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Created page with "'''Home * Search * with Random Leaf Values''' FILE:Momiji 紅葉するヤマモミジ B221212.JPG|border|right|thumb| [https://en.wikipedia.org/wiki/Acer_..."
'''[[Main Page|Home]] * [[Search]] * with Random Leaf Values'''
[[FILE:Momiji 紅葉するヤマモミジ B221212.JPG|border|right|thumb| [https://en.wikipedia.org/wiki/Acer_palmatum Japanese maple] [https://en.wikipedia.org/wiki/Autumn_leaf_color autumn leaves] <ref>[https://en.wikipedia.org/wiki/Acer_palmatum Acer palmatum] subsp. matsumurae (Koidz) Ogata, [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 image] by [https://zh.wikipedia.org/wiki/User:%E6%9D%BE%E5%B2%A1%E6%98%8E%E8%8A%B3 松岡明芳], November 22, 2006, [https://creativecommons.org/licenses/by/3.0/deed.en CC BY 3.0], [https://en.wikipedia.org/wiki/Wikimedia_Commons Wikimedia Commons], [https://en.wikipedia.org/wiki/Autumn_leaf_color Autumn leaf color from Wikipedia]</ref> ]]
'''Search with Random Leaf Values''' is of interest concerning [[Playing Strength|playing strength]], [[Match Statistics|match statistics]] and [[Search Pathology|search pathology]]. Randomized [[Evaluation|evaluation]] by adding [https://en.wikipedia.org/wiki/Noise_(electronics) noise] concerns evaluation accuracy and evaluation error analysis - it might be used in introducing and [[Learning|learning]] new evaluation terms for various [[Games|games]] or [[General Game Playing|general game playing]] programs, or simply in randomizing or weakening engine play.
<span id="BealEffect"></span>
=The Beal Effect=
Random evaluation was first examined for the game of chess by [[Don Beal]] <ref>The term "Beal Effect" was coined by [[Robert Hyatt]], see [http://www.open-chess.org/viewtopic.php?f=5&t=18&p=1963 Re: To kick off some technical discussions] by [[Robert Hyatt]], [[Computer Chess Forums|OpenChess Forum]], June 20, 2010</ref> and [[Martin C. Smith]] at the [[Advances in Computer Chess 7]] conference at [[Maastricht University|University of Limburg]], July 1993, published in the [[ICGA Journal#17_1|ICCA Journal]] and conference proceedings <ref>[[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[Advances in Computer Chess 7]]</ref>, and further analyzed by [[Mark Levene]] and [[Trevor Fenner]] in 1995 <ref>[[Mark Levene]], [[Trevor Fenner]] ('''1995'''). ''A Partial Analysis of Minimaxing Game Trees with Random Leaf Values''. [[ICGA Journal#18_1|ICCA Journal, Vol. 18, No. 1]]</ref> and 2001 <ref>[[Mark Levene]], [[Trevor Fenner]] ('''2001'''). ''The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 130, No. 1</ref>. Although using [https://en.wikipedia.org/wiki/Random_number random numbers] as "evaluation" results in random play with a one [[Ply|ply]] [[Search|search]] (root-random), it was found that the [[Playing Strength|strength of play]] rises rapidly with increased [[Depth|depth]] (lookahead-random) using a full-width [[Minimax|minimax]] search. While a natural assumption is that lookahead on random numbers would also result in a random choice at the [[Root|root]] as well, random evaluation would create a statistical preference for positions with large [[Mobility|mobilty]], and thus likely strong [[Material|material]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=60582&start=1 Re: "random mover" chess programs] by [[Harm Geert Muller]], [[CCC]], June 24, 2016</ref>.
=Setup=
To demonstrate this so called '''Beal Effect''' it is neccessary to consider awareness of [[Terminal Node|terminal nodes]] where [[Score#MateScores|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 [[Leaf Node|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: [[Draw|Draws]] by [[Stalemate|stalemate]] and four cases of [[Material#InsufficientMaterial|insufficient material]] were recognized (KK, KNK, KBK, KNNK), but [[Fifty-move Rule|50-move rule]] or threefold [[Repetitions|repetition]] discarded. Therefor games were limited to 200 moves and then WDL adjudicated by +=- material balance (which happend rarely) <ref>[[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|ICCA Journal, Vol. 17, No. 1]]</ref>.
