Endgame

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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 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, if the opponent's 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, it might be good to evaluate the opponent's king being forced to go to the corner with the 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 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
 * Pawn Endgame
 * Rule of the Square

Pieces

 * Bishops of Opposite Colors
 * Wrong Color Bishop and Rook Pawn
 * Bishop versus Knight
 * KBNK Endgame
 * 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 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, Mathematical Center Amdsterdam. pdf
 * Pericles Negri (1977). Inductive Learning in a Hierarchical Model for Representing Knowledge in Chess End Games. pdf
 * Ryszard Michalski, Pericles Negri (1977). An experiment on inductive learning in chess endgames. Machine Intelligence 8, pdf
 * Kenneth W. Church (1978). 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). Chess-End-Game. Your Computer, 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. ICCA Journal, Vol. 10, No. 4
 * Lars Rasmussen (1987). Correcting grandmasters' Analyses in Elementary Endgames. ICCA Journal, Vol. 10, No. 4

1990 ...

 * Lars Rasmussen (1992). Queen versus Rook and Pawn. ICCA Journal, Vol. 15, No. 2
 * Wilhelm Barth, Stephan Barth (1992). Validating a Range of Endgame Programs. 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, zipped ps

1995 ...

 * Lewis Stiller (1996). Multilinear Algebra and Chess Endgames. Games of No Chance edited by Richard J. Nowakowski, pdf
 * Roberto Cifuentes, Maarten De Zeeuw, Jan van Reek (1997). Secrets of Chess Endings. ICCA Journal, Vol. 20, No. 4
 * Kevin Coplan (1998). Synthesis of Chess and Chess-like Endgames by Recursive Optimisation. ICCA Journal, Vol. 21, No. 3
 * Noam D. Elkies (1999). On numbers and endgames: Combinatorial game theory in chess endgames. pdf, differs only in trivial stylistic details from the (1996) version published in Games of No Chance edited by Richard J. Nowakowski
 * Philip G. K. Reiser, Patricia J. Riddle (1999). Evolving Logic Programs to Classify Chess-Endgame Positions. Simulated Evolution and Learning, Canberra, Australia. Lecture Notes in Artificial Intelligence, No. 1585, Springer, pdf » Learning

2000 ...

 * Matthias Lüscher (2000). Automatic Generation of an Evaluation Function for Chess Endgames. ETH Zurich Supervisors: Thomas Lincke and Christoph Wirth, pdf » Neural Networks
 * Kevin Coplan (2001). Synthesis of Chess and Chess-like Endgames: A Proof of Correctness. 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. EuroGP 2005, pdf
 * Omid David, Ariel Felner, Nathan S. Netanyahu (2006). Blockage Detection in Pawn Endgames. LNCS 3846, Springer
 * Ami Hauptman, Moshe Sipper (2007). Emergence of Complex Strategies in the Evolution of Chess Endgame Players. Advances in Complex Systems 10
 * John Nunn (2009). Understanding Chess Endgames. Gambit

2010 ...

 * John Nunn (2010). Nunn's Chess Endings, volume 1. Gambit
 * John Nunn (2010). Nunn's Chess Endings, volume 2. Gambit
 * John Nunn (2013). Discoveries in R+2P vs. R+P Endings. ICGA Journal, Vol. 36, No. 3 » Lomonosov Tablebases
 * Karsten Müller, Guy Haworth (2013). Rook vs. Bishop. 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. CSEDU 2013

2015 ...

 * Michael Hartisch, Ingo Althöfer (2015). Optimal Robot Play in Certain Chess Endgame Situations. ICGA Journal, Vol. 38, No. 3
 * Efstratios Grivas (2017). The Modern Endgame Manual. ICGA Journal, Vol. 39, No. 2
 * Karsten Müller (2017). Tablebases, Fermat, Knights and Knightmares. ICGA Journal, Vol. 39, No. 2
 * Guy Haworth (2017). Understanding Rook Endgames. ICGA Journal, Vol. 39, No. 2

=Forum Posts=

2000 ...

 * Endgame evaluation by Benny Antonsson, CCC, November 25, 2001
 * Piece Values in the Endgame by Guy Haworth, CCC, February 11, 2004 » Point Value
 * transition to endgame by Eric Oldre, CCC, April 02, 2004
 * Improving the endgame of my engine by Albert Bertilsson, CCC, April 08, 2004 » Sharper
 * Definition of "endgame"? by Jouni Uski, CCC, January 30, 2008

2010 ...

 * End-game evaluation by H.G.Muller, CCC, October 04, 2011
 * Start EndGame - A matter of fine tuning ??? by Lourenço Araujo de Oliveira Junior, CCC, February 09, 2013
 * End Game Heuristics by Laurie Tunnicliffe, CCC, March 20, 2014
 * Define end game by Laurie Tunnicliffe, CCC, November 16, 2016 » Tapered Eval
 * Testing endgame strength by Álvaro Begué, CCC, June 21, 2017 » Engine Testing, RuyDos

=External Links=
 * Chess endgame from Wikipedia
 * Pawnless chess endgame from Wikipedia

=References=

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