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Created page with "'''Home * Evaluation * Game Phases * Endgame''' FILE:TanningEndGame.jpg|border|right|thumb|link=https://www.dorotheatanning.org/life-and-work/view/229..."
'''[[Main Page|Home]] * [[Evaluation]] * [[Game Phases]] * Endgame'''
[[FILE:TanningEndGame.jpg|border|right|thumb|link=https://www.dorotheatanning.org/life-and-work/view/229/||[[Arts#Tanning|Dorothea Tanning]] - End Game, 1944 <ref>[[Arts#Tanning|Dorothea Tanning]] - End Game, 1944, from [http://www.artnet.com/magazineus/reviews/davis/davis11-1-05.asp artnet Magazine - We Are Duchampians by Ben Davis], [https://www.dorotheatanning.org/life-and-work/view/229/ Endgame | Dorothea Tanning]</ref> ]]
In the '''Endgame''' chess programs usually have quite a lot of difficulties. Even the most simple endgames often just lead to a mate after 10 to 15 plys or more, which is far beyond the horizon for engines without the specific endgame knowledge. There are some concepts that a chess programmer should implement to overcome the most basic problems. Usually chess engines activate this special Endgame knowledge as soon as the material on board reaches a certain lower-bound.
=Transposition Tables=
Nowhere else are the [[Transposition Table|Transposition Hash Tables]] more efficient than in Endgames. They are invaluable.
=Evaluation=
When doing a positional evaluation, in the endgame, the chess engines should change some parameters. So for example in the [[Middlegame|middlegame]], if the opponent's [[King|king]] is trapped in the center, it should be evaluated much better for the program than the opponent's king, safely standing at the border. In the '''endgame''' however, its the other way round. A king on the edge or even in the corner has not so many squares to escape to and is more beneficial for the other player. Furthermore, if you only have one [[Bishop|bishop]], it might be good to evaluate the opponent's king being forced to go to the corner with the [[Color|color]] of the bishop a higher bonus, than for the other corner. In addition Pawn promotion is a very important aim in most endgames. The chess engines should consider that by evaluating the strength of [[Passed Pawn|passed pawns]].
=Special Knowledge=
Some endgames are extensively covered by theory, and for that reason one can supply a vast number of heuristics for playing them. Typical examples include:
* [[Blockage Detection]]
* [[Draw Evaluation]]
* [[Mop-up Evaluation]]
==King and Pawns==
* [[Corresponding Squares]]
* [[King Centralization]]
* [[King Pawn Tropism]]
* [[KPK]] database/rules
* [[Pawn Endgame]]
* [[Rule of the Square]]
==Pieces==
* [[Bishops of Same Color]] endgame
* [[Bishops of Opposite Colors]] endgame
* [[Wrong color Bishop and rook pawn]]
* [[Bishop versus Knight]]
* Mating in [[KBNK Endgame|KNBK]]
* [[KRK]]
* [[Rook Endgame]]
* [[Queen Endgame]]
==Endgame Tablebases==
''see main article [[Endgame Tablebases]].''
Currently many engines support the usage of [[Endgame Tablebases]], precalculated databases that hold for every possible position in a certain endgame, whether it is drawn or how many moves are left for a side to win/lose assuming perfect play. With the help of those, chess engines can simply lookup, if it is advisable to do a certain exchange or not, as well as how to finish some of the more tricky endgames. The advantage of Endgame Tablebases is the ability to determine the definite outcome of a certain position, but on the other side, Tablebases are very space consuming and the disk-access tends to be slow.
