Difference between revisions of "Chess"

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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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* [[Match Statistics]]
 
* [[Match Statistics]]
 
* [[Playing Strength]]
 
* [[Playing Strength]]
* [[Rules of Chess]] (Computer Chess related)
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* [[Rules of Chess]]
 
* [[Time Management]]
 
* [[Time Management]]
  
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<span id="Maxima"></span>
 
<span id="Maxima"></span>
 
=Chess Maxima=  
 
=Chess Maxima=  
 +
* In 1950 [[Claude Shannon]] gave a conservative lower bound ([https://en.wikipedia.org/wiki/Shannon_number the Shannon number]) of the game-tree complexity of chess of 10^120 (possible games), and 10^43 for the amount of possible positions.<ref>[https://www.computerhistory.org/chess/doc-431614f453dde/ Programming a Computer for Playing Chess. download pdf from The Computer History Museum]</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>
 
* 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>  
+
* 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]]
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 +
=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)]]
* [[:Category:Chess Legend|Chess Legends]]
 
 
* [[Chess Query Language]]
 
* [[Chess Query Language]]
 
* [[Cognition]]
 
* [[Cognition]]
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* [[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''. M.Sc. thesis, [[Technical University of Łódź]]
 
* [[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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* [[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>
 
* [[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>
 
* [[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>
 +
* [[Monroe Newborn|Monty Newborn]] ('''2021'''). ''Mad Monty Chess''. [[ICGA Journal#43_1|ICGA Journal, Vol. 43, No. 1]]
 +
* [[Maximilian Alexander Gehrke]] ('''2021'''). ''Assessing Popular Chess Variants Using Deep Reinforcement Learning''. Master thesis, [[Darmstadt University of Technology|TU Darmstadt]], [https://ml-research.github.io/papers/gehrke2021assessing.pdf pdf] » [[CrazyAra]]
 +
* [[Dominik Klein]] ('''2021'''). ''[https://github.com/asdfjkl/neural_network_chess Neural Networks For Chess]''. [https://github.com/asdfjkl/neural_network_chess/releases/tag/v1.1 Release Version 1.1 · GitHub] <ref>[https://www.talkchess.com/forum3/viewtopic.php?f=2&t=78283 Book about Neural Networks for Chess] by dkl, [[CCC]], September 29, 2021</ref>
 +
* [[Guy Haworth]] ('''2021'''). ''Chess without draws''. [[ICGA Journal#43_2|ICGA Journal, Vol. 43, No. 2]]
 +
* [[Thomas McGrath]], [[Andrei Kapishnikov]], [[Nenad Tomašev]], [[Adam Pearce]], [[Demis Hassabis]], [[Been Kim]], [[Ulrich Paquet]], [[Vladimir Kramnik]] ('''2021'''). ''Acquisition of Chess Knowledge in AlphaZero''. [https://arxiv.org/abs/2111.09259 arXiv:2111.09259] » [[AlphaZero]] <ref>[https://en.chessbase.com/post/acquisition-of-chess-knowledge-in-alphazero Acquisition of Chess Knowledge in AlphaZero], [[ChessBase|ChessBase News]], November 18, 2021</ref>
 +
* [[Miha Bizjak]], [[Matej Guid]] ('''2021'''). ''Automatic Recognition of Similar Chess Motifs''. [[Advances in Computer Games 17]]
 +
* [[Nenad Tomašev]], [[Ulrich Paquet]], [[Demis Hassabis]], [[Vladimir Kramnik]] ('''2022'''). ''[https://cacm.acm.org/magazines/2022/2/258230-reimagining-chess-with-alphazero/fulltext Reimagining Chess with AlphaZero]''. [[ACM#Communications|Communications of the ACM]], Vol. 65, No. 2 » [[AlphaZero]]
  
 
=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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'''2019'''
 
