Search+with+Random+Leaf+Values

toc =The Beal Effect= Random evaluation was first examined for the game of chess by Don Beal and Martin C. Smith at the Advances in Computer Chess 7 conference at University of Limburg, July 1993, published in the ICCA Journal and conference proceedings, and further analyzed by Mark Levene and Trevor Fenner in 1995 and 2001. Although using [|random numbers] as "evaluation" results in random play with a one ply search (root-random), it was found that the strength of play rises rapidly with increased depth (lookahead-random) using a full-width minimax search. While a natural assumption is that lookahead on random numbers would also result in a random choice at the root as well, random evaluation would create a statistical preference for positions with large mobilty, and thus likely strong material.
 * Home * Search * with Random Leaf Values**
 * [[image:Momiji_B221212.JPG link="https://commons.wikimedia.org/wiki/File:Momiji_%E7%B4%85%E8%91%89%E3%81%99%E3%82%8B%E3%83%A4%E3%83%9E%E3%83%A2%E3%83%9F%E3%82%B8_B221212.JPG"]] ||~ || **Search with Random Leaf Values** is of interest concerning playing strength, match statistics and search pathology. Randomized evaluation by adding [|noise] concerns evaluation accuracy and evaluation error analysis - it might be used in introducing and learning new evaluation terms for various games or general game playing programs, or simply in randomizing or weakening engine play. ||
 * [|Japanese maple] [|autumn leaves] ||~ ||^ ||

=Setup= To demonstrate this so called **Beal Effect** it is neccessary to consider awareness of terminal nodes where mate scores would favour deeper lookahead. Therefor root-random is replaced by lookahead-zero, performing a lookahead with the same search depth as lookahead-random, but non terminal leaves evaluated as zero, only tie-breaking at the root by a random number. Still a very weak player, a five ply search was already sufficient to win all of 100 games versus a random player.

Beal and Smith used following setup to automatically play the games: Draws by stalemate and four cases of insufficient material were recognized (KK, KNK, KBK, KNNK), but 50-move rule or threefold repetition discarded. Therefor games were limited to 200 moves and then WDL adjudicated by material balance (which happend rarely).

=Further Experiments= Beal and Smith further applied random evaluations to components rather than the whole evaluation. They used material balance as dominating term plus a random number below one pawn unit. While a five ply search with random component only gained 63% over zero component, quiescing the material balance by exploring a capture tree in order to obtain the chess specific part of the evaluation, the random component gained 97% within the same search depth of five plies.

=See also=
 * Conspiracy Numbers
 * Depth
 * Diminishing Returns
 * Evaluation
 * Leaf Node
 * Match Statistics
 * Mobility
 * Playing Strength
 * Pseudorandom Number Generator
 * Score Granularity
 * Scoring Root Moves
 * Search Instability
 * Search Pathology
 * Search versus Knowledge
 * Temporal Difference Learning

=Publications=

1985 ...

 * Bruce Abramson (**1985**). //A Cure for Pathological Behavior in Games that Use Minimax.// Workshop on Uncertainty in Artificial Intelligence, [|arXiv:1304.3444]
 * Bruce Abramson, Richard Korf (**1987**). //A Model of Two-Player Evaluation Functions.// [|AAAI-87]. [|pdf]

1990 ...

 * Bruce Abramson (**1990**). //[|Expected-Outcome: A General Model of Static Evaluation]//. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 12, No. 2
 * Don Beal, Martin C. Smith (**1994**). //Random Evaluations in Chess//. ICCA Journal, Vol. 17, No. 1
 * Don Beal, Martin C. Smith (**1994**). //Random Evaluations in Chess//. Advances in Computer Chess 7
 * Mark Levene, Trevor Fenner (**1995**). //A Partial Analysis of Minimaxing Game Trees with Random Leaf Values//. ICCA Journal, Vol. 18, No. 1
 * Andreas Junghanns, Jonathan Schaeffer (**1997**). //Search versus knowledge in game-playing programs revisited//. IJCAI-97, Vol 1, [|pdf] » Search versus Knowledge in Practice

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]
 * Ulf Lorenz, Burkhard Monien (**2002**). //[|The Secret of Selective Game Tree Search, When Using Random-Error Evaluations]//. Proceedings of 19th Annual Symposium on Theoretical Aspects of Computer Science (STACS), [|pdf]
 * Ingo Althöfer, Susanne Heuser (**2005**). //Randomised Evaluations in Single-Agent Search//. ICGA Journal, Vol. 28, No. 1, [|preprint as pdf]
 * Brandon Wilson, Austin Parker, Dana Nau (**2009**). //Error Minimizing Minimax: Avoiding Search Pathology in Game Trees//. [|pdf]

=Forum Posts=

1990 ...

