Checkmate

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Checkmate (often shortened to mate) occurs if a king is under immediate attack by one (or two) opponent pieces (in check) and has no way to remove it from attack on the next move. Checkmate is the object of the game of chess, it ends with the mate giving player as the winner, and the mated player the loser.

=Mate Score =

At the Root
At the root the score of a mated player is the worst score one can get, that is a negative score with the greatest absolute value of the score range. It is quite common and sufficient to use something like this in C, C++: /* (-32768/2 = -16384) */ Inside a 16-bit short integer range, assuming centipawn evaluation, it translates to roughly being 16 queens down. Note that using SHRT_MIN instead of SHRT_MIN/2 as mate value has issues in greater/less comparisons of additive expressions, where summands around SHRT_MIN or SHRT_MAX may under- or overflow, which has somehow relaxed with the advent of the usual 32-bit sign-extension.
 * 1) include 
 * 1) define VALUE_MATED (SHRT_MIN/2)

Down the Tree
Inside a negamax based search, most programs assign VALUE_MATED + ply distance to the root as worst case score if entering a node, which if propagated as mate score along the Principal Variation to the root, translates in mate in odd plies (positive values), or getting mated in even plies. However, those scores need ply-adjustment if stored as exact score inside the transposition table, and re-adjustment if retrieving from TT. An alternative approach, not only related to mate scores was proposed by Harm Geert Muller, The Delay Penalty as implemented in Micro-Max.

=Detecting Mate= Some programs rely on pseudo-legal move generation, and find Checkmate if all those moves are in fact illegal after making and finding the "refutation" of capturing the king. At the latest, if no legal move was found, programs need the information whether the king is in check to decide about checkmate or stalemate score. Despite, most programs (should be) are aware of check in advance, and use special move generator(s) if in check or even in double check:


 * 1) Double check
 * 2) Only King moves or captures
 * 3) Single check
 * 4) Capture the checking piece
 * 5) King moves or captures
 * 6) In case of distant checks, interposing a piece between the threatening sliding piece and the king

=See also=
 * Check
 * Chess Problems, Compositions and Studies
 * Mate at a Glance
 * Mate Distance Pruning
 * Mate-in-two
 * Mate Search
 * Stalemate

=Publications=

1952

 * Dietrich Prinz (1952). Robot Chess. Research, Vol. 6, reprinted 1988 in Computer Chess Compendium » Mate-in-two

1965 ...

 * George W. Baylor (1965). Report on a Mating Combinations Program. SDC Paper, No. SP-2150, System Development Corporation, Santa Monica, Calif. » Mater
 * George W. Baylor, Herbert A. Simon (1966). A chess mating combinations program. AFIPS Joint Computer Conferences, reprinted  in Herbert A. Simon (1979). Models of Thought. Yale University Press, pp. 181-200, in David Levy (ed.) (1988). Computer Chess Compendium.
 * George W. Baylor (1966). A Computer Model of Checkmating Behaviour in Chess. in Adriaan de Groot, Walter R. Reitman (eds.) (1966). Heuristic Processes in Thinking. International Congress of Psychology, Nauka, Moscow
 * Vladimir E. Alekseev (1969). Compilation of Chess Problems on a Computer. Technical translation FSTC-HT-23-124-69, US Army, NTIS AD 689470 (Problemy Kibernetiki, 19, 1967)

1980 ...

 * John Birmingham, Peter Kent (1980). Mate at a Glance. Advances in Computer Chess 2, reprinted in Computer Chess Compendium
 * Max Bramer (1982). Finding Checkmates. Computer & Video Games, Spring 1982, pdf hosted by Mike Watters » Mater
 * Don Beal (1984). Mating Sequences in the Quiescence Search. ICCA Journal, Vol. 7, No. 3

1990 ...

 * Thomas Mally (1993). Matt in Wieviel? PC Schach 3/93 (German)

2000 ...

 * Vladan Vučković (2004). Realization of the Chess Mate Solver Application. Yugoslav Journal of Operations Research, Volume 14, Number 2, pdf
 * Fridel Fainshtein (2006). An Orthodox k-Move Problem-Composer for Chess Directmates. M.Sc. thesis, Bar-Ilan University, pdf
 * Fridel Fainshtein, Yaakov HaCohen-Kerner (2006). A Chess Composer of Two-Move Mate Problems. ICGA Journal, Vol. 29, No. 1, pdf
 * Ami Hauptman, Moshe Sipper (2007). Evolution of an Efficient Search Algorithm for the Mate-In-N Problem in Chess. EuroGP 2007, pdf

2010 ...

