven Move Generation	Feb 19, 2017
Vector Attacks	Dec 15, 2017

Up one Level

Candidate Passed Pawn

GerdIsenberg — Sat, 11 Nov 2017 09:32:23 GMT

Home * Evaluation * Pawn Structure * Candidate Passed Pawn

		Candidate passed pawn, a pawn on a half-open file, which, if the board had only pawns on it, would eventually become a passed pawn by moving forward. Whereas this definition is obvious for a human, in a form presented above it would require no less than a separate recursive search routine. For that reason, computers have to use approximations of that rule. One possibility is to define a pawn as a candidate, if no square on its path is controlled by more enemy pawns than own pawns. However, this simple heuristics rules out an early recognition of a candidate passed pawns. For example with white pawns on a4 and b5 and black pawn on a7, the b5 pawn would be viewed as a candidate passer only after a4-a5.
White and Black candidates (b5, g5)

Forum Posts

How to define a candidate passer by Jan Willem de Kort, CCC, January 03, 2006
Outside passer and candidate passer: definition wanted! :-) by Alessandro Scotti, CCC, February 27, 2006
Improving evaluation of passed pawns by Ben-Hur Carlos Vieira Langoni Junior, CCC, January 22, 2011 » Passed Pawn

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

What links here?

Page	Date Edited
More Links
Alessandro Scotti	Feb 27, 2014
Ben-Hur Carlos Vieira Langoni Junior	Dec 17, 2013
Bismark	Apr 22, 2015
Candidate Passed Pawn	Nov 11, 2017
Candidates (Bitboards)	Nov 11, 2017
Chexa	Feb 18, 2014
Clarabit	Nov 3, 2011
Coiled	Mar 12, 2017
Dartmouth CP	Jan 19, 2018
Dictionary	Aug 24, 2017
Doubled Pawn	Mar 27, 2017
Faker	Nov 11, 2017
Garbochess	Sep 23, 2017
Hans Kmoch	Nov 11, 2017
Hidden Passed Pawn	Nov 11, 2017
ISA	Apr 2, 2018
Nebula	Feb 7, 2015
Open Pawns (Bitboards)	Aug 24, 2017
Outside passed pawn	Jun 7, 2012
Passed Pawn	Oct 11, 2017

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

Connected Passed Pawns

GerdIsenberg — Fri, 27 Mar 2015 19:27:45 GMT

Home * Evaluation * Pawn Structure * Passed Pawn * Connected Passed Pawns

Connected Passed Pawns,
two or more passed pawns on adjacent files, either as duo mutually protecting their stop squares, or as protected passed pawn defended by the second passer, may advance in tandem and are more difficult to blockade than isolated passers. In a chain they may be best countered by a bishop blocking or controlling their stop squares. The opponent king can also hold the chain on both stop squares, but is often obligated to stay inside the square of the more advanced peak. Connected passers are in particularly strong in rook endgames, but may be worse than two distant isolated passers in pawn endgames ^[1].

Forum Posts

WAC.002 by evaluation? by Luca Hemmerich, CCC, April 18, 2010 » Win at Chess
Improving SF passer code by Lyudmil Tsvetkov, CCC, March 26, 2015 » Stockfish

External Links

References

^ Re: passed pawn evaluation by Robert Hyatt, CCC, January 12, 2004

What links here?

Page	Date Edited
Amyan	Dec 10, 2013
Bishops of Opposite Colors	Aug 22, 2012
Blockade of Stop	Oct 11, 2016
Cheese	Feb 17, 2018
Chunker	Jul 12, 2016
Connected Passed Pawns	Mar 27, 2015
Luca Hemmerich	Jun 19, 2017
Outside passed pawn	Jun 7, 2012
Passed Pawn	Oct 11, 2017
Pawn Endgame	Oct 11, 2017
Protected Passed Pawn	Jun 7, 2012
Shield	May 17, 2017
Stockfish	Apr 7, 2018
Tucano	Dec 16, 2017
Win at Chess	Sep 25, 2017
Wing	Oct 26, 2017
Zurichess	Mar 12, 2018

Up one Level

Corresponding Squares

GerdIsenberg — Mon, 09 Oct 2017 19:01:00 GMT

Theory

Finding Critical Squares

Constructing Corresponding Square System

Using the Corresponding Square System

Computer Chess Implementation

Algorithm by Moshammer

Home * Evaluation * Game Phases * Endgame * Pawn Endgame * Corresponding Squares

Corresponding Squares, also called Co-ordinate Squares is a concept to analyze pawn endgames. Using retrograde analysis, Zugzwang positions and Critical Squares are found. Corresponding Squares Systems were one of the first human attempts of finding formulas and finally solving certain chess positions. This concept is only possible due to the limited mobility in pawn endgames. King-oppositions and Zugzwangs are the main motives arising.

Theory

To get an idea, the concept is described using an example position by Charles Dealtry Lockock, 1892 ^[1] :

Finding Critical Squares

In the presented position there exist two critical squares. First when the white king reaches d4, white threatens 1. e5 dxe5 2. Kxe5 (threatening attacking both Pd7 and Pg4 in the next move). To defend this threat the black king must be able to move to f6 after Kd4. Secondly when the white king reaches e3, white threatens 1. Kf4 ... 2. Kxg4. In order to avoid this the black king must stand on g5.

To summarize, the two critical squares are e5 and f4. The according corresponding squares where both sides have mutual zugzwang are Kd4 - Kf6 and Ke3 - Kg5.

Constructing Corresponding Square System

This particular example, where two Corresponding Squares are connected diagonally and there is enough space for a 3x3 square, Averbakh called the eight-square system. The construction of this Corresponding Square System starts with numbering the first two Corresponding Squares 1 and 2 accordingly. The square connecting the two receives the number 3. The outer squares of the 3x3 field receive the numbers 4 to 8. Further outside the numbering can continue by using the number of a square exactly two squares away either diagonally, horizontally or vertically. The image below should exemplify this process.