=Further Experiments=
Beal and Smith further applied random evaluations to components rather than the whole evaluation. They used [[Material#Balance|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, [[Quiescence Search|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]]
* [[Depth#DiminishingReturns|Diminishing Returns]]
* [[Evaluation]]
* [[Leaf Node]]
* [[Match Statistics]]
* [[Mobility]]
* [[Playing Strength]]
* [[Pseudorandom Number Generator]]
* [[Score#Grain|Score Granularity]]
* [[Ronald de Man#ScoringRootMoves|Scoring Root Moves]]
* [[Search Instability]]
* [[Search Pathology]]
* [[Knowledge#SearchversusKnowledge|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, [https://arxiv.org/abs/1304.3444 arXiv:1304.3444]
* [[Bruce Abramson]], [[Richard Korf]] ('''1987'''). ''A Model of Two-Player Evaluation Functions.'' [http://www.aaai.org/Conferences/AAAI/aaai87.php AAAI-87]. [http://www.aaai.org/Papers/AAAI/1987/AAAI87-016.pdf pdf]
==1990 ...==
* [[Bruce Abramson]] ('''1990'''). ''[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=44404 Expected-Outcome: A General Model of Static Evaluation]''. [[TPAMI|IEEE Transactions on Pattern Analysis and Machine Intelligence]], Vol. 12, No. 2
* [[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|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''. [[ICGA Journal#18_1|ICCA Journal, Vol. 18, No. 1]]
* [[Andreas Junghanns]], [[Jonathan Schaeffer]] ('''1997'''). ''Search versus knowledge in game-playing programs revisited''. [[Conferences#IJCAI1997|IJCAI-97]], Vol 1, [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.32.168&rep=rep1&type=pdf pdf] » [[Knowledge#InPractice|Search versus Knowledge in Practice]]
==2000 ...==
* [[Mark Levene]], [[Trevor Fenner]] ('''2001'''). ''The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 130, No. 1, Review in [[ICGA Journal#18_1|ICGA Journal, Vol. 24, No. 4]], [https://pdfs.semanticscholar.org/eb82/03fe314d912cdf52aa9fbdabd073751e5a2d.pdf pdf]
* [[Ulf Lorenz]], [[Burkhard Monien]] ('''2002'''). ''[http://www.springerlink.com/content/f6b4wb6l63dpd0jv/ The Secret of Selective Game Tree Search, When Using Random-Error Evaluations]''. Proceedings of 19th Annual Symposium on Theoretical Aspects of Computer Science (STACS), [http://www.top-5000.nl/ps/The%20secret%20of%20selective%20earch%20when%20using%20random.pdf pdf]
* [[Ingo Althöfer]], [[Susanne Heuser]] ('''2005'''). ''Randomised Evaluations in Single-Agent Search''. [[ICGA Journal#28_1|ICGA Journal, Vol. 28, No. 1]], [https://www.minet.uni-jena.de/preprints/althoefer_05/altheuser.pdf preprint as pdf]
* [[Brandon Wilson]], [[Austin Parker]], [[Dana Nau]] ('''2009'''). ''Error Minimizing Minimax: Avoiding Search Pathology in Game Trees''. [http://www.cs.umd.edu/~nau/papers/wilson2009error.pdf pdf]
=Forum Posts=
==1990 ...==
* [https://groups.google.com/d/msg/rec.games.chess/Qe_5lhAWTsc/79h9BQslCWIJ Re: Weakest Chess Program needed] by Kenneth S A Oksanen, [[Computer Chess Forums|rgc]], November 12, 1991
* [https://groups.google.com/d/msg/rec.games.chess/xIvJfi92jMc/BQP231Z0V84J Re: Human VS computer] by [[Don Beal]], [[Computer Chess Forums|rgc]], July 11, 1994
==1995 ...==
