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'''[[Main Page|Home]] * Chess'''
 
'''[[Main Page|Home]] * Chess'''
  
[[FILE:Breaking Point 1.png|border|right|thumb|Chess <ref> An illustration by [https://en.wikipedia.org/wiki/Alex_Ebel Ebel] for [https://en.wikipedia.org/wiki/James_E._Gunn_(writer) James E. Gunn's] Breaking Point, appeared in [https://en.wikipedia.org/wiki/Space_Science_Fiction Space Science Fiction], March 1953</ref> ]]  
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[[FILE:Breaking Point 1.png|border|right|thumb|Chess <ref>An [https://commons.wikimedia.org/wiki/File:Breaking_Point_1.png illustration] by [https://en.wikipedia.org/wiki/Alex_Ebel Ebel] for [https://en.wikipedia.org/wiki/James_E._Gunn_(writer) James E. Gunn's] Breaking Point, appeared in [https://en.wikipedia.org/wiki/Space_Science_Fiction Space Science Fiction], March 1953</ref> ]]  
  
 
'''Chess''',<br/>
 
'''Chess''',<br/>
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* In 1966, Eero Bonsdorff, [https://en.wikipedia.org/wiki/Karl_Fabel Karl Fabel], and Olvai Riihimaa gave 5899 as the maximum number of [[Moves|moves]] in a chess game <ref>Eero Bonsdorff, [https://en.wikipedia.org/wiki/Karl_Fabel Karl Fabel], Olvai Riihimaa ('''1966''') ''Schach und Zahl - Unterhaltsame Schachmathematik''. Seite 11-13, Walter Rau Verlag, Düsseldorf (German)</ref> <ref>[http://de.wikipedia.org/wiki/50-Z%C3%BCge-Regel#Schachmathematik 50-Züge-Regel - Schachmathematik from Wikipedia.de] (German)</ref> <ref>[http://www.xs4all.nl/~timkr/chess2/honor.htm Defending Humanity's Honor] by [https://en.wikipedia.org/wiki/Tim_Krabb%C3%A9 Tim Krabbé], see game [[Rival|NewRival]] - [[Faile]] with 493 moves, and playing 402 moves with bare kings!</ref>
 
* In 1966, Eero Bonsdorff, [https://en.wikipedia.org/wiki/Karl_Fabel Karl Fabel], and Olvai Riihimaa gave 5899 as the maximum number of [[Moves|moves]] in a chess game <ref>Eero Bonsdorff, [https://en.wikipedia.org/wiki/Karl_Fabel Karl Fabel], Olvai Riihimaa ('''1966''') ''Schach und Zahl - Unterhaltsame Schachmathematik''. Seite 11-13, Walter Rau Verlag, Düsseldorf (German)</ref> <ref>[http://de.wikipedia.org/wiki/50-Z%C3%BCge-Regel#Schachmathematik 50-Züge-Regel - Schachmathematik from Wikipedia.de] (German)</ref> <ref>[http://www.xs4all.nl/~timkr/chess2/honor.htm Defending Humanity's Honor] by [https://en.wikipedia.org/wiki/Tim_Krabb%C3%A9 Tim Krabbé], see game [[Rival|NewRival]] - [[Faile]] with 493 moves, and playing 402 moves with bare kings!</ref>
 
* [[Shirish Chinchalkar]] has determined a [https://en.wikipedia.org/wiki/Game_complexity#State-space_complexity state-space complexity] of 10<span style="font-size: 80%; vertical-align: super;">46.25</span> as upper bound for the number of reachable [[Chess Position|chess positions]] <ref>[[Shirish Chinchalkar]] ('''1996'''). ''An Upper Bound for the Number of Reachable Positions''. [[ICGA Journal#19_3|ICCA Journal, Vol. 19, No. 3]]</ref>, [[John Tromp]] gives about 10^45.888 <ref>[http://tromp.github.io/chess/chess.html John's Chess Playground - Number of chess diagrams and positions]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=51744&start=3 Re: Total possible chess positions?] by [[Álvaro Begué]], [[CCC]], March 26, 2014</ref>
 