Using the Corresponding Square System

The numbers tell us that if the white king manages to step on a square with the same number as the square on which the black king is standing, he automatically wins the fight for the critical squares. The same case occurs if the white king can step on a square the black king can not reach in the next move. The contrary is also possible. As soon as the black king moves on the same numbered square as the white king he can automatically defend the Corresponding Squares.

The way to take advantage of the Corresponding Square System is easy now. White must move towards the critical squares, never stepping on squares the black king can defend.

1. Kb1! (steps on 3, the black king can not reach any 3-squares) Kg7
2. Kc1 (steps on the same number as the black king: 5) Kg6
3. Kd1 Kg5 4. Kc2 Kh5 5. Kc3 Kg5 6. Kc4 Kg6 7. Kd3 Kg5 8. Ke3

Computer Chess Implementation

First of all it must be noted that the concept of Corresponding Squares was designed to give the human chess player a tool to efficiently analyze a complex pawn endgame. Computers can very easily solve such positions using their Transposition Tables. Just as an example it takes Computers only a couple of seconds to reach > depth 20 in the Lasker-Reichhelm position, also referred as Fine #70 ^[2] and thus find the opponent's Zugzwang. Nevertheless Computers also have some disadvantages. The main problem is the point where the chess engine has to decide whether to enter a certain pawn ending or not. Usually these positions offer a lot more mobility, thus conducting a deep enough search seems infeasible.

The first attempt of tackling Corresponding Squares with a computer chess engine was made by Rafael B. Andrist and his chess program Wilhelm ^[3] ^[4] .

More recent research was done by Edmund Moshammer:

Algorithm by Moshammer

In principle this approach is quite similar to an Endgame Tablebase Generation process. The main difference is its optimization to be used on the fly in chess engines. To represent the Corresponding Squares 64 bitboards are used, which for every position of the attacking king represent the squares where the opponent king must stand to prevent the attacker from achieving a predefined objective.

definitions:

U64 legalSq[2]; // stores the squares where attacking/defending king may move to
                //     (ie.: not attacked by a pawn or occupied by a own pawn)
U64 coSq[64];   // stores the Corresponding Squares for each attacking king position
U64 bbSQ[64];   // bbSQ[i] = 1 << i;
int kingmoves[8] = {-9, -8, -7, -1, 1, 7, 8, 9};  // used for move generation later
 
U64 mgen_fill_KING(U64 squares);  // shifts squares one step in all 8 directions

The main retrograde routine to build the Corresponding Square system:

initialize coSq: for every position of the attacking king, the defending one may not stand on neighboring squares or squares previously defined illegal (attacked by attacker's pawns or occupied by own pawns)
set changes to a full bitboard - ie: all squares have to be looked at in the first pass
loop until all Zugzwang situations have been resolved:changes == 0
loop through all unresolved positions of the board
- reset the square on 'changes', as the position is being examined now
- initialize Katt: squares from which the attacking King can move to attack the current square
- initialize Kdef: squares from which the defending King can defend the attacking king to reach the current square - ie: the neighboring squares of the current square and the squares one king move away from the corresponding squares of the current position
- for each of the attacking king moves
  - checks that the move is on the board and is part of the legal moves (Katt)
  - if coSq is changed on the resulting position, set 'changes' accordingly, so that the changes are considered in the next pass
  - the Corresponding Squares of each neighboring attacking King position have to collide with the Corresponding Squares one Kingmove away from this position

// attacker .. attacking side
// coSq ...... pointer to the Corresponding Squares Bitboards
 
void coSq_setupSystem(int attacker, U64 * coSq) {
    for (int i=0; i<64; i++) coSq[i] &= ~mgen_fill_KING(bbSQ[i]) & ~bbSQ[i] & legalSq[!attacker];
 
    U64 changes = 0xFFFFFFFFFFFFFFFF;
    while (changes) {
        for (int i=0; i<64; i++) {
            if (changes & bbSQ[i]) {
                changes ^= bbSQ[i];
                U64 Katt = mgen_fill_KING(bbSQ[i]) & legalSq[attacker];
                U64 Kdef = mgen_fill_KING(bbSQ[i]) | mgen_fill_KING(coSq[i]);
 
                for (int j=0; j<8; j++) {
                    int Ksq = i + kingmoves[j];
                    if (!(Ksq & ~0x3F) && (bbSQ[Ksq] & Katt)) {
                        changes |= bbSQ[Ksq] * ((coSq[Ksq] & ~Kdef) != 0);
                        coSq[Ksq] &= Kdef;
                    }
                }
            }
        }
    }
}

Before the function above is called, the Corresponding Squares must be initialized. Therefore all bits in the coSq-bitboards get set. Then the first Critical Squares are defined by setting the bitboard of the attacking king at the Critical Square to 0. In other words, if the king manages to occupy the square the defending king has no squares to stand on from which he can defend the threat.

The setupSystem function itself does nothing else than looping through the bitboards and uses the rule that the defending king may only stand on a square from which he can reach all corresponding squares the attacking king may create within one move. This is done as long as no further changes are made to the bitboard.

The time it takes to analyze a position is about linear. For the Lasker-Reichhelm position (Fine #70), it took 10 cycles through the 64 squares of the board to find out that the black king can impossibly defend all of its pawns.

There is however one open question - the definition of the Critical Square. A straight forward approach would be to set the critical Squares to capturing the opponent's pawns. If in the end alpha > 0 and the defending king is standing on a Corresponding Square one can safely fail low at that point. A more complex approach would be necessary to find out whether a position is won or drawn.