=See also=
* [[Endgame Tablebases]]
* [[Opening]]
* [[Middlegame]]
* [[Retrograde Analysis]]
=Publications=
==1960 ...==
* [[Barbara Liskov|Barbara J. Huberman]] ('''1968'''). ''A Program to Play Chess End Games''. Technical Report no. CS-106, Ph.D. thesis. [[Stanford University]], Computer Science Department
==1970 ...==
* [[Coen Zuidema]] ('''1974'''). ''Chess: How to Program the Exceptions?'' Technical Report IW21/74, Department of Informatics, [https://en.wikipedia.org/wiki/Centrum_Wiskunde_%26_Informatica Mathematical Center Amdsterdam]. [http://oai.cwi.nl/oai/asset/9480/9480A.pdf pdf]
* [[Pericles Negri]] ('''1977'''). ''Inductive Learning in a Hierarchical Model for Representing Knowledge in Chess End Games''. [http://www.mli.gmu.edu/papers/69-78/77-2.pdf pdf]
* [[Ryszard Michalski]], [[Pericles Negri]] ('''1977'''). ''An experiment on inductive learning in chess endgames''. [http://www.doc.ic.ac.uk/~shm/MI/mi8.html Machine Intelligence 8], [http://www.mli.gmu.edu/papers/69-78/77-1.pdf pdf]
* [[Kenneth W. Church]] ('''1978'''). ''[http://dl.acm.org/citation.cfm?id=67030 Co-ordinate Squares: A Solution to Many Chess Pawn Endgames]''. B.Sc. thesis, [[Massachusetts Institute of Technology]], reprinted 1988 in [[Computer Chess Compendium]] » [[Corresponding Squares]]
* [[Ivan Bratko]], [[Tim Niblett]] ('''1979'''). ''Conjectures and Refutations in a Framework for Chess Endgames''. in Expert Systems in the Micro-Electronic Age ([[Donald Michie]], ed.), Edinburgh: Edinburgh University Press, 1979.
* [[Ross Quinlan]] ('''1979'''). ''Discovering Rules by Induction from Large Collections of Examples''. Expert Systems in the Micro-electronic Age, pp. 168-201. Edinburgh University Press (Introducing ID3)
==1980 ...==
* [[Danny Kopec]], [[Tim Niblett]] ('''1980'''). ''How Hard is the Play of the King-Rook-King-Knight Ending?'' [[Advances in Computer Chess 2]]
* [[John F. White]] ('''1981'''). ''[http://yourcomputeronline.wordpress.com/2010/12/27/chess-end-game/ Chess-End-Game]''. [[Your Computer]], [http://yourcomputeronline.wordpress.com/2010/12/10/december-1981-%E2%80%93-contents-and-editorial/ December 1981]
* [[Alen Shapiro]], [[Tim Niblett]] ('''1982'''). ''Automatic Induction of Classification Rules for Chess End game.'' [[Advances in Computer Chess 3]]
* [[Ross Quinlan]] ('''1983'''). ''Learning efficient classification procedures and their application to chess end games''. In Machine Learning: An Artificial Intelligence Approach, pages 463–482. Tioga, Palo Alto
* [[Denis Verhoef]], [[Jacco H. Wesselius]] ('''1987'''). ''Two-ply KRKN: Safely overtaking Quinlan''. [[ICGA Journal#10_4|ICCA Journal, Vol. 10, No. 4]]
* [[Lars Rasmussen]] ('''1987'''). ''Correcting grandmasters' Analyses in Elementary Endgames''. [[ICGA Journal#10_4|ICCA Journal, Vol. 10, No. 4]]
==1990 ...==
* [[Lars Rasmussen]] ('''1992'''). ''Queen versus Rook and Pawn''. [[ICGA Journal#15_2|ICCA Journal, Vol. 15, No. 2]]
* [[Wilhelm Barth]], [[Stephan Barth]] ('''1992'''). ''Validating a Range of Endgame Programs''. [[ICGA Journal#15_3|ICCA Journal, Vol. 15, No. 3]]
* [[Jean-Christophe Weill]] ('''1994'''). ''How Hard is the Correct Coding of an Easy Endgame?'' [[Advances in Computer Chess 7]], [http://www.recherche.enac.fr/%7Eweill/publications/acc7.ps.gz zipped ps]
==1995 ...==
* [[Lewis Stiller]] ('''1996'''). ''Multilinear Algebra and Chess Endgames''. [http://library.msri.org/books/Book29/index.html Games of No Chance] edited by [[Richard J. Nowakowski]], [http://www.msri.org/publications/books/Book29/files/stiller.pdf pdf]