* [[Shirish Chinchalkar]] has determined a [https://en.wikipedia.org/wiki/Game_complexity#State-space_complexity state-space complexity] of 10<span style="font-size: 80%; vertical-align: super;">46.25</span> as upper bound for the number of reachable [[Chess Position|chess positions]] <ref>[[Shirish Chinchalkar]] ('''1996'''). ''An Upper Bound for the Number of Reachable Positions''. [[ICGA Journal#19_3|ICCA Journal, Vol. 19, No. 3]]</ref>, [[John Tromp]] gives about 10^45.888 <ref>[http://tromp.github.io/chess/chess.html John's Chess Playground - Number of chess diagrams and positions]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=51744&start=3 Re: Total possible chess positions?] by [[Álvaro Begué]], [[CCC]], March 26, 2014</ref>
* The [[Encoding Moves#MoveIndex|maximum number of moves]] per [[Chess Position|chess position]] seems 218 <ref>[https://www.stmintz.com/ccc/index.php?id=272654 Does this position blow up your program?] by [[Michael Byrne|Mike Byrne]], [[CCC]], December 23, 2002</ref> <ref>[https://www.stmintz.com/ccc/index.php?id=424966 Subject: Maximum Number of Legal Moves] by [http://onezero.org/ Andrew Shapira], [[CCC]], May 08, 2005</ref>  
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* The [[Encoding Moves#MoveIndex|maximum number of moves]] per [[Chess Position|chess position]] seems 218 <ref>[https://www.stmintz.com/ccc/index.php?id=272654 Does this position blow up your program?] by [[Michael Byrne|Mike Byrne]], [[CCC]], December 23, 2002</ref> <ref>[https://www.stmintz.com/ccc/index.php?id=424966 Subject: Maximum Number of Legal Moves] by [[Andrew Shapira]], [[CCC]], May 08, 2005</ref>  
 
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* [[Chess 0.5X]] by [[Wim Elsenaar]]
 
* [[Chess 0.5X]] by [[Wim Elsenaar]]
 
* [[Chess 2001]], [[Dedicated Chess Computers]]
 
* [[Chess 2001]], [[Dedicated Chess Computers]]
* [[Chess 2013|Chess 201x]] by [[Filip Höfer]]
+
* [[Chess 2020|Chess 20xx]] by [[Filip Höfer]]
 
* [[Chess-64]] by [[Fabien Letouzey]]
 
* [[Chess-64]] by [[Fabien Letouzey]]
 
* [[Chess 7.0]] by [[Larry Atkin]]
 
* [[Chess 7.0]] by [[Larry Atkin]]
 +
 +
=Categories=
 +
* [[:Category:Chess Suffix|Category: Chess Suffix]]
 +
* [[:Category:CP Suffix|Category: Chess Program (CP) Suffix]]
 +
* [[:Category:Chess Legend|Category: Chess Legends]]
  
 
=See also=  
 
=See also=  
 
* [[Anti-Computerchess]]
 
* [[Anti-Computerchess]]
* [[Arts]]
 
 
* [[Cartoons]]
 
* [[Cartoons]]
 
* [[Databases|Chess Databases]]
 
* [[Databases|Chess Databases]]
 
* [[Engines|Chess Engines]]
 
* [[Engines|Chess Engines]]
 
* [[Morphy#ChessFever|Chess Fever (Shakhmatnaya goryachka)]]
 
* [[Morphy#ChessFever|Chess Fever (Shakhmatnaya goryachka)]]
* [[Various Classifications#ChessLegend|Chess Legends]]
 
 
* [[Chess Query Language]]
 
* [[Chess Query Language]]
 
* [[Cognition]]
 
* [[Cognition]]
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==2000 ...==  
 
==2000 ...==  
 
* [[Ingo Althöfer]] ('''2001'''). ''Grandmaster Chess with one-sided Computer Help.'' [[ICGA Journal#24_4|ICGA Journal, Vol. 24, No.4]]
 