* [https://groups.google.com/d/msg/rec.games.chess/NXEDz2iTbRc/k6uH2zBMmxMJ Primitive Chess Program] by David Ewart, [[Computer Chess Forums|rgc]], June 09, 1995
* [https://groups.google.com/d/msg/rec.games.chess.computer/47bgYzU2kyQ/-dkD4FhigHYJ Re: Incoporating chess knowledge in chess programs] by [[Bruce Moreland]], [[Computer Chess Forums|rgcc]], June 28, 1996 » [[Mobility]]
* [https://groups.google.com/d/msg/rec.games.chess.computer/AI3xadkLEIk/lqWaLrHtl7AJ random play] by [[Robert Hyatt]], [[Computer Chess Forums|rgcc]], November 25, 1996 » [[Ronald de Man#ScoringRootMoves|Scoring Root Moves]]
* [https://groups.google.com/d/msg/rec.games.chess.computer/ul-HWewM5FQ/sXcqhGL06UQJ Randomness in move selection] by [[Robert Hyatt]], [[Computer Chess Forums|rgcc]], December 01, 1996
* [https://www.stmintz.com/ccc/index.php?id=28699 Re: Interesting random chess question - What is probability to win?] by [[Jari Huikari]], [[CCC]], October 03, 1998 » [[Nero]]
* [https://www.stmintz.com/ccc/index.php?id=29571 Random chess statistics, part two] by [[Jari Huikari]], [[CCC]], October 14, 1998
* [https://groups.google.com/d/msg/rec.games.chess.computer/mGbD5Lky-8E/gAv0u4YOrVkJ Re: Heinz, Hyatt and Newborn next best move paradox] by [[Robert Hyatt]], [[Computer Chess Forums|rgcc]], March 19, 1999
* [https://www.stmintz.com/ccc/index.php?id=78795 Freeware program with RANDOM eval] by [[Georg von Zimmermann]], [[CCC]], November 20, 1999
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=150687 Simple Learning Technique and Random Play] by [[Miguel A. Ballicora]], [[CCC]], January 18, 2001 » [[Persistent Hash Table]]
* [https://www.stmintz.com/ccc/index.php?id=175314 Random factor in static evaluation!] by Tiago Ribeiro, [[CCC]], June 15, 2001
* [https://www.stmintz.com/ccc/index.php?id=292517 Random play] by [[Russell Reagan]], [[CCC]], April 08, 2003
* [https://www.stmintz.com/ccc/index.php?id=378514 A question about random numbers] by Antonio Senatore, [[CCC]], July 22, 2004
==2005 ...==
* [https://groups.google.com/d/msg/rec.games.chess.computer/GW48x_Pk7CU/luDZWBl8vBkJ What is "randomness" for a CM9k personality?] by Wilma, [[Computer Chess Forums|rgcc]], June 12, 2005 » [[Chessmaster]]
* [https://groups.google.com/d/msg/rec.games.chess.computer/Ab9uA1-8Hlw/UjT_JXTiHuIJ Random number mobility scores] by Guest, [[Computer Chess Forums|rgcc]], September 20, 2008
==2010 ...==
* [http://www.open-chess.org/viewtopic.php?f=5&t=18&p=1942#p1942 Re: To kick off some technical discussions] by [[Robert Hyatt]], [[Computer Chess Forums|OpenChess Forum]], June 20, 2010
: [http://www.open-chess.org/viewtopic.php?f=5&t=18&p=1963 Re: To kick off some technical discussions] by [[Robert Hyatt]], [[Computer Chess Forums|OpenChess Forum]], June 20, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=35538 Pathology on Game trees] by [[Gerd Isenberg]], [[CCC]], July 22, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=41902&start=5 Re: Depth vs playing strength] by [[John Merlino]], [[CCC]], January 10, 2012 » [[The King]]
* [http://www.talkchess.com/forum/viewtopic.php?t=54387 Implications of Lazy eval on Don Beal effect in Fail Soft] by [[Henk van den Belt]], [[CCC]], November 19, 2014