* [https://en.wikipedia.org/wiki/Roberto_Cifuentes Roberto Cifuentes], [http://www.newinchess.com/De_Zeeuw__Maarten-ip-185.html Maarten De Zeeuw], [[Jan van Reek]] ('''1997'''). ''Secrets of Chess Endings''. [[ICGA Journal#20_4|ICCA Journal, Vol. 20, No. 4]]
* [[Kevin Coplan]] ('''1998'''). ''Synthesis of Chess and Chess-like Endgames by Recursive Optimisation''. [[ICGA Journal#21_3|ICCA Journal, Vol. 21, No. 3]]
* [[Noam Elkies|Noam D. Elkies]] ('''1999'''). ''On numbers and endgames: Combinatorial game theory in chess endgames''. [http://arxiv.org/PS_cache/math/pdf/9905/9905198v1.pdf pdf], differs only in trivial stylistic details from the ('''1996''') version published in [http://library.msri.org/books/Book29/index.html Games of No Chance] edited by [[Richard J. Nowakowski]]
* [[Philip G. K. Reiser]], [[Patricia J. Riddle]] ('''1999'''). ''[http://link.springer.com/chapter/10.1007%2F3-540-48873-1_19 Evolving Logic Programs to Classify Chess-Endgame Positions]''. [http://link.springer.com/book/10.1007%2F3-540-48873-1 Simulated Evolution and Learning], [https://en.wikipedia.org/wiki/Canberra Canberra], Australia. [http://www.springer.com/series/1244 Lecture Notes in Artificial Intelligence], No. 1585, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer], [http://stancomb.co.uk/Papers/seal98.pdf pdf] » [[Learning]]
==2000 ...==
* [[Matthias Lüscher]] ('''2000'''). ''Automatic Generation of an Evaluation Function for Chess Endgames''. [[ETH Zurich]] Supervisors: [[Thomas Lincke]] and [[Christoph Wirth]], [http://www.datacomm.ch/m.luescher/evaluation_function_en.pdf pdf] » [[Neural Networks]]
* [[Kevin Coplan]] ('''2001'''). ''[http://ilk.uvt.nl/icga/journal/contents/content24-1.htm#SYNTHESIS%20OF%20CHESS Synthesis of Chess and Chess-like Endgames: A Proof of Correctness]''. [[ICGA Journal#24_1|ICCA Journal, Vol. 24, No. 1]]
* [[Kevin Coplan]] ('''2001'''). ''Synthesis of Chess-like Endgames: Towards a Proof of Correctness''. [[Advances in Computer Games 9]]
==2005 ...==
* [[Ami Hauptman]], [[Moshe Sipper]] ('''2005'''). ''GP-EndChess: Using Genetic Programming to Evolve Chess Endgame Players''. [http://www.informatik.uni-trier.de/~ley/db/conf/eurogp/eurogp2005.html#HauptmanS05 EuroGP 2005], [http://www.cs.bgu.ac.il/~sipper/papabs/eurogpchess-final.pdf pdf]
* [[Omid David]], [[Ariel Felner]], [[Nathan S. Netanyahu]] ('''2006'''). ''Blockage Detection in Pawn Endgames''. [https://en.wikipedia.org/wiki/Lecture_Notes_in_Computer_Science LNCS] 3846, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer]
* [[Ami Hauptman]], [[Moshe Sipper]] ('''2007'''). ''Emergence of Complex Strategies in the Evolution of Chess Endgame Players''. [http://www.informatik.uni-trier.de/~ley/db/journals/advcs/advcs10.html#HauptmanS07 Advances in Complex Systems 10]
* [[John Nunn]] ('''2009'''). ''[http://www.newinchess.com/Understanding_Chess_Endgames-p-1843.html Understanding Chess Endgames]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit] <ref>[http://www.chessbase.com/post/nunn-on-understanding-che-endgames Nunn on Understanding Chess Endgames], [[ChessBase|ChessBase News]], September 13, 2009</ref>
==2010 ...==
* [[John Nunn]] ('''2010'''). ''[http://www.newinchess.com/Nunn_s_Chess_Endings__Volume_1-p-5025.html Nunn's Chess Endings, volume 1]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit] <ref>[http://www.chessbase.com/post/nunn-s-che-endings-volume-one Nunn’s Chess Endings Volume One], [[ChessBase|ChessBase News]], May 28, 2010</ref>
* [[John Nunn]] ('''2010'''). ''[http://www.newinchess.com/Nunn_s_Chess_Endings__Volume_2-p-5053.html Nunn's Chess Endings, volume 2]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit]