* [[Ingo Althöfer]] ('''2001'''). ''Grandmaster Chess with one-sided Computer Help.'' [[ICGA Journal#24_4|ICGA Journal, Vol. 24, No.4]]
* [[Marek Strejczek]] ('''2004'''). ''Some aspects of chess programming''. [[Technical University of Łódź]], Faculty of Electrical and Electronic Engineering, Department of Computer Science, Supervisor [[Maciej Szmit]], [http://nesik.republika.pl/download//SomeAspectsOfChessProgramming.zip zipped pdf], [http://www.top-5000.nl/ps/SomeAspectsOfChessProgramming.pdf pdf]
+
* [[Marek Strejczek]] ('''2004'''). ''Some aspects of chess programming''. M.Sc. thesis, [[Technical University of Łódź]]
* [[Henk Mannen]], [[Marco Wiering]] ('''2004'''). ''Learning to play chess using TD(λ)-learning with database games''. [http://students.uu.nl/en/hum/cognitive-artificial-intelligence Cognitive Artificial Intelligence], [https://en.wikipedia.org/wiki/Utrecht_University Utrecht University], Benelearn’04
+
* [[Henk Mannen]], [[Marco Wiering]] ('''2004'''). ''[https://www.semanticscholar.org/paper/Learning-to-Play-Chess-using-TD(lambda)-learning-Mannen-Wiering/00a6f81c8ebe8408c147841f26ed27eb13fb07f3 Learning to play chess using TD(λ)-learning with database games]''. Cognitive Artificial Intelligence, [https://en.wikipedia.org/wiki/Utrecht_University Utrecht University], Benelearn’04, [https://www.ai.rug.nl/~mwiering/GROUP/ARTICLES/learning-chess.pdf pdf]
 
==2005 ...==  
 
==2005 ...==  
 
* [[Fernand Gobet]], [[Peter Jansen]] ('''2005'''). ''Training in Chess: A Scientific Approach''. [http://www.brunel.ac.uk/~hsstffg/preprints/Training_in_chess.PDF pdf]
 
* [[Fernand Gobet]], [[Peter Jansen]] ('''2005'''). ''Training in Chess: A Scientific Approach''. [http://www.brunel.ac.uk/~hsstffg/preprints/Training_in_chess.PDF pdf]
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* [[David Silver]], [[Thomas Hubert]], [[Julian Schrittwieser]], [[Ioannis Antonoglou]], [[Matthew Lai]], [[Arthur Guez]], [[Marc Lanctot]], [[Laurent Sifre]], [[Dharshan Kumaran]], [[Thore Graepel]], [[Timothy Lillicrap]], [[Karen Simonyan]], [[Demis Hassabis]] ('''2018'''). ''[http://science.sciencemag.org/content/362/6419/1140 A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play]''. [https://en.wikipedia.org/wiki/Science_(journal) Science], Vol. 362, No. 6419 <ref>[https://deepmind.com/blog/alphazero-shedding-new-light-grand-games-chess-shogi-and-go/ AlphaZero: Shedding new light on the grand games of chess, shogi and Go] by [[David Silver]], [[Thomas Hubert]], [[Julian Schrittwieser]] and [[Demis Hassabis]], [[DeepMind]], December 03, 2018</ref>
 
* [[David Silver]], [[Thomas Hubert]], [[Julian Schrittwieser]], [[Ioannis Antonoglou]], [[Matthew Lai]], [[Arthur Guez]], [[Marc Lanctot]], [[Laurent Sifre]], [[Dharshan Kumaran]], [[Thore Graepel]], [[Timothy Lillicrap]], [[Karen Simonyan]], [[Demis Hassabis]] ('''2018'''). ''[http://science.sciencemag.org/content/362/6419/1140 A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play]''. [https://en.wikipedia.org/wiki/Science_(journal) Science], Vol. 362, No. 6419 <ref>[https://deepmind.com/blog/alphazero-shedding-new-light-grand-games-chess-shogi-and-go/ AlphaZero: Shedding new light on the grand games of chess, shogi and Go] by [[David Silver]], [[Thomas Hubert]], [[Julian Schrittwieser]] and [[Demis Hassabis]], [[DeepMind]], December 03, 2018</ref>
 
* [[Garry Kasparov]] ('''2018'''). ''[http://science.sciencemag.org/content/362/6419/1087 Chess, a Drosophila of reasoning]''. [https://en.wikipedia.org/wiki/Science_(journal) Science], Vol. 362, No. 6419
 