'''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
 
* [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]]
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=77685 On the number of chess positions] by [[John Tromp]], [[CCC]], July 09, 2021 » [[Chess Position]]
 +
* [https://www.talkchess.com/forum3/viewtopic.php?f=7&t=78464 Open Chess Game Database Standard (OCGDB)] by [[Pham Hong Nguyen|Nguyen Pham]], [[CCC]], October 20, 2021 » [[Databases|Chess Databases]]
 +
'''2022'''
 +
* [https://www.talkchess.com/forum3/viewtopic.php?f=7&t=77685&start=34 Re: On the number of chess positions] by [[John Tromp]], [[CCC]], April 02, 2022 » [[Chess Position]]
 +
'''2023'''
 +
* [https://talkchess.com/forum3/viewtopic.php?f=2&t=81858 The Next Big Thing in Computer Chess?] by [[Srdja Matovic]], [[CCC]], April 12, 2023 » [[Artificial Intelligence]], [[Programming]], [[Hardware]]
 +
:[https://talkchess.com/forum3/viewtopic.php?f=2&t=81858&start=100#p951488 Re: The Next Big Thing in Computer Chess?] by [[Srdja Matovic]], [[CCC]],  August 20, 2023
 +
* [https://talkchess.com/forum3/viewtopic.php?f=2&t=82826 Is there any project coming to solve chess?] by Jouni, [[CCC]], November 06, 2023
  
 
=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 19:47, 22 November 2023

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

Chess Variants

Chess Problems

Chess and Mathematics

Chess Maxima

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

Chess and Psychology

Chess and Philosophy

Quote from Philosophy Looks at Chess [14] :

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 [15] 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

2022

2023

Re: The Next Big Thing in Computer Chess? by Srdja Matovic, CCC, August 20, 2023

External Links

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. Programming a Computer for Playing Chess. download pdf from The Computer History Museum
  6. Eero Bonsdorff, Karl Fabel, Olvai Riihimaa (1966) Schach und Zahl - Unterhaltsame Schachmathematik. Seite 11-13, Walter Rau Verlag, Düsseldorf (German)
  7. 50-Züge-Regel - Schachmathematik from Wikipedia.de (German)
  8. Defending Humanity's Honor by Tim Krabbé, see game NewRival - Faile with 493 moves, and playing 402 moves with bare kings!
  9. Shirish Chinchalkar (1996). An Upper Bound for the Number of Reachable Positions. ICCA Journal, Vol. 19, No. 3
  10. John's Chess Playground - Number of chess diagrams and positions
  11. Re: Total possible chess positions? by Álvaro Begué, CCC, March 26, 2014
  12. Does this position blow up your program? by Mike Byrne, CCC, December 23, 2002
  13. Subject: Maximum Number of Legal Moves by Andrew Shapira, CCC, May 08, 2005
  14. Philosophy Looks at Chess by Benjamin Hale
  15. Jean-Jacques Rousseau and Chess by Edward Winter
  16. Chess Metaphors – Artificial Intelligence and the Human Mind by Diego Rasskin-Gutman, ChessBase News, January 28, 2010
  17. Zipf's law from WIkipedia
  18. Machine creativity: what it is and what it isn't by Albert Silver, ChessBase News, August 28, 2016
  19. First-order logic from Wikipedia
  20. The joys of chess – and the value of the pieces, ChessBase News, December 21, 2011
  21. Re: Tony's positional test suite by Louis Zulli, CCC, August 01, 2017
  22. Progressive chess from Wikipedia
  23. Using GAN to play chess by Evgeniy Zheltonozhskiy, CCC, February 23, 2017
  24. The Secret of Chess by Lyudmil Tsvetkov, CCC, August 01, 2017
  25. 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
  26. New DeepMind paper by GregNeto, CCC, November 21, 2019
  27. Armageddon chess from Wikipedia
  28. MuZero: Mastering Go, chess, shogi and Atari without rules
  29. Book about Neural Networks for Chess by dkl, CCC, September 29, 2021
  30. Acquisition of Chess Knowledge in AlphaZero, ChessBase News, November 18, 2021
  31. BBC Computer Chess Radio Programme by Harvey Williamson, Hiarcs Forum, September 11, 2010

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