* [[John Nunn]] ('''2013'''). ''Discoveries in R+2P vs. R+P Endings''. [[ICGA Journal#36_3|ICGA Journal, Vol. 36, No. 3]] » [[Lomonosov Tablebases]]
* [[Karsten Müller]], [[Guy Haworth]] ('''2013'''). ''Rook vs. Bishop''. [[ICGA Journal#36_4|ICGA Journal, Vol. 36, No. 4]]
* [[Matej Guid]], [[Martin Možina]], [[Ciril Bohak]], [[Aleksander Sadikov]], [[Ivan Bratko]] ('''2013'''). ''Building an Intelligent Tutoring System for Chess Endgames''. [http://dblp.uni-trier.de/db/conf/csedu/csedu2013.html#GuidMBSB13 CSEDU 2013]
==2015 ...==
* [[Michael Hartisch]], [[Ingo Althöfer]] ('''2015'''). ''Optimal Robot Play in Certain Chess Endgame Situations''. [[ICGA Journal#38_3|ICGA Journal, Vol. 38, No. 3]]
* [[Efstratios Grivas]] ('''2017'''). ''The Modern Endgame Manual''. [[ICGA Journal#39_2|ICGA Journal, Vol. 39, No. 2]]
* [[Karsten Müller]] ('''2017'''). ''Tablebases, Fermat, Knights and Knightmares''. [[ICGA Journal#39_2|ICGA Journal, Vol. 39, No. 2]]
* [[Guy Haworth]] ('''2017'''). ''Understanding Rook Endgames''. [[ICGA Journal#39_2|ICGA Journal, Vol. 39, No. 2]]
=Forum Posts=
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=198870 Endgame evaluation] by [[Benny Antonsson]], [[CCC]], November 25, 2001
* [https://www.stmintz.com/ccc/index.php?id=348493 Piece Values in the Endgame] by [[Guy Haworth]], [[CCC]], February 11, 2004 » [[Point Value]]
* [https://www.stmintz.com/ccc/index.php?id=358108 transition to endgame] by [[Eric Oldre]], [[CCC]], April 02, 2004
* [https://www.stmintz.com/ccc/index.php?id=359113 Improving the endgame of my engine] by [[Albert Bertilsson]], [[CCC]], April 08, 2004 » [[Sharper]]
* [http://www.talkchess.com/forum/viewtopic.php?t=19296 Definition of "endgame"?] by [[Jouni Uski]], [[CCC]], January 30, 2008
==2010 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=40629 End-game evaluation] by [[Harm Geert Muller|H.G.Muller]], [[CCC]], October 04, 2011
* [http://www.talkchess.com/forum/viewtopic.php?t=47173 Start EndGame - A matter of fine tuning ???] by [[Lourenço Araujo de Oliveira Junior]], [[CCC]], February 09, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=51672 End Game Heuristics] by [[Laurie Tunnicliffe]], [[CCC]], March 20, 2014
* [http://www.talkchess.com/forum/viewtopic.php?t=62153 Define end game] by [[Laurie Tunnicliffe]], [[CCC]], November 16, 2016 » [[Tapered Eval]]
* [http://www.talkchess.com/forum/viewtopic.php?t=64356 Testing endgame strength] by [[Álvaro Begué]], [[CCC]], June 21, 2017 » [[Engine Testing]], [[RuyDos]]
=External Links=
* [https://en.wikipedia.org/wiki/Chess_endgame Chess endgame from Wikipedia]
* [https://en.wikipedia.org/wiki/Pawnless_chess_endgame Pawnless chess endgame from Wikipedia]
=References=
<references />
'''[[Game Phases|Up one level]]'''
[[Category:Dorothea Tanning]]
[[FILE:TanningEndGame.jpg|border|right|thumb|link=https://www.dorotheatanning.org/life-and-work/view/229/||[[Arts#Tanning|Dorothea Tanning]] - End Game, 1944 <ref>[[Arts#Tanning|Dorothea Tanning]] - End Game, 1944, from [http://www.artnet.com/magazineus/reviews/davis/davis11-1-05.asp artnet Magazine - We Are Duchampians by Ben Davis], [https://www.dorotheatanning.org/life-and-work/view/229/ Endgame | Dorothea Tanning]</ref> ]]
In the '''Endgame''' chess programs usually have quite a lot of difficulties. Even the most simple endgames often just lead to a mate after 10 to 15 plys or more, which is far beyond the horizon for engines without the specific endgame knowledge. There are some concepts that a chess programmer should implement to overcome the most basic problems. Usually chess engines activate this special Endgame knowledge as soon as the material on board reaches a certain lower-bound.