Publications

Vitaly Halberstadt and Marcel Duchamp (1932). L'opposition et les cases conjuguées sont réconciliées.
Paris-Brussels 1932, German Edition 2001 Opposition und Schwesterfelder, ISBN 3-932170-35-0
Kenneth W. Church (1978). Co-ordinate Squares: A Solution to Many Chess Pawn Endgames. B.Sc. thesis, Massachusetts Institute of Technology, reprinted 1988 in Computer Chess Compendium
Kenneth W. Church (1979). Co-ordinate Squares: A Solution to Many Chess Pawn Endgames. (abbreviated version of B.Sc. thesis), IJCAI-79, Tokyo, Japan
Peter W. Frey, Larry Atkin (1979). Creating a Chess-Player, Part 4: Thoughts on Strategy. In Blaise W. Liffick (ed.), The Byte Book of Pascal, pp. 143-155. Byte Publications, also BYTE, Vol. 4, No. 1
Mike Clarke (1980). The Theory of Coordinate Squares. Advances in Computer Chess 2, pp. 97-102
Yuri Averbakh, Ilia Maizelis (1987). Comprehensive Chess Endings Vol 4: Pawn Endings. Cadogan Books 1987
Karsten Müller, Frank Lamprecht (2000). Secrets of Pawn Endings. Everyman Chess, (2007). re-issue by Gambit Publications
Karsten Müller (2004). Endgame Corner - The Mystical Sister Squares, pdf from ChessCafe.com
Omid David, Ariel Felner, Nathan S. Netanyahu (2004). Blockage Detection in Pawn Endgames. ICGA Journal, Vol. 27, No. 3

Postings

chess program "Wilhelm" released by Rafael B. Andrist, CCC, August 19, 2001
Re: Fine 70 same 7 engines (more) by Rafael B. Andrist, CCC, September 10, 2001
A new(?) technique to recognize draws by Heiner Marxen, CCC, June 01, 2002 » Chest
Corresponding squares, easy position by Vincent Lejeune, CCC, September 20, 2012
Corresponding Squares 1 by Árpád Rusz, Chess Endgame Study Composition, November 24, 2016

External Links

References

^ Position by Charles Dealtry Lockock, 1892, from Yuri Averbakh, Ilia Maizelis (1987). Comprehensive Chess Endings Vol 4: PawnEndings, Cadogan Books 1987.
^ Reuben Fine (1941). Basic Chess Endings
^ chess program "Wilhelm" released by Rafael B. Andrist, CCC, August 19, 2001
^ Gegenfeldsysteme und Schachprogramm by Rafael B. Andrist, ChessBits Forum, August 19, 2001 (German)

What links here?

Page	Date Edited
Árpád Rusz	Oct 9, 2017
Blockage Detection	Oct 19, 2017
Byte Magazine	Nov 20, 2016
Chest	Mar 3, 2015
Corresponding Squares	Oct 9, 2017
Draw	Apr 14, 2018
Edmund Moshammer	Sep 23, 2017
Endgame	Sep 18, 2017
Fill Algorithms	Nov 6, 2013
Heiner Marxen	Apr 19, 2014
Kenneth W. Church	Nov 12, 2014
King	Feb 26, 2013
Lasker-Reichhelm Position	Oct 24, 2017
Nexus	Jan 7, 2016
Opposition	Dec 2, 2014
Pawn Endgame	Oct 11, 2017
Peasant	May 21, 2015
Rafael B. Andrist	May 30, 2017
Repetitions	Jan 16, 2018
Retrograde Analysis	Mar 21, 2017
Squares	Feb 15, 2015
Triangulation	Apr 4, 2013
Wilhelm	Oct 6, 2015
Zugzwang	Dec 8, 2017

Up one level

Defended Pawns (Bitboards)

GerdIsenberg — Fri, 27 Feb 2015 14:46:51 GMT

Defended

Defenders

Defended Defenders

Not Defended Defenders

Not Defending Defended

Forum Posts

What links here?

Home * Board Representation * Bitboards * Pawn Pattern and Properties * Defended Pawns

Working in the bitboard centric world to determine pawn related pattern set-wise.

Each pawn, member of the own pawn attack set is obviously defended by a pawn, thus likely not a winning capture target for opponent pieces (except pawns). If a defended pawn is open, opponent rooks on half-open files bang one's head against a brick wall.

Defended

Again, it is advantageous to keep disjoint east-west attack sets for a unique 1:1 source-target relationship. On demand we can use the union or intersection on the fly. Note that attack direction is related to the target square. East attack is from south/north-west to north/south-east

white pawns         defended            defended
                    from west ->        from east <-
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . 1 . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . 1 .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

U64 wPawnDefendedFromWest(U64 wpawns) {
   return wpawns & wPawnEastAttacks(wpawns);
}
 
U64 wPawnDefendedFromEast(U64 wpawns) {
   return wpawns & wPawnWestAttacks(wpawns);
}

Defenders

To get the set of defenders on the fly, we use the intersection of white pawns with it's "black" attacks:

white pawns         defenders           defenders
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . . .
. . 1 . . . . 1     . . 1 . . . . .     . . . . . . . 1
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

U64 wPawnDefendersFromWest(U64 wpawns) {
   return wpawns & bPawnWestAttacks(wpawns);
}
 
U64 wPawnDefendersFromEast(U64 wpawns) {
   return wpawns & bPawnEastAttacks(wpawns);
}

Otherwise, if the set of defenders was already determined (or vice versa), we can already take advantage of the unique target/source relation ship:

wPawnDefendersFromWest = wPawnDefendedFromWest >> 9;
wPawnDefendersFromEast = wPawnDefendedFromEast >> 7;

Defended Defenders

Defended defenders already are the inner pawns of a at least triple-chain, the d5 pawn for instance:

white pawns         defended            defended
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . 1 . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . 1 .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
 
white pawns         defenders           defenders
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . . .
. . 1 . . . . 1     . . 1 . . . . .     . . . . . . . 1
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
 
                    defenders and       defenders and
white pawns         defended            defended
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . 1 . . . .     . . . . . . . .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

Not Defended Defenders

Not defended defenders are the base of a chain - target of opponent attacks:

                    not defended        not defended
white pawns         defenders           defenders
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . . . . .     . . . . . . . .
. . . 1 . . 1 .     . . . . . . . .     . . . . . . . .
. . 1 . . . . 1     . . 1 . . . . .     . . . . . . . 1
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

Not Defending Defended

Defended pawns not defending other pawns are likely the peak of a chain.

                    not defending       not defending
white pawns         defended            defended
                    from west           from east
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . 1 . . .     . . . . 1 . . .     . . . . . . . .
. . . 1 . . 1 .     . . . . . . . .     . . . . . . 1 .
. . 1 . . . . 1     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .

Forum Posts

pattern coding in bitboards by Pawel Koziol, CCC, February 26, 2015 » Pawn chain

What links here?

Page	Date Edited
More Links
Connected Passed Pawns	Mar 27, 2015
Dartmouth CP	Jan 19, 2018
Defended Pawns (Bitboards)	Feb 27, 2015
Demolito	Mar 1, 2018
Gk	Oct 9, 2017
Pawel Koziol	Dec 17, 2017
Pawn chain	Jan 17, 2018
Pawn Levers (Bitboards)	Nov 11, 2017
Pawn Pattern and Properties	Nov 11, 2017
Protected Passed Pawn	Jun 7, 2012

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

Double and Triple (Bitboards)

GerdIsenberg — Thu, 12 May 2016 19:25:45 GMT

Home * Board Representation * Bitboards * Pawn Pattern and Properties * Double and Triple

By Square

Working in the square centric world of the board implies using a square index of one particular pawn, likely from bitboard traversal.

For doubled (twins) or multiple pawns on a file, we simply intersect the file-mask by own-pawns and perform a population count. This symmetrical property appears to be equal for white and black pawns, except for the before- and behind semantic.

wPawnsOnFile = arrFiles[sqOfWhitePawn] & pawnBB[white];
if ( wPawnsOnFile & (wPawnsOnFile-1) ) -> white pawn is a least double pawn
if ( wPawnsOnFile & arrNortRay[sqOfWhitePawns] ) -> white pawn has own pawn ahead
if ( wPawnsOnFile & arrSoutRay[sqOfWhitePawns] ) -> white pawn has own pawn behind

arrFiles[d*]
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .
. . . 1 . . . .

The arrFiles might be condensed to eight bitboards only, instead of 64 - if we index by

file(sq) == sq & 7

instead of square.

Multiple Pawns

Working in the bitboard centric world to determine pawn related pattern set-wise.

All pawns that are member of the rearspan of all own pawns, have at least one pawn in front on the same file. All pawns that are member of the frontspan of all own pawns, have at least one pawn behind on the same file.

// pawns with at least one pawn in front on the same file
U64 wPawnsBehindOwn(U64 wpawns) {return wpawns & wRearSpans(wpawns);}
 
// pawns with at least one pawn behind on the same file
U64 wPawnsInfrontOwn (U64 wpawns) {return wpawns & wFrontSpans(wpawns);}

Obviously, since each pawn in front of a pawn implies this pawn behind, the number of pawns in front is equal the number of pawns behind.

popCount(wPawnsBehindOwn) == popCount(wPawnsInfrontOwn)

The intersection of both sets implies at least a triple, thus a pawn in front and behind.

U64 wPawnsInfrontAndBehindOwn (U64 wpawns) {
   return wPawnsInfrontOwn(wpawns) &  wPawnsBehindOwn(wpawns);
}

If the intersection is empty on a file, it is a double pawn or a twin.

fileWithAtLeastTriple = fileFill(infrontAndBehindOwn);
rearTwin  = behindOwn  & ~fileWithAtLeastTriple;
frontTwin = infrontOwn & ~fileWithAtLeastTriple;

Forum Posts

Doubled and Backward Pawn Engine "Definitions" by Brian Richardson, CCC, September 07, 2009
Doubled pawns by Stefano Gemma, CCC, May 11, 2016

What links here?

Page	Date Edited
Aegon 1993	Mar 26, 2017
Dispersion and Distortion	Nov 11, 2017
Double and Triple (Bitboards)	May 12, 2016
Doubled Pawn	Mar 27, 2017
Hans Kmoch	Nov 11, 2017
Pawn Pattern and Properties	Nov 11, 2017

Up one Level

Doubled Pawn

GerdIsenberg — Mon, 27 Mar 2017 14:06:49 GMT

Types of Doubled Pawns

Crippled Majority

All About Doubled Pawns

Home * Evaluation * Pawn Structure * Doubled Pawn

A Pawn is doubled (or, sad to say, tripled) if there are more pawns of the same color on a given file. Early programs and papers advocated evaluation it as half a pawn, today the penalty uses to be less severe.

It might be argued that, given a perfect pawn structure evaluation, a term such as doubled pawns would not be needed, since they usually introduce another pawn structure weaknesses: some kind of backwardness, lack of a candidate passer that otherwise would be there etc. However, most evaluation functions do not go into such details as to justify removing this term.

Types of Doubled Pawns

Hans Berliner characterizes doubled pawns by their exchange potential against opponent pawns on adjacent files ^[1]^[2]:

		`The doubled pawns on the b-file are the best situation, the f-file pawns are next. The h-file pawns are the worst situation because two pawns are held back by one opposing pawn, so the second pawn has little value.`
8/1p6/p3pp1p/8/8/1PP2P1P/1P3P1P/8 w - -

Crippled Majority

A doubled pawn of a so called "crippled" majority devalue that majority. Hans Berliner on following position in Some Innovations Introduced by Hitech ^[3]:

		`Our pawn-structure algorithm is quite simple, detecting only isolated and multiple Pawns, and the effect of multiple Pawns on viable pawn majorities. For instance, in Diagram 1 the value of White's doubled Pawn is negligible, while Black's is almost full-valued. This distinction, an innovation, was first introduced in Patsoc ^[4], and we were able to adapt the code to make up tables to be loaded into six identical hardware units computing pawn structure in parallel.`
8/1pp2ppp/1p6/8/8/5P2/PPP2PPP/8 w - -

All About Doubled Pawns

The vast amount of detailed knowledge about doubled pawns, which rarely gets implemented, can be found in the article All About Doubled Pawns by Larry Kaufman ^[5].