* [[Garry Kasparov]] ('''2018'''). ''[http://science.sciencemag.org/content/362/6419/1087 Chess, a Drosophila of reasoning]''. [https://en.wikipedia.org/wiki/Science_(journal) Science], Vol. 362, No. 6419
 +
* [[Jaap van den Herik]] ('''2018'''). ''Computer chess: From idea to DeepMind''. [[ICGA Journal#40_3|ICGA Journal, Vol. 40, No. 3]]
 +
* [[Julian Schrittwieser]], [[Ioannis Antonoglou]], [[Thomas Hubert]], [[Karen Simonyan]], [[Laurent Sifre]], [[Simon Schmitt]], [[Arthur Guez]], [[Edward Lockhart]], [[Demis Hassabis]], [[Thore Graepel]], [[Timothy Lillicrap]], [[David Silver]] ('''2019'''). ''Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model''. [https://arxiv.org/abs/1911.08265 arXiv:1911.08265] <ref>[http://www.talkchess.com/forum3/viewtopic.php?f=2&t=72381 New DeepMind paper] by GregNeto, [[CCC]], November 21, 2019</ref>
 +
* [[Vladimir Vargas-Calderón]] ('''2019'''). ''Are Armageddon chess games implemented fairly?'' [[ICGA Journal#41_4|ICGA Journal, Vol. 41, No. 4]] <ref>[https://en.wikipedia.org/wiki/Fast_chess#Armageddon Armageddon chess from Wikipedia]</ref>
 +
==2020 ...==
 +
* [[Manuel Cristóbal López-Michelone]], [[Jorge Luis Ortega-Arjona]] ('''2020'''). ''A description language for chess''. [[ICGA Journal#42_1|ICGA Journal, Vol. 42, No. 1]]
 +
* [[Nenad Tomašev]], [[Ulrich Paquet]], [[Demis Hassabis]], [[Vladimir Kramnik]] ('''2020'''). ''Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess''. [https://arxiv.org/abs/2009.04374 arXiv:2009.04374] » [[AlphaZero]]
 +
* [[Julian Schrittwieser]], [[Ioannis Antonoglou]], [[Thomas Hubert]], [[Karen Simonyan]], [[Laurent Sifre]], [[Simon Schmitt]], [[Arthur Guez]], [[Edward Lockhart]], [[Demis Hassabis]], [[Thore Graepel]], [[Timothy Lillicrap]], [[David Silver]] ('''2020'''). ''[https://www.nature.com/articles/s41586-020-03051-4 Mastering Atari, Go, chess and shogi by planning with a learned model]''. [https://en.wikipedia.org/wiki/Nature_%28journal%29 Nature], Vol. 588 <ref>[https://deepmind.com/blog/article/muzero-mastering-go-chess-shogi-and-atari-without-rules?fbclid=IwAR3mSwrn1YXDKr9uuGm2GlFKh76wBilex7f8QvBiQecwiVmAvD6Bkyjx-rE MuZero: Mastering Go, chess, shogi and Atari without rules]</ref>
  
 
=Forum Posts=  
 
=Forum Posts=  
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==2000 ...==
 
==2000 ...==
 
* [https://www.stmintz.com/ccc/index.php?id=272654 Does this position blow up your program?] by [[Michael Byrne|Mike Byrne]], [[CCC]], December 23, 2002
 
* [https://www.stmintz.com/ccc/index.php?id=272654 Does this position blow up your program?] by [[Michael Byrne|Mike Byrne]], [[CCC]], December 23, 2002
* [https://www.stmintz.com/ccc/index.php?id=424966 Subject: Maximum Number of Legal Moves] by [http://onezero.org/ Andrew Shapira], [[CCC]], May 08, 2005
+
* [https://www.stmintz.com/ccc/index.php?id=424966 Subject: Maximum Number of Legal Moves] by [[Andrew Shapira]], [[CCC]], May 08, 2005
 
* [http://www.talkchess.com/forum/viewtopic.php?t=17338 Variants and Board Size] by [[Harm Geert Muller]], [[CCC]], October 25, 2007
 
* [http://www.talkchess.com/forum/viewtopic.php?t=17338 Variants and Board Size] by [[Harm Geert Muller]], [[CCC]], October 25, 2007
 
==2010 ...==
 
==2010 ...==
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* [http://www.talkchess.com/forum/viewtopic.php?t=65292 Weakly vs strongly solving chess] by Greg Simpson, [[CCC]], September 26, 2017
 
* [http://www.talkchess.com/forum/viewtopic.php?t=65292 Weakly vs strongly solving chess] by Greg Simpson, [[CCC]], September 26, 2017
 
* [http://www.talkchess.com/forum/viewtopic.php?t=65962 best board representation for variants (javascript) ?] by [[Mahmoud Uthman]], [[CCC]], December 10, 2017 » [[Board Representation]], [[JavaScript]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=65962 best board representation for variants (javascript) ?] by [[Mahmoud Uthman]], [[CCC]], December 10, 2017 » [[Board Representation]], [[JavaScript]]
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=66003 One idea to solve chess?] by [[Mario Carbonell Martinez|Mario Carbonell]], [[CCC]], December 13, 2017
 