=Transposition Tables=
Nowhere else are the [[Transposition Table|Transposition Hash Tables]] more efficient than in Endgames. They are invaluable.
=Evaluation=
When doing a positional evaluation, in the endgame, the chess engines should change some parameters. So for example in the [[Middlegame|middlegame]], if the opponent's [[King|king]] is trapped in the center, it should be evaluated much better for the program than the opponent's king, safely standing at the border. In the '''endgame''' however, its the other way round. A king on the edge or even in the corner has not so many squares to escape to and is more beneficial for the other player. Furthermore, if you only have one [[Bishop|bishop]], it might be good to evaluate the opponent's king being forced to go to the corner with the [[Color|color]] of the bishop a higher bonus, than for the other corner. In addition Pawn promotion is a very important aim in most endgames. The chess engines should consider that by evaluating the strength of [[Passed Pawn|passed pawns]].
=Special Knowledge=
Some endgames are extensively covered by theory, and for that reason one can supply a vast number of heuristics for playing them. Typical examples include:
* [[Blockage Detection]]
* [[Draw Evaluation]]
* [[Mop-up Evaluation]]
==King and Pawns==
* [[Corresponding Squares]]
* [[King Centralization]]
* [[King Pawn Tropism]]
* [[KPK]] database/rules
* [[Pawn Endgame]]
* [[Rule of the Square]]
==Pieces==
* [[Bishops of Same Color]] endgame
* [[Bishops of Opposite Colors]] endgame
* [[Wrong color Bishop and rook pawn]]
* [[Bishop versus Knight]]
* Mating in [[KBNK Endgame|KNBK]]
* [[KRK]]
* [[Rook Endgame]]
* [[Queen Endgame]]
==Endgame Tablebases==
''see main article [[Endgame Tablebases]].''
Currently many engines support the usage of [[Endgame Tablebases]], precalculated databases that hold for every possible position in a certain endgame, whether it is drawn or how many moves are left for a side to win/lose assuming perfect play. With the help of those, chess engines can simply lookup, if it is advisable to do a certain exchange or not, as well as how to finish some of the more tricky endgames. The advantage of Endgame Tablebases is the ability to determine the definite outcome of a certain position, but on the other side, Tablebases are very space consuming and the disk-access tends to be slow.