Publications

Larry Kaufman (2005). All About Doubled Pawns. (first published in Chess Life, May 2005, p.22)

Forum Posts

Doubled and Backward Pawn Engine "Definitions" by Brian Richardson, CCC, September 07, 2009
passed but doubled pawns by Jon Dart, CCC, June 15, 2015 » Passed Pawn
Doubled pawns by Stefano Gemma, CCC, May 11, 2016

External Links

Doubled Pawn from Wikipedia
All About Doubled Pawns by IM Larry Kaufman
Doubled Pawns Strength and weakness by Georgi Orlov
Ástor Piazzolla - Tristezas de un Doble A, Montreux Jazz Festival, 1985 YouTube Videos

References

^ Hans Berliner (1999). The System: A World Champion's Approach to Chess, Gambit Publications, ISBN 1-901983-10-2
^ Types of doubled pawns from Wikipedia
^ Hans Berliner (1987). Some Innovations Introduced by Hitech. ICCA Journal, Vol. 10, No. 3, pp. 111-117
^ Hans Berliner (1985). Computer Chess at Carnegie Mellon University. Advances in Computer Chess 4
^ Larry Kaufman (2005). All About Doubled Pawns. (first published in Chess Life, May 2005, p.22)

What links here?

Page	Date Edited
More Links
Alarm	Jun 7, 2017
Amyan	Dec 10, 2013
Applied Concepts	Dec 25, 2017
Bismark	Apr 22, 2015
Cheese	Feb 17, 2018
Cheops (Miller)	Jan 13, 2017
chess22k	Apr 23, 2018
ChessBrainVB	Jun 24, 2017
Clarabit	Nov 3, 2011
Coiled	Mar 12, 2017
Cyrus	Jul 22, 2014
Dartmouth CP	Jan 19, 2018
Defenchess	Mar 18, 2018
Diablo	May 17, 2016
Dispersion and Distortion	Nov 11, 2017
Donna	Aug 17, 2017
Dorpsgek	Apr 2, 2018
Double and Triple (Bitboards)	May 12, 2016
Doubled Pawn	Mar 27, 2017
Eval Tuning in Deep Thought	Jun 7, 2016
Evaluation function draft	Jul 11, 2014
Evaluation Overlap	Jul 19, 2016
Exacto	Oct 3, 2015
Garbochess	Sep 23, 2017
Gk	Oct 9, 2017
Gogobello	Jul 30, 2017
GopherCheck	Feb 3, 2017
Hakkapeliitta	Apr 26, 2016
Hans Kmoch	Nov 11, 2017
ISA	Apr 2, 2018
Kaissa	Apr 9, 2018
Larry Kaufman	Jan 28, 2018
Marvin	Feb 10, 2018
Nebula	Feb 7, 2015
Neurosis	Dec 23, 2017
Passed Pawn	Oct 11, 2017
Patsoc	Jan 7, 2016
Paul	Jan 8, 2016
Pawn Center	Feb 12, 2015
Pawn Majority	Jun 8, 2012

Up one Level

Duo Trio Quart (Bitboards)

GerdIsenberg — Fri, 18 Aug 2017 17:28:27 GMT

Home * Board Representation * Bitboards * Pawn Pattern and Properties * Duo Trio Quart

Pawn-Duo, (Phalanx) ^[1]
two adjacent pawns of the same color on the same rank that mutually cover the other's stop square. A Trio are three horizontal friendly pawns, a Quart four horizontal friendly pawns.

Working in the bitboard centric world to determine pawn related pattern set-wise.

The code snippets rely on shifting bitboards, specially by one step only.

Neighbors

To get pawns with east or west neighbors is simple:

U64 pawnsWithEastNeighbors(U64 pawns) {
   return pawns & westOne (pawns);
}
 
U64 pawnsWithWestNeighbors(U64 pawns) {
   return pawnsWithEastNeighbors(pawns) << 1; // * 2
}

U64 pawnsWithWestNeighbors(U64 pawns) {
   return pawns & eastOne (pawns);
}
 
U64 pawnsWithEastNeighbors(U64 pawns) {
   return pawnsWithWestNeighbors(pawns) >> 1;
}

pawns               pawns with east     pawns with west     pawns with east
                    neighbors           neighbors           and west neighbors
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
1 1 1 . . . . .     1 1 . . . . . .     . 1 1 . . . . .     . 1 . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . 1 1 .     . . . . . 1 . .     . . . . . . 1 .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .

Neighbor Algebra

Pawns with east or west neighbors are at least member of a duo. Pawns with east and west neighbors at least member of a trio. If two neighbors have both east and west neighbors, it is at least a quart.

An exclusive pawn duo is therefor a pawn with one neighbor, while this neighbor has no other neighbor as well.

U64 duo (U64 pawns) {
   U64 withWestNeighbors = pawnsWithWestNeighbors(pawns);
   U64 withEastNeighbors = withWestNeighbors >> 1;
 
   U64 withOneExclusiveNeighbor  = withWestNeighbors ^ withEastNeighbors;
   U64 withExclusiveWestNeighbor = withWestNeighbors & withOneExclusiveNeighbor;
   U64 withExclusiveEastNeighbor = withEastNeighbors & withOneExclusiveNeighbor;
 
   U64 duoWestOne = withEclusiveEastNeighbor & (withEclusiveWestNeighbor >> 1);
   U64 duoEastOne = duoWestOne << 1;
   return duoWestOne | duoEastOne;
}

pawns               pawns with excl.    pawns with excl.    duo
                    east neighbor       west neighbor
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
1 1 1 . . . . .     1 . . . . . . .     . . 1 . . . . .     . . . . . . . .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .
. . . . . 1 1 .     . . . . . 1 . .     . . . . . . 1 .     . . . . . 1 1 .
. . . . . . . .     . . . . . . . .     . . . . . . . .     . . . . . . . .