 * [|Re: Weakest Chess Program needed] by Kenneth S A Oksanen, rgc, November 12, 1991
 * [|Re: Human VS computer] by Don Beal, rgc, July 11, 1994

1995 ...

 * [|Primitive Chess Program] by David Ewart, rgc, June 09, 1995
 * [|Re: Incoporating chess knowledge in chess programs] by Bruce Moreland, rgcc, June 28, 1996 » Mobility
 * [|random play] by Robert Hyatt, rgcc, November 25, 1996 » Scoring Root Moves
 * [|Randomness in move selection] by Robert Hyatt, rgcc, December 01, 1996
 * [|Re: Interesting random chess question - What is probability to win?] by Jari Huikari, CCC, October 03, 1998 » Nero
 * [|Random chess statistics, part two] by Jari Huikari, CCC, October 14, 1998
 * [|Re: Heinz, Hyatt and Newborn next best move paradox] by Robert Hyatt, rgcc, March 19, 1999
 * [|Freeware program with RANDOM eval] by Georg von Zimmermann, CCC, November 20, 1999

2000 ...

 * [|Simple Learning Technique and Random Play] by Miguel A. Ballicora, CCC, January 18, 2001 » Persistent Hash Table
 * [|Random factor in static evaluation!] by Tiago Ribeiro, CCC, June 15, 2001
 * [|Random play] by Russell Reagan, CCC, April 08, 2003
 * [|A question about random numbers] by Antonio Senatore, CCC, July 22, 2004

2005 ...

 * [|What is "randomness" for a CM9k personality?] by Wilma, rgcc, June 12, 2005 » Chessmaster
 * [|Random number mobility scores] by Guest, rgcc, September 20, 2008

2010 ...
> [|Re: To kick off some technical discussions] by Robert Hyatt, OpenChess Forum, June 20, 2010
 * [|Re: To kick off some technical discussions] by Robert Hyatt, OpenChess Forum, June 20, 2010
 * [|Pathology on Game trees] by Gerd Isenberg, CCC, July 22, 2010
 * [|Re: Depth vs playing strength] by John Merlino, CCC, January 10, 2012 » The King
 * [|Implications of Lazy eval on Don Beal effect in Fail Soft] by Henk van den Belt, CCC, November 19, 2014

2015 ...

 * [|How to dumb down/weaken/humanize an engine algorithmically?] by Dominik Klein, CCC, January 18, 2015
 * [|"random mover" chess programs] by Norbert Raimund Leisner, CCC, June 24, 2016
 * [|Strategies for weaker play levels] by Evert Glebbeek, CCC, June 28, 2016
 * [|Adding a random small number to the evaluation function] by Uri Blass, CCC, September 03, 2016
 * [|random evaluation perturbation factor] by Stuart Cracraft, CCC, April 24, 2017
 * [|Randomizing an evaluation and retiring opening books] by Ivan Ivec, FishCooking, November 18, 2017

=External Links= > feat. Miles Davis, [|Hank Jones], [|Sam Jones] and [|Art Blakey] > media type="youtube" key="dsp5OASh7bg"
 * [|Randomization from Wikipedia]
 * [|Randomized algorithm from Wikipedia]
 * [|Randomness from Wikipedia]
 * [|Random tree from Wikipedia]
 * [|Random walk from Wikipedia]
 * [|Cannonball Adderley] - [|Autumn Leaves] ([|Somethin' Else] 1958), [|YouTube] Video

=References= =What links here?= include page="Search with Random Leaf Values" component="backlinks" limit="80"
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