=See also=
* [[Endgame Tablebases]]
* [[Opening]]
* [[Middlegame]]
* [[Retrograde Analysis]]
=Publications=
==1960 ...==
* [[Barbara Liskov|Barbara J. Huberman]] ('''1968'''). ''A Program to Play Chess End Games''. Technical Report no. CS-106, Ph.D. thesis. [[Stanford University]], Computer Science Department
==1970 ...==
* [[Coen Zuidema]] ('''1974'''). ''Chess: How to Program the Exceptions?'' Technical Report IW21/74, Department of Informatics, [https://en.wikipedia.org/wiki/Centrum_Wiskunde_%26_Informatica Mathematical Center Amdsterdam]. [http://oai.cwi.nl/oai/asset/9480/9480A.pdf pdf]
* [[Pericles Negri]] ('''1977'''). ''Inductive Learning in a Hierarchical Model for Representing Knowledge in Chess End Games''. [http://www.mli.gmu.edu/papers/69-78/77-2.pdf pdf]
* [[Ryszard Michalski]], [[Pericles Negri]] ('''1977'''). ''An experiment on inductive learning in chess endgames''. [http://www.doc.ic.ac.uk/~shm/MI/mi8.html Machine Intelligence 8], [http://www.mli.gmu.edu/papers/69-78/77-1.pdf pdf]
* [[Kenneth W. Church]] ('''1978'''). ''[http://dl.acm.org/citation.cfm?id=67030 Co-ordinate Squares: A Solution to Many Chess Pawn Endgames]''. B.Sc. thesis, [[Massachusetts Institute of Technology]], reprinted 1988 in [[Computer Chess Compendium]] » [[Corresponding Squares]]
* [[Ivan Bratko]], [[Tim Niblett]] ('''1979'''). ''Conjectures and Refutations in a Framework for Chess Endgames''. in Expert Systems in the Micro-Electronic Age ([[Donald Michie]], ed.), Edinburgh: Edinburgh University Press, 1979.
* [[Ross Quinlan]] ('''1979'''). ''Discovering Rules by Induction from Large Collections of Examples''. Expert Systems in the Micro-electronic Age, pp. 168-201. Edinburgh University Press (Introducing ID3)
==1980 ...==
* [[Danny Kopec]], [[Tim Niblett]] ('''1980'''). ''How Hard is the Play of the King-Rook-King-Knight Ending?'' [[Advances in Computer Chess 2]]
* [[John F. White]] ('''1981'''). ''[http://yourcomputeronline.wordpress.com/2010/12/27/chess-end-game/ Chess-End-Game]''. [[Your Computer]], [http://yourcomputeronline.wordpress.com/2010/12/10/december-1981-%E2%80%93-contents-and-editorial/ December 1981]
* [[Alen Shapiro]], [[Tim Niblett]] ('''1982'''). ''Automatic Induction of Classification Rules for Chess End game.'' [[Advances in Computer Chess 3]]
* [[Ross Quinlan]] ('''1983'''). ''Learning efficient classification procedures and their application to chess end games''. In Machine Learning: An Artificial Intelligence Approach, pages 463–482. Tioga, Palo Alto
* [[Denis Verhoef]], [[Jacco H. Wesselius]] ('''1987'''). ''Two-ply KRKN: Safely overtaking Quinlan''. [[ICGA Journal#10_4|ICCA Journal, Vol. 10, No. 4]]
* [[Lars Rasmussen]] ('''1987'''). ''Correcting grandmasters' Analyses in Elementary Endgames''. [[ICGA Journal#10_4|ICCA Journal, Vol. 10, No. 4]]
==1990 ...==
* [[Lars Rasmussen]] ('''1992'''). ''Queen versus Rook and Pawn''. [[ICGA Journal#15_2|ICCA Journal, Vol. 15, No. 2]]
* [[Wilhelm Barth]], [[Stephan Barth]] ('''1992'''). ''Validating a Range of Endgame Programs''. [[ICGA Journal#15_3|ICCA Journal, Vol. 15, No. 3]]
* [[Jean-Christophe Weill]] ('''1994'''). ''How Hard is the Correct Coding of an Easy Endgame?'' [[Advances in Computer Chess 7]], [http://www.recherche.enac.fr/%7Eweill/publications/acc7.ps.gz zipped ps]
==1995 ...==