'''2018'''
 
'''2018'''
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66298 Is modern chess software lossless or lossy?] by Meni Rosenfeld, [[CCC]], January 10, 2018 » [[Playing Strength]], [[Selectivity]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66298 Is modern chess software lossless or lossy?] by Meni Rosenfeld, [[CCC]], January 10, 2018 » [[Playing Strength]], [[Selectivity]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66302 Is chess still 99% tactics?] by [[Alvaro Cardoso]], [[CCC]], January 11, 2018 » [[Tactics]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66302 Is chess still 99% tactics?] by [[Alvaro Cardoso]], [[CCC]], January 11, 2018 » [[Tactics]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66364 A Chess variant with low draw rate] by [[Kai Laskos]], [[CCC]], January 19, 2018 » [[Games#ChessVariants|Chess Variants]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=66364 A Chess variant with low draw rate] by [[Kai Laskos]], [[CCC]], January 19, 2018 » [[Games#ChessVariants|Chess Variants]]
 +
'''2019'''
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=70723 The Plan-9 to finally solve chess :)] by [[Sergei Markoff|Sergei S. Markoff]], [[CCC]], May 11, 2019
 +
==2020 ...==
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=75606 Transhuman Chess with NN and RL...] by [[Srdja Matovic]], [[CCC]], October 30, 2020 » [[Neural Networks|NN]], [[Reinforcement Learning|RL]]
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=75667 New PGN Tag: VariantFamily] by [[ Harm Geert Muller]], [[CCC]], November 03, 2020 » [[#Variants|Chess Variants]], [[Portable Game Notation|PGN]]
 +
'''2021'''
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=76382 correspondence chess in the age of NNUE] by [[Larry Kaufman]], [[CCC]], January 21, 2021 » [[NNUE]]
  
 
=External Links=  
 
=External Links=  
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=References=  
 
=References=  
 
<references />
 
<references />
'''[[Main Page|Home]]'''
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'''[[Main Page|Up one Level]]'''
 
[[Category:Anthony Braxton]]
 
[[Category:Anthony Braxton]]
 
[[Category:Marcel Duchamp]]
 
[[Category:Marcel Duchamp]]

Latest revision as of 11:21, 16 April 2021

Home * Chess

Chess [1]

Chess,
a two-player zero-sum abstract strategy board game with perfect information as classified by John von Neumann. Chess has an estimated state-space complexity of 1046 [2] , the estimated game tree complexity of 10123 is based on an average branching factor of 35 and an average game length of 80 ply [3] . This page is about the basic chess items, chessboard, pieces and moves, and how they are considered or encoded inside a chess program, to either represent a chess position inside its search and to play the game of chess. It sub-pages intersect with evaluation, board representation and even search topics.

Board and Squares

Pieces and Moves

Color and Side

The Game of Chess

During the Game

The End

Chess Variants

Chess Problems

Chess and Mathematics

Chess Maxima

    
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    
    
    
    
    
    
      
       
      
       
      
      
     
  
♖      ♖
   ♕    
 ♕    ♕ 
    ♕   
  ♕    ♕
♕    ♕  
♟♟ ♕    
♚♗♘♘ ♔♗ 
R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1

Chess and Psychology

Chess and Philosophy

Quote from Philosophy Looks at Chess [13] :

The game of chess has endured since at least the sixth century. Its earliest variant, the Indian game of Chaturanga, was from the beginning a game for thinkers. Since its inception, scholars, statesmen, strategists, and warriors have been fascinated by the game and its variants. German philosopher Emanuel Lasker and famed French artist Marcel Duchamp were both Grandmasters at chess. Karl Marx played chess avidly, as did Sir Bertrand Russell, Jean-Paul Sartre, and the logical positivist Max Black. Jean-Jacques Rousseau [14] mentions in his Confessions that, at the time, he "had another expedient, not less solid, in the game of chess, to which I regularly dedicated, at Maugis's, the evenings on which I did not go to the theater. I became acquainted with M. de Légal, M. Husson, Philidor, and all the great chess players of the day, without making the least improvement in the game." More recently, philosopher Stuart Rachels reports that his father, the late philosopher and prominent ethicist James Rachels, received a bribe from a Russian Grandmaster while he was the chair of the U.S. Chess Federation's Ethics committee. 