==2015 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=55011 How to dumb down/weaken/humanize an engine algorithmically?] by Dominik Klein, [[CCC]], January 18, 2015
* [http://www.talkchess.com/forum/viewtopic.php?t=60582 "random mover" chess programs] by [[Norbert Raimund Leisner]], [[CCC]], June 24, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=60635 Strategies for weaker play levels] by [[Evert Glebbeek]], [[CCC]], June 28, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=61315 Adding a random small number to the evaluation function] by [[Uri Blass]], [[CCC]], September 03, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=63803 random evaluation perturbation factor] by [[Stuart Cracraft]], [[CCC]], April 24, 2017
* [https://groups.google.com/forum/#!topic/fishcooking/SVkQcfGai8U Randomizing an evaluation and retiring opening books] by [[Ivan Ivec]], [[Computer Chess Forums|FishCooking]], November 18, 2017
=External Links=
* [https://en.wikipedia.org/wiki/Randomization Randomization from Wikipedia]
* [https://en.wikipedia.org/wiki/Randomized_algorithm Randomized algorithm from Wikipedia]
* [https://en.wikipedia.org/wiki/Randomness Randomness from Wikipedia]
* [https://en.wikipedia.org/wiki/Random_tree Random tree from Wikipedia]
* [https://en.wikipedia.org/wiki/Random_walk Random walk from Wikipedia]
* [https://en.wikipedia.org/wiki/Cannonball_Adderley Cannonball Adderley] - [https://en.wikipedia.org/wiki/Autumn_Leaves_(1945_song) Autumn Leaves] ([https://en.wikipedia.org/wiki/Somethin%27_Else_(Cannonball_Adderley_album) Somethin' Else] 1958), [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: feat. [[Videos#MilesDavis|Miles Davis]], [https://en.wikipedia.org/wiki/Hank_Jones Hank Jones], [https://en.wikipedia.org/wiki/Sam_Jones_(musician) Sam Jones] and [https://en.wikipedia.org/wiki/Art_Blakey Art Blakey]
: {{#evu:https://www.youtube.com/watch?v=dsp5OASh7bg|alignment=left|valignment=top}}
=References=
<references />
'''[[Search|Up one Level]]'''
[[FILE:Momiji 紅葉するヤマモミジ B221212.JPG|border|right|thumb| [https://en.wikipedia.org/wiki/Acer_palmatum Japanese maple] [https://en.wikipedia.org/wiki/Autumn_leaf_color autumn leaves] <ref>[https://en.wikipedia.org/wiki/Acer_palmatum Acer palmatum] subsp. matsumurae (Koidz) Ogata, [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 image] by [https://zh.wikipedia.org/wiki/User:%E6%9D%BE%E5%B2%A1%E6%98%8E%E8%8A%B3 松岡明芳], November 22, 2006, [https://creativecommons.org/licenses/by/3.0/deed.en CC BY 3.0], [https://en.wikipedia.org/wiki/Wikimedia_Commons Wikimedia Commons], [https://en.wikipedia.org/wiki/Autumn_leaf_color Autumn leaf color from Wikipedia]</ref> ]]
'''Search with Random Leaf Values''' is of interest concerning [[Playing Strength|playing strength]], [[Match Statistics|match statistics]] and [[Search Pathology|search pathology]]. Randomized [[Evaluation|evaluation]] by adding [https://en.wikipedia.org/wiki/Noise_(electronics) noise] concerns evaluation accuracy and evaluation error analysis - it might be used in introducing and [[Learning|learning]] new evaluation terms for various [[Games|games]] or [[General Game Playing|general game playing]] programs, or simply in randomizing or weakening engine play.