* [[Lewis Stiller]] ('''1996'''). ''Multilinear Algebra and Chess Endgames''. [http://library.msri.org/books/Book29/index.html Games of No Chance] edited by [[Richard J. Nowakowski]], [http://www.msri.org/publications/books/Book29/files/stiller.pdf pdf]
* [https://en.wikipedia.org/wiki/Roberto_Cifuentes Roberto Cifuentes], [http://www.newinchess.com/De_Zeeuw__Maarten-ip-185.html Maarten De Zeeuw], [[Jan van Reek]] ('''1997'''). ''Secrets of Chess Endings''. [[ICGA Journal#20_4|ICCA Journal, Vol. 20, No. 4]]
* [[Kevin Coplan]] ('''1998'''). ''Synthesis of Chess and Chess-like Endgames by Recursive Optimisation''. [[ICGA Journal#21_3|ICCA Journal, Vol. 21, No. 3]]
* [[Noam Elkies|Noam D. Elkies]] ('''1999'''). ''On numbers and endgames: Combinatorial game theory in chess endgames''. [http://arxiv.org/PS_cache/math/pdf/9905/9905198v1.pdf pdf], differs only in trivial stylistic details from the ('''1996''') version published in [http://library.msri.org/books/Book29/index.html Games of No Chance] edited by [[Richard J. Nowakowski]]
* [[Philip G. K. Reiser]], [[Patricia J. Riddle]] ('''1999'''). ''[http://link.springer.com/chapter/10.1007%2F3-540-48873-1_19 Evolving Logic Programs to Classify Chess-Endgame Positions]''. [http://link.springer.com/book/10.1007%2F3-540-48873-1 Simulated Evolution and Learning], [https://en.wikipedia.org/wiki/Canberra Canberra], Australia. [http://www.springer.com/series/1244 Lecture Notes in Artificial Intelligence], No. 1585, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer], [http://stancomb.co.uk/Papers/seal98.pdf pdf] » [[Learning]]
==2000 ...==
* [[Matthias Lüscher]] ('''2000'''). ''Automatic Generation of an Evaluation Function for Chess Endgames''. [[ETH Zurich]] Supervisors: [[Thomas Lincke]] and [[Christoph Wirth]], [http://www.datacomm.ch/m.luescher/evaluation_function_en.pdf pdf] » [[Neural Networks]]
* [[Kevin Coplan]] ('''2001'''). ''[http://ilk.uvt.nl/icga/journal/contents/content24-1.htm#SYNTHESIS%20OF%20CHESS Synthesis of Chess and Chess-like Endgames: A Proof of Correctness]''. [[ICGA Journal#24_1|ICCA Journal, Vol. 24, No. 1]]
* [[Kevin Coplan]] ('''2001'''). ''Synthesis of Chess-like Endgames: Towards a Proof of Correctness''. [[Advances in Computer Games 9]]
==2005 ...==
* [[Ami Hauptman]], [[Moshe Sipper]] ('''2005'''). ''GP-EndChess: Using Genetic Programming to Evolve Chess Endgame Players''. [http://www.informatik.uni-trier.de/~ley/db/conf/eurogp/eurogp2005.html#HauptmanS05 EuroGP 2005], [http://www.cs.bgu.ac.il/~sipper/papabs/eurogpchess-final.pdf pdf]
* [[Omid David]], [[Ariel Felner]], [[Nathan S. Netanyahu]] ('''2006'''). ''Blockage Detection in Pawn Endgames''. [https://en.wikipedia.org/wiki/Lecture_Notes_in_Computer_Science LNCS] 3846, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer]
* [[Ami Hauptman]], [[Moshe Sipper]] ('''2007'''). ''Emergence of Complex Strategies in the Evolution of Chess Endgame Players''. [http://www.informatik.uni-trier.de/~ley/db/journals/advcs/advcs10.html#HauptmanS07 Advances in Complex Systems 10]
* [[John Nunn]] ('''2009'''). ''[http://www.newinchess.com/Understanding_Chess_Endgames-p-1843.html Understanding Chess Endgames]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit] <ref>[http://www.chessbase.com/post/nunn-on-understanding-che-endgames Nunn on Understanding Chess Endgames], [[ChessBase|ChessBase News]], September 13, 2009</ref>