Forum Posts

The phalanx concept by Lyudmil Tsvetkov, CCC, May 21, 2014

External Links

Pawn Structure (General) | Page 5 of 5 | Phalanx Formation
Duet from Wikipedia
Phalanx from Wikipedia
Trio from Wikipedia
Kinga Głyk Trio - Walking Baby, VisionInMusica, Terni, March 10, 2017, YouTube Video
Kinga Głyk, Irek Głyk, Rafal Stepien
Quart (disambiguation) from Wikipedia
Panta Rhei plays Bartók's Quarts, 1977, YouTube Video

References

^ Pawn Structure (General) | Page 5 of 5 | Phalanx Formation

What links here?

Page	Date Edited
Backward Pawns (Bitboards)	May 5, 2017
ChessBrainVB	Jun 24, 2017
Connected Passed Pawns	Mar 27, 2015
Dartmouth CP	Jan 19, 2018
Demolito	Mar 1, 2018
Design Principles	Jan 17, 2018
Duo Trio Quart (Bitboards)	Aug 18, 2017
En prise	Oct 11, 2016
GopherCheck	Feb 3, 2017
Hanging pawns	Aug 5, 2015
Hanging Piece	Jan 14, 2017
Hans Kmoch	Nov 11, 2017
Isolated Pawns (Bitboards)	Nov 18, 2012
Kaissa	Apr 9, 2018
Lyudmil Tsvetkov	Mar 28, 2018
Pawn Pattern and Properties	Nov 11, 2017
Pawn Structure	Oct 2, 2017
Pawns Breakthrough	May 4, 2014
Protected Passed Pawn	Jun 7, 2012
Stockfish	Apr 7, 2018

Up one Level

Evaluation of Pieces

GerdIsenberg — Mon, 08 Jan 2018 21:52:17 GMT

Home * Evaluation * of Pieces

This page serves as a quick reference for those who look for ideas about evaluating different kinds of pieces.

Pawn

Pawn Structure
Pawn Center
Blockade of Stop
penalty for "d" and "e" pawns blocked on their initial squares

Knight

Decreasing value as pawns disappear
Outposts
Knight trapped on A8/H8/A7/H7 or A1/H1/A2/H2 - see Trapped Pieces
Penalty for blocking a "c" pawn in closed openings (Crafty defines it as follows: white knight on c3, white pawns on c2 and d4, no white pawn on e4)
When calculating knight mobility, it is advisable to omit squares controlled by enemy pawns
Marginal bonus for a knight defended by a pawn
Penalty for an undefended minor piece (Stockfish)

Bishop

Bad Bishop
Bishop Pair
Bishop versus Knight
Color Weakness
Fianchetto
Returning Bishop
Bishop trapped by enemy pawns on A2/H2/A7/H7 or on A3/H3/A6/H6, see Trapped Pieces
Penalty for an undefended minor piece (Stockfish)

Rook

Increasing value as pawns disappear
Rook on open file
Rook on seventh (possibly also eigth) rank
Tarrasch Rule (Rook behind Passed Pawn)
Penalty for a Rook blocked by an uncastled King
Small bonus for a rook with enemy queen on the same file (doesn't matter if it's open or not)
Rooks defending each other (Rebel uses a piece/square table for that, making suppoeted rook on 7th rank even more valuable)

Queen

Penalty for early development ^[1]
Some programs do not evaluate queen mobility
Some versions of Fruit replace queen mobility by king tropism
If king safety evaluation relies on king tropism, queen tends to get somewhat higher bonus

King

King safety in the middlegame
King centralization in the endgame
Mate at a Glance
Penalty for standing on a wing with no pawns present in the endgame
Pins/X-ray
Castling Rights

Forum Posts

Knight Evaluation by Jonathan Rosenthal, CCC, February 24, 2015
eval pieces by Daniel Anulliero, CCC, June 15, 2015

References

^ Queen wandering, was: Crafty 14,9 by Roland Pfister, CCC, May 11, 1998

What links here?

Page	Date Edited
Bad bishop	Jun 22, 2015
Betsabe	Jul 23, 2017
BigLion	Sep 28, 2016
Bishop Pair	Sep 10, 2017
Bishop versus knight	May 17, 2016
Blockade of Stop	Oct 11, 2016
Chenard	Sep 5, 2015
Clarabit	Nov 3, 2011
Coiled	Mar 12, 2017
Color Weakness	Nov 24, 2017
Demolito	Mar 1, 2018
Evaluation	Feb 1, 2018
Evaluation of Pieces	Jan 8, 2018
Exacto	Oct 3, 2015
Faile	May 27, 2014
Genie	Feb 7, 2016
Gk	Oct 9, 2017
Ifrit	Feb 7, 2016
Influence Quantity of Pieces	Jul 21, 2017
Jabba	Sep 10, 2016
KnockOut	Sep 20, 2016
MadChess	Jul 4, 2017
Monsoon	Feb 8, 2015
Pawn Center	Feb 12, 2015
Piece-Square Tables	Mar 31, 2018
Pieces	Feb 19, 2018
Returning Bishop	Mar 16, 2013
Rival	Jul 30, 2017
Robocide	May 11, 2016
Rook on Open File	Apr 24, 2017
Rook On Seventh	May 24, 2009
Sayuri	Oct 1, 2017
Scidlet	May 31, 2014
Simplex	Mar 6, 2016
Slow Chess	May 17, 2016
Tarrasch Rule	Jun 2, 2014
Tucano	Dec 16, 2017
Tunguska	Sep 16, 2017
Y!	Sep 10, 2017

Up one Level

Faker

GerdIsenberg — Sat, 11 Nov 2017 09:14:51 GMT

Home * Evaluation * Pawn Structure * Faker

		Faker, a "faked" candidate with more opponent sentries than own helpers ^[1] ^[2]. The opponent sentries control the stop square (or tele-stop) of the faker, while the helpers defend the appropriate squares. If the number of helpers becomes equal (for instance due to a pawn-capture) the faker becomes a real candidate. A faker should not receive a candidate bonus, but is not that bad as a backward pawn. Also two opponent sentries which control the same stop square, leave a hole between both sentries, which might be considered elsewhere.
Faker c4, two sentries, but only one helper

External Links

Pawn Power in Chess by Hans Kmoch - Glossary of Terms - Chess Forums - Chess.com

Fake

Fake News

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

What links here?