<span id="BealEffect"></span>
=The Beal Effect=
Random evaluation was first examined for the game of chess by [[Don Beal]] <ref>The term "Beal Effect" was coined by [[Robert Hyatt]], see [http://www.open-chess.org/viewtopic.php?f=5&t=18&p=1963 Re: To kick off some technical discussions] by [[Robert Hyatt]], [[Computer Chess Forums|OpenChess Forum]], June 20, 2010</ref> and [[Martin C. Smith]] at the [[Advances in Computer Chess 7]] conference at [[Maastricht University|University of Limburg]], July 1993, published in the [[ICGA Journal#17_1|ICCA Journal]] and conference proceedings <ref>[[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[Advances in Computer Chess 7]]</ref>, and further analyzed by [[Mark Levene]] and [[Trevor Fenner]] in 1995 <ref>[[Mark Levene]], [[Trevor Fenner]] ('''1995'''). ''A Partial Analysis of Minimaxing Game Trees with Random Leaf Values''. [[ICGA Journal#18_1|ICCA Journal, Vol. 18, No. 1]]</ref> and 2001 <ref>[[Mark Levene]], [[Trevor Fenner]] ('''2001'''). ''The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 130, No. 1</ref>. Although using [https://en.wikipedia.org/wiki/Random_number random numbers] as "evaluation" results in random play with a one [[Ply|ply]] [[Search|search]] (root-random), it was found that the [[Playing Strength|strength of play]] rises rapidly with increased [[Depth|depth]] (lookahead-random) using a full-width [[Minimax|minimax]] search. While a natural assumption is that lookahead on random numbers would also result in a random choice at the [[Root|root]] as well, random evaluation would create a statistical preference for positions with large [[Mobility|mobilty]], and thus likely strong [[Material|material]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=60582&start=1 Re: "random mover" chess programs] by [[Harm Geert Muller]], [[CCC]], June 24, 2016</ref>.
=Setup=
To demonstrate this so called '''Beal Effect''' it is neccessary to consider awareness of [[Terminal Node|terminal nodes]] where [[Score#MateScores|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 [[Leaf Node|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: [[Draw|Draws]] by [[Stalemate|stalemate]] and four cases of [[Material#InsufficientMaterial|insufficient material]] were recognized (KK, KNK, KBK, KNNK), but [[Fifty-move Rule|50-move rule]] or threefold [[Repetitions|repetition]] discarded. Therefor games were limited to 200 moves and then WDL adjudicated by +=- material balance (which happend rarely) <ref>[[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|ICCA Journal, Vol. 17, No. 1]]</ref>.
=Further Experiments=
Beal and Smith further applied random evaluations to components rather than the whole evaluation. They used [[Material#Balance|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, [[Quiescence Search|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]]
* [[Depth#DiminishingReturns|Diminishing Returns]]
* [[Evaluation]]
* [[Leaf Node]]
* [[Match Statistics]]
* [[Mobility]]
* [[Playing Strength]]
* [[Pseudorandom Number Generator]]
* [[Score#Grain|Score Granularity]]
* [[Ronald de Man#ScoringRootMoves|Scoring Root Moves]]
* [[Search Instability]]
* [[Search Pathology]]
* [[Knowledge#SearchversusKnowledge|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, [https://arxiv.org/abs/1304.3444 arXiv:1304.3444]
* [[Bruce Abramson]], [[Richard Korf]] ('''1987'''). ''A Model of Two-Player Evaluation Functions.'' [http://www.aaai.org/Conferences/AAAI/aaai87.php AAAI-87]. [http://www.aaai.org/Papers/AAAI/1987/AAAI87-016.pdf pdf]
==1990 ...==