Chess Programs called Chess

Categories

See also

Publications

1949

1950 ...

1955 ...

1960 ...

  • Alan Kotok (1962). A Chess Playing Program for the IBM 7090, B.S. Thesis, MIT, AI Project Memo 41, Computation Center, Cambridge MA. pdf

1965 ...

1970 ...

1975 ...

1980 ...

1985 ...

  • Ingo Althöfer (1985). Das 3-Hirn - Entscheidungsteilung im Schach. Computerschach und Spiele, pp. 20-22 (German)
  • Ingo Althöfer (1989). A Survey of Some Results in Theoretical Game Tree Search and the 'Dreihirn'-experiment. Proceedings Workshop on New Directions in Game-tree Search, pp. 16-32. Edmonton, Canada.

1990 ...

1995 ...

2000 ...

2005 ...

2010 ...

2015 ...

2020 ...

Forum Posts

1989

1990 ...

2000 ...

2010 ...

2014

2015 ...

2016

2017

2018

2019

2020 ...

2021

External Links

Wikipedia

Chess theory from Wikipedia
Computer chess from Wikipedia
First-move advantage in chess from Wikipedia
Outline of chess from Wikipedia
Rules of Chess from Wikipedia
School of chess from Wikipedia
Solving chess from Wikipedia
Glossary of chess from Wikipedia

Chess

Chess Variants

Misc

References

  1. An illustration by Ebel for James E. Gunn's Breaking Point, appeared in Space Science Fiction, March 1953
  2. Shirish Chinchalkar (1996). An Upper Bound for the Number of Reachable Positions. ICCA Journal, Vol. 19, No. 3, pp. 181-183
  3. Victor Allis (1994). Searching for Solutions in Games and Artificial Intelligence. Ph.D. Thesis, University of Limburg, pdf, 6.3.9 Chess pp. 171
  4. Seirawan chess from Wikipedia
  5. Eero Bonsdorff, Karl Fabel, Olvai Riihimaa (1966) Schach und Zahl - Unterhaltsame Schachmathematik. Seite 11-13, Walter Rau Verlag, Düsseldorf (German)
  6. 50-Züge-Regel - Schachmathematik from Wikipedia.de (German)
  7. Defending Humanity's Honor by Tim Krabbé, see game NewRival - Faile with 493 moves, and playing 402 moves with bare kings!
  8. Shirish Chinchalkar (1996). An Upper Bound for the Number of Reachable Positions. ICCA Journal, Vol. 19, No. 3
  9. John's Chess Playground - Number of chess diagrams and positions
  10. Re: Total possible chess positions? by Álvaro Begué, CCC, March 26, 2014
  11. Does this position blow up your program? by Mike Byrne, CCC, December 23, 2002
  12. Subject: Maximum Number of Legal Moves by Andrew Shapira, CCC, May 08, 2005
  13. Philosophy Looks at Chess by Benjamin Hale
  14. Jean-Jacques Rousseau and Chess by Edward Winter
  15. Chess Metaphors – Artificial Intelligence and the Human Mind by Diego Rasskin-Gutman, ChessBase News, January 28, 2010
  16. Zipf's law from WIkipedia
  17. Machine creativity: what it is and what it isn't by Albert Silver, ChessBase News, August 28, 2016
  18. First-order logic from Wikipedia
  19. The joys of chess – and the value of the pieces, ChessBase News, December 21, 2011
  20. Re: Tony's positional test suite by Louis Zulli, CCC, August 01, 2017
  21. Progressive chess from Wikipedia
  22. Using GAN to play chess by Evgeniy Zheltonozhskiy, CCC, February 23, 2017
  23. The Secret of Chess by Lyudmil Tsvetkov, CCC, August 01, 2017
  24. AlphaZero: Shedding new light on the grand games of chess, shogi and Go by David Silver, Thomas Hubert, Julian Schrittwieser and Demis Hassabis, DeepMind, December 03, 2018
  25. New DeepMind paper by GregNeto, CCC, November 21, 2019
  26. Armageddon chess from Wikipedia
  27. MuZero: Mastering Go, chess, shogi and Atari without rules
  28. BBC Computer Chess Radio Programme by Harvey Williamson, Hiarcs Forum, September 11, 2010

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