Page	Date Edited
Backward Pawn	May 5, 2017
Backward Pawns (Bitboards)	May 5, 2017
Candidate Passed Pawn	Nov 11, 2017
Candidates (Bitboards)	Nov 11, 2017
Coiled	Mar 12, 2017
Dictionary	Aug 24, 2017
Faker	Nov 11, 2017
Hidden Passed Pawn	Nov 11, 2017
Pawn Structure	Oct 2, 2017

Up one Level

Half-open file

GerdIsenberg — Tue, 11 Mar 2014 19:14:27 GMT

See also

External Links

What links here?

Home * Dictionary * Half-open file

Half-open file or semi-open file, is a file on which we do not have a pawn, but the opponent has at least one. It can be used to increase the vertical mobility of the major pieces, to attack weak pawns and to pressure enemy position or to create an outpost.

External Links

Half-open file from Wikipedia

What links here?

Page	Date Edited
Backward Pawn	May 5, 2017
Battery	Jan 29, 2017
Candidate Passed Pawn	Nov 11, 2017
Dictionary	Aug 24, 2017
Exacto	Oct 3, 2015
Files	Nov 22, 2015
Half-open file	Mar 11, 2014
Hanging pawns	Aug 5, 2015
Isolated Pawn	Nov 18, 2012
Minority Attack	Jun 6, 2012
Open file	Feb 15, 2015
Open Pawns (Bitboards)	Aug 24, 2017
Outposts	Apr 24, 2017
Pawn Fills	Jul 18, 2014
Pawns and Files (Bitboards)	Jan 16, 2013
Rook on Open File	Apr 24, 2017

Up one Level

Hanging pawns

GerdIsenberg — Wed, 05 Aug 2015 21:42:03 GMT

The Hanging Pawns formation

See also

External Links

What links here?

Home * Evaluation * Pawn Structure * Hanging pawns

Hanging pawns are an open, half-isolated duo. It means that they are standing next to each other on the adjacent half-open files, usually on the fourth rank, mutually protecting their stop squares. They share a number of characteristics of weak pawns - they are not directly protected by other pawns and may become targets of attack - but unlike them they have dynamic potential of executing a pawn breakthrough and thus creating a passed pawn (admittedly being an isolated pawn at the same time). The side with hanging pawns also tends to enjoy a space advantage.

The term "hanging" in chess otherwise refers attacked to undefended pieces en prise.

The Hanging Pawns formation

8/pp3ppp/4p3/8/2PP4/8/P4PPP/8 w - -

Most of the programs do not have a special evaluation of hanging pawns, relying on search to decide if they are an asset or a liability in a given position.

External Links

The Queen's Gambit - Hanging Pawns from Pawn structure at Wikipedia
Hanging Pawns, Ten Cents a Pair review by Larry Tapper from ChessCafe.com
Hanging Pawns from chessgames.com
The Lounge Lizards - Snakes Can´t Sleep (the hanging), Jazz Gipfel 89, Liederhalle, Stuttgart, July 22, 1989, YouTube Video

What links here?

Page	Date Edited
Connected Passed Pawns	Mar 27, 2015
Dictionary	Aug 24, 2017
Duo Trio Quart (Bitboards)	Aug 18, 2017
En prise	Oct 11, 2016
Hanging pawns	Aug 5, 2015
Hanging Piece	Jan 14, 2017
Isolated Pawns (Bitboards)	Nov 18, 2012
Pawn Structure	Oct 2, 2017
Weak Pawns	Dec 19, 2013

Up one Level

Hidden Passed Pawn

GerdIsenberg — Sat, 11 Nov 2017 09:25:01 GMT

Sample

Comparison with Candidates

See also

References

What links here?

Home * Evaluation * Pawn Structure * Hidden Passed Pawn

The Hidden Passed Pawn is an evaluation term used in Crafty, in the terminology proposed by Hans Kmoch it is referred to as a Sneaker ^[1] ^[2]. It is a rammed pawn already on the opponent side of the board without further sentries, which may become a passer through a sacrificial combination usually by a faker, which possibly allows the opponent to establish a passer as well, though at least two ranks less advanced and losing the pawn race assuming both unstoppable.

Sample

Suppose that white has pawns on a6 and b5, and black on a7. At first glance we have a backward pawn on b5, which is bad for white. However, after playing b5-b6, white gets a passed pawn either there or on a6. For that reason the pawn on a6 should be termed "a hidden passed pawn" and awarded a bonus if "unstoppable".

Fakers on b5 and g4 make a6 and h5 Sneakers

Comparison with Candidates

If we put the sneakers of the above position one rank back so that they become helpers of the now neighbored candidates, the usual idea is to advance the candidates instead of the helpers. The lonesome sentry, forced to capture, may be recaptured to establish an exclusive passer on the candidate's file. Alternatively instead of the recapture, the helper may advance to become a passer as well, which yields to a transposition of the hidden passed pawn idea. This may be stronger if the pawn becomes an unstoppable passer leaving the opponent king outside its square, while the candidate could be caught.

a5 or b5?