* [[Bruce Abramson]] ('''1990'''). ''[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=44404 Expected-Outcome: A General Model of Static Evaluation]''. [[TPAMI|IEEE Transactions on Pattern Analysis and Machine Intelligence]], Vol. 12, No. 2
* [[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|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''. [[ICGA Journal#18_1|ICCA Journal, Vol. 18, No. 1]]
* [[Andreas Junghanns]], [[Jonathan Schaeffer]] ('''1997'''). ''Search versus knowledge in game-playing programs revisited''. [[Conferences#IJCAI1997|IJCAI-97]], Vol 1, [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.32.168&rep=rep1&type=pdf pdf] » [[Knowledge#InPractice|Search versus Knowledge in Practice]]
==2000 ...==
* [[Mark Levene]], [[Trevor Fenner]] ('''2001'''). ''The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 130, No. 1, Review in [[ICGA Journal#18_1|ICGA Journal, Vol. 24, No. 4]], [https://pdfs.semanticscholar.org/eb82/03fe314d912cdf52aa9fbdabd073751e5a2d.pdf pdf]
* [[Ulf Lorenz]], [[Burkhard Monien]] ('''2002'''). ''[http://www.springerlink.com/content/f6b4wb6l63dpd0jv/ The Secret of Selective Game Tree Search, When Using Random-Error Evaluations]''. Proceedings of 19th Annual Symposium on Theoretical Aspects of Computer Science (STACS), [http://www.top-5000.nl/ps/The%20secret%20of%20selective%20earch%20when%20using%20random.pdf pdf]
* [[Ingo Althöfer]], [[Susanne Heuser]] ('''2005'''). ''Randomised Evaluations in Single-Agent Search''. [[ICGA Journal#28_1|ICGA Journal, Vol. 28, No. 1]], [https://www.minet.uni-jena.de/preprints/althoefer_05/altheuser.pdf preprint as pdf]
* [[Brandon Wilson]], [[Austin Parker]], [[Dana Nau]] ('''2009'''). ''Error Minimizing Minimax: Avoiding Search Pathology in Game Trees''. [http://www.cs.umd.edu/~nau/papers/wilson2009error.pdf pdf]
=Forum Posts=
==1990 ...==
* [https://groups.google.com/d/msg/rec.games.chess/Qe_5lhAWTsc/79h9BQslCWIJ Re: Weakest Chess Program needed] by Kenneth S A Oksanen, [[Computer Chess Forums|rgc]], November 12, 1991
* [https://groups.google.com/d/msg/rec.games.chess/xIvJfi92jMc/BQP231Z0V84J Re: Human VS computer] by [[Don Beal]], [[Computer Chess Forums|rgc]], July 11, 1994
==1995 ...==
* [https://groups.google.com/d/msg/rec.games.chess/NXEDz2iTbRc/k6uH2zBMmxMJ Primitive Chess Program] by David Ewart, [[Computer Chess Forums|rgc]], June 09, 1995
* [https://groups.google.com/d/msg/rec.games.chess.computer/47bgYzU2kyQ/-dkD4FhigHYJ Re: Incoporating chess knowledge in chess programs] by [[Bruce Moreland]], [[Computer Chess Forums|rgcc]], June 28, 1996 » [[Mobility]]
* [https://groups.google.com/d/msg/rec.games.chess.computer/AI3xadkLEIk/lqWaLrHtl7AJ random play] by [[Robert Hyatt]], [[Computer Chess Forums|rgcc]], November 25, 1996 » [[Ronald de Man#ScoringRootMoves|Scoring Root Moves]]
* [https://groups.google.com/d/msg/rec.games.chess.computer/ul-HWewM5FQ/sXcqhGL06UQJ Randomness in move selection] by [[Robert Hyatt]], [[Computer Chess Forums|rgcc]], December 01, 1996
* [https://www.stmintz.com/ccc/index.php?id=28699 Re: Interesting random chess question - What is probability to win?] by [[Jari Huikari]], [[CCC]], October 03, 1998 » [[Nero]]
* [https://www.stmintz.com/ccc/index.php?id=29571 Random chess statistics, part two] by [[Jari Huikari]], [[CCC]], October 14, 1998
* [https://groups.google.com/d/msg/rec.games.chess.computer/mGbD5Lky-8E/gAv0u4YOrVkJ Re: Heinz, Hyatt and Newborn next best move paradox] by [[Robert Hyatt]], [[Computer Chess Forums|rgcc]], March 19, 1999
* [https://www.stmintz.com/ccc/index.php?id=78795 Freeware program with RANDOM eval] by [[Georg von Zimmermann]], [[CCC]], November 20, 1999
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=150687 Simple Learning Technique and Random Play] by [[Miguel A. Ballicora]], [[CCC]], January 18, 2001 » [[Persistent Hash Table]]