==2010 ...==
* [[John Nunn]] ('''2010'''). ''[http://www.newinchess.com/Nunn_s_Chess_Endings__Volume_1-p-5025.html Nunn's Chess Endings, volume 1]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit] <ref>[http://www.chessbase.com/post/nunn-s-che-endings-volume-one Nunn’s Chess Endings Volume One], [[ChessBase|ChessBase News]], May 28, 2010</ref>
* [[John Nunn]] ('''2010'''). ''[http://www.newinchess.com/Nunn_s_Chess_Endings__Volume_2-p-5053.html Nunn's Chess Endings, volume 2]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit]
* [[John Nunn]] ('''2013'''). ''Discoveries in R+2P vs. R+P Endings''. [[ICGA Journal#36_3|ICGA Journal, Vol. 36, No. 3]] » [[Lomonosov Tablebases]]
* [[Karsten Müller]], [[Guy Haworth]] ('''2013'''). ''Rook vs. Bishop''. [[ICGA Journal#36_4|ICGA Journal, Vol. 36, No. 4]]
* [[Matej Guid]], [[Martin Možina]], [[Ciril Bohak]], [[Aleksander Sadikov]], [[Ivan Bratko]] ('''2013'''). ''Building an Intelligent Tutoring System for Chess Endgames''. [http://dblp.uni-trier.de/db/conf/csedu/csedu2013.html#GuidMBSB13 CSEDU 2013]
==2015 ...==
* [[Michael Hartisch]], [[Ingo Althöfer]] ('''2015'''). ''Optimal Robot Play in Certain Chess Endgame Situations''. [[ICGA Journal#38_3|ICGA Journal, Vol. 38, No. 3]]
* [[Efstratios Grivas]] ('''2017'''). ''The Modern Endgame Manual''. [[ICGA Journal#39_2|ICGA Journal, Vol. 39, No. 2]]
* [[Karsten Müller]] ('''2017'''). ''Tablebases, Fermat, Knights and Knightmares''. [[ICGA Journal#39_2|ICGA Journal, Vol. 39, No. 2]]
* [[Guy Haworth]] ('''2017'''). ''Understanding Rook Endgames''. [[ICGA Journal#39_2|ICGA Journal, Vol. 39, No. 2]]
=Forum Posts=
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=198870 Endgame evaluation] by [[Benny Antonsson]], [[CCC]], November 25, 2001
* [https://www.stmintz.com/ccc/index.php?id=348493 Piece Values in the Endgame] by [[Guy Haworth]], [[CCC]], February 11, 2004 » [[Point Value]]
* [https://www.stmintz.com/ccc/index.php?id=358108 transition to endgame] by [[Eric Oldre]], [[CCC]], April 02, 2004
* [https://www.stmintz.com/ccc/index.php?id=359113 Improving the endgame of my engine] by [[Albert Bertilsson]], [[CCC]], April 08, 2004 » [[Sharper]]
* [http://www.talkchess.com/forum/viewtopic.php?t=19296 Definition of "endgame"?] by [[Jouni Uski]], [[CCC]], January 30, 2008
==2010 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=40629 End-game evaluation] by [[Harm Geert Muller|H.G.Muller]], [[CCC]], October 04, 2011
* [http://www.talkchess.com/forum/viewtopic.php?t=47173 Start EndGame - A matter of fine tuning ???] by [[Lourenço Araujo de Oliveira Junior]], [[CCC]], February 09, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=51672 End Game Heuristics] by [[Laurie Tunnicliffe]], [[CCC]], March 20, 2014
* [http://www.talkchess.com/forum/viewtopic.php?t=62153 Define end game] by [[Laurie Tunnicliffe]], [[CCC]], November 16, 2016 » [[Tapered Eval]]
* [http://www.talkchess.com/forum/viewtopic.php?t=64356 Testing endgame strength] by [[Álvaro Begué]], [[CCC]], June 21, 2017 » [[Engine Testing]], [[RuyDos]]
=External Links=
* [https://en.wikipedia.org/wiki/Chess_endgame Chess endgame from Wikipedia]
* [https://en.wikipedia.org/wiki/Pawnless_chess_endgame Pawnless chess endgame from Wikipedia]
=References=
<references />
'''[[Game Phases|Up one level]]'''
[[Category:Dorothea Tanning]]