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

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Amundsen	Sep 3, 2013
Backward Pawn	May 5, 2017
Backward Pawns (Bitboards)	May 5, 2017
Candidate Passed Pawn	Nov 11, 2017
Candidates (Bitboards)	Nov 11, 2017
Coiled	Mar 12, 2017
Dictionary	Aug 24, 2017
Hans Kmoch	Nov 11, 2017
Hidden Passed Pawn	Nov 11, 2017
Passed Pawn	Oct 11, 2017
Passed Pawns (Bitboards)	Aug 23, 2010
Pawn Endgame	Oct 11, 2017
Pawn Structure	Oct 2, 2017
Unstoppable Passer	Jun 21, 2016

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Holes

GerdIsenberg — Mon, 16 Oct 2017 19:42:41 GMT

Home * Evaluation * Pawn Structure * Holes

		Holes, squares that cannot be possibly covered by own pawns, usually also controlled by the enemy pawns. A typical example is d4 square after White forms a triangle consisting of pawns on c4, d3 and e4. Holes are excellent locations for enemy minor pieces, safer than outposts. For that reason one should keep minor pieces to cover the holes in one's position. Along with bitboard pawn patterns, holes may be determined by the relative complement of front attack spans usually restricted to the area of the own 3rd and 4th rank of the extended center.
Simulated view of a black hole ^[1]

Forum Posts

Pawn Structure "Holes" and Move Ordering by Daniel A. Thies in rgcc February 12, 1996 » Move Ordering
Re: Did Cray Blitz really have a win? by Robert Hyatt, rec.games.chess.misc, March 12, 1999 » ACM 1985, WCCC 1986, Cray Blitz

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^ Simulated view of a black hole (center) in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the Milky Way disk appears distorted into an arc. Image by Alain r, September 08, 2006 CC BY-SA 2.5, Wikimedia Commons

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ACM 1985	Jun 21, 2017
Blockade of Stop	Oct 11, 2016
CC Sapiens	Oct 29, 2014
Cray Blitz	Dec 25, 2017
Dartmouth CP	Jan 19, 2018
Demolito	Mar 1, 2018
Faker	Nov 11, 2017
Fianchetto	Feb 18, 2015
Holes	Oct 16, 2017
Move Ordering	Feb 27, 2018
Outposts	Apr 24, 2017
Pawn Structure	Oct 2, 2017

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Isolated Pawn

GerdIsenberg — Sun, 18 Nov 2012 10:38:41 GMT

Home * Evaluation * Pawn Structure * Isolated Pawn

		Isolated Pawn, a pawn with no pawns of the same color on the neighboring files. It is usually evaluated just like a backward pawn, except the penalty tends to be bigger, as it is more open to attacks. It may be considered even weaker if positioned on the half-open file, as then it is open to attack by enemy rooks. Many programs tend to evaluate an isolated pawn in the center as weaker than on the wing, as it can be attacked from more directions ^[1].
Isolated Pawn by Elke Rehder ^[2]

Examples

There is a whole class of openings characterized by the presence of an isolated queen's pawn. In exchange for this structural weakness the side with an IQP gets greater mobility, therefore this kind of positions can be used for balancing the evaluation functions parameters.

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^ Re: Self-test and others rating stuffs... by Amir Ban, CCC, January 02, 1998

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Cheese	Feb 17, 2018
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chess22k	Apr 23, 2018
ChessBrainVB	Jun 24, 2017
Clarabit	Nov 3, 2011
Coiled	Mar 12, 2017
Cyrus	Jul 22, 2014
Dartmouth CP	Jan 19, 2018
Defenchess	Mar 18, 2018
Demolito	Mar 1, 2018
Dispersion and Distortion	Nov 11, 2017
Donna	Aug 17, 2017
Dorpsgek	Apr 2, 2018
Doubled Pawn	Mar 27, 2017
Evaluation function draft	Jul 11, 2014
Evaluation Overlap	Jul 19, 2016
Exacto	Oct 3, 2015
Garbochess	Sep 23, 2017
Gk	Oct 9, 2017
Gogobello	Jul 30, 2017
GopherCheck	Feb 3, 2017
Hakkapeliitta	Apr 26, 2016
Hanging pawns	Aug 5, 2015
Hans Kmoch	Nov 11, 2017
ISA	Apr 2, 2018
Isolated Pawn	Nov 18, 2012
Isolated Pawns (Bitboards)	Nov 18, 2012
Kaissa	Apr 9, 2018
Marvin	Feb 10, 2018
Minority Attack	Jun 6, 2012
Nebula	Feb 7, 2015
Neurosis	Dec 23, 2017
NoonianChess	Jan 7, 2016
Open Pawns (Bitboards)	Aug 24, 2017
Pawn Rams (Bitboards)	Nov 11, 2017
Pawn Structure	Oct 2, 2017
Pawns and Files (Bitboards)	Jan 16, 2013

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Attack Spans

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Backward Pawn

Table of Contents

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Publications

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2000 ...

2010 ...

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Backward Pawns (Bitboards)

Table of Contents

Backward

Straggler

Telestop Weakness

Dynamic Backwardness

A further Pass

Stops with negative SEE

See also

Publications

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Butterfly Boards

Table of Contents

Layout

Valid Entries

The Eponym

The Butterfly

Single Shape

Connected Shapes

C-Code

Analogy in Astronomy

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Publications

External links

Wikipedia

Musicvideo

References

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Candidate Passed Pawn

Table of Contents

See also

Forum Posts

External Links

References

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Candidates (Bitboards)

Table of Contents

Candidate and Faker

Advanced Candidates

Less Advanced

The Sneaker

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Connected Passed Pawns

Table of Contents

See also

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Corresponding Squares

Table of Contents

Theory

Finding Critical Squares

Constructing Corresponding Square System

Using the Corresponding Square System

Computer Chess Implementation

Algorithm by Moshammer

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