* [https://www.stmintz.com/ccc/index.php?id=175314 Random factor in static evaluation!] by Tiago Ribeiro, [[CCC]], June 15, 2001
* [https://www.stmintz.com/ccc/index.php?id=292517 Random play] by [[Russell Reagan]], [[CCC]], April 08, 2003
* [https://www.stmintz.com/ccc/index.php?id=378514 A question about random numbers] by Antonio Senatore, [[CCC]], July 22, 2004
==2005 ...==
* [https://groups.google.com/d/msg/rec.games.chess.computer/GW48x_Pk7CU/luDZWBl8vBkJ What is "randomness" for a CM9k personality?] by Wilma, [[Computer Chess Forums|rgcc]], June 12, 2005 » [[Chessmaster]]
* [https://groups.google.com/d/msg/rec.games.chess.computer/Ab9uA1-8Hlw/UjT_JXTiHuIJ Random number mobility scores] by Guest, [[Computer Chess Forums|rgcc]], September 20, 2008
==2010 ...==
* [http://www.open-chess.org/viewtopic.php?f=5&t=18&p=1942#p1942 Re: To kick off some technical discussions] by [[Robert Hyatt]], [[Computer Chess Forums|OpenChess Forum]], June 20, 2010
: [http://www.open-chess.org/viewtopic.php?f=5&t=18&p=1963 Re: To kick off some technical discussions] by [[Robert Hyatt]], [[Computer Chess Forums|OpenChess Forum]], June 20, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=35538 Pathology on Game trees] by [[Gerd Isenberg]], [[CCC]], July 22, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=41902&start=5 Re: Depth vs playing strength] by [[John Merlino]], [[CCC]], January 10, 2012 » [[The King]]
* [http://www.talkchess.com/forum/viewtopic.php?t=54387 Implications of Lazy eval on Don Beal effect in Fail Soft] by [[Henk van den Belt]], [[CCC]], November 19, 2014
==2015 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=55011 How to dumb down/weaken/humanize an engine algorithmically?] by Dominik Klein, [[CCC]], January 18, 2015
* [http://www.talkchess.com/forum/viewtopic.php?t=60582 "random mover" chess programs] by [[Norbert Raimund Leisner]], [[CCC]], June 24, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=60635 Strategies for weaker play levels] by [[Evert Glebbeek]], [[CCC]], June 28, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=61315 Adding a random small number to the evaluation function] by [[Uri Blass]], [[CCC]], September 03, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=63803 random evaluation perturbation factor] by [[Stuart Cracraft]], [[CCC]], April 24, 2017
* [https://groups.google.com/forum/#!topic/fishcooking/SVkQcfGai8U Randomizing an evaluation and retiring opening books] by [[Ivan Ivec]], [[Computer Chess Forums|FishCooking]], November 18, 2017
=External Links=
* [https://en.wikipedia.org/wiki/Randomization Randomization from Wikipedia]
* [https://en.wikipedia.org/wiki/Randomized_algorithm Randomized algorithm from Wikipedia]
* [https://en.wikipedia.org/wiki/Randomness Randomness from Wikipedia]
* [https://en.wikipedia.org/wiki/Random_tree Random tree from Wikipedia]
* [https://en.wikipedia.org/wiki/Random_walk Random walk from Wikipedia]
* [https://en.wikipedia.org/wiki/Cannonball_Adderley Cannonball Adderley] - [https://en.wikipedia.org/wiki/Autumn_Leaves_(1945_song) Autumn Leaves] ([https://en.wikipedia.org/wiki/Somethin%27_Else_(Cannonball_Adderley_album) Somethin' Else] 1958), [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: feat. [[Videos#MilesDavis|Miles Davis]], [https://en.wikipedia.org/wiki/Hank_Jones Hank Jones], [https://en.wikipedia.org/wiki/Sam_Jones_(musician) Sam Jones] and [https://en.wikipedia.org/wiki/Art_Blakey Art Blakey]
: {{#evu:https://www.youtube.com/watch?v=dsp5OASh7bg|alignment=left|valignment=top}}
=References=
<references />
'''[[Search|Up one Level]]'''