 * Azlan Iqbal (2010). Aesthetics in Mate-In-3 Combinations. Part I Combinatorics and Weights, ICGA Journal, Vol. 33, No. 3
 * Azlan Iqbal (2010). Aesthetics in Mate-In-3 Combinations. Part II Normality, ICGA Journal, Vol. 33, No. 4
 * Taichi Ishitobi, Alessandro Cincotti, Hiroyuki Iida (2013). Shape-Keeping Technique and Its Application to Checkmate Problem Composition. 2013 AIIDE Workshop

=Forum Posts=

1997 ...

 * Mate in 4 explanation by Howard Exner, CCC, October 07, 1997
 * Mate in 30 testposition for Rebel 9! by Jouni Uski, CCC, November 20, 1997 » Rebel
 * Mate in 18 moves? by Ed Schröder, CCC, January 09, 1998
 * Using too-shallow mate scores from the hash table by David Eppstein, CCC, July 05, 1998
 * Re: Using too-shallow mate scores from the hash table by David Eppstein, CCC, July 06, 1998
 * Re: Using too-shallow mate scores from the hash table by Don Dailey, CCC, July 07, 1998


 * Solve for Mate by Trefor Deane, CCC, July 11, 1998
 * Mate the Royal Couple by Hans Havermann, CCC, November 14, 1998
 * Estimated # of checkmate positions? by Jeff Anderson, CCC, July 07, 1999
 * Mate solvers... by Dann Corbit, CCC, September 07, 1999
 * Interesting mate test for hashing by Robert Hyatt, CCC, September 10, 1999 » Transposition Table
 * Is "Interesting mate test..." the longest ever thread.... by Tina Long, CCC, September 11, 1999

2000 ...

 * Mate in 1 - but Fritz 6 needs 1 hour!!! by Christoph Fieberg, CCC, August 10, 2000
 * What's the fastest mate-finder? by Michel Langeveld, CCC, August 27, 2000
 * Questions about Mate Searching by William Bryant, CCC, September 23, 2000 » Mate Search
 * Mate in 7 moves - diagram by Eduard Nemeth, CCC, September 27, 2000 » Zugzwang
 * Static Mate Detection by Gerd Isenberg, CCC, January 22, 2002 » Mate at a Glance
 * First mate in 2, then mate in 3 by Albert Bertilsson, CCC, March 03, 2003
 * Easy mate by Frank Phillips, CCC, September 13, 2003

2005 ...

 * Shortest ever mate? by Tord Romstad, CCC, October 30, 2005
 * The Code for the Rybka-Mate-Bug by Chrilly Donninger, CCC, December 13, 2005 » Rybka
 * Unusual Mate in 3 by Charles Roberson, CCC, March 02, 2006
 * Delayed-loss-bonus discussion goes here by Harm Geert Muller, CCC, September 28, 2007
 * mate detetion issue by Mike Adams, CCC, October 24, 2008 » Connect Four, Fail-Soft
 * How to check for checkmate/stalemate programmatically? by Valentin, Rybka Forum, November 22, 2008 » Stalemate
 * Draw by repetition when mate is possible by Mathieu Pagé, CCC, December 30, 2008 » Repetitions

2010 ...

 * Puzzle with mate scores in TT by Robert Purves, CCC, December 10, 2010 » Score, Transposition Table
 * Yet Another Mate Solving Test by Jouni Uski, CCC, January 14, 2011
 * Mate score in TT by Marco Costalba, CCC, December 28, 2011 » Score, Transposition Table
 * Checkmate In Zero by Christopher Conkie, CCC, January 02, 2013
 * Quiescence Search and Checkmates by CDaley11, OpenChess Forum, January 11, 2013 » Quiescence Search
 * To be, or not to be checkmated by Harm Geert Muller, CCC, April 18, 2014
 * Mate score from the transposition table by Evert Glebbeek, CCC, October 25, 2014 » Score, Transposition Table

2015 ...

 * Remember Leonid Liberman (author of LLCHESS)? by Dann Corbit, CCC, May 23, 2015 » Leonid's Positions
 * TT Mate scores by rgoomes, OpenChess Forum, February 10, 2016 » Score, Transposition Table
 * Funny mate in 6 by Sergei S. Markoff, CCC, February 17, 2016
 * Mate scores from IID by Matthew R. Brades, CCC, August 16, 2016 » Internal Iterative Deepening
 * Why do engines lack mate solving? by Rasmus Althoff, CCC, October 15, 2016 » Mate Search
 * Mate Score by Tamás Kuzmics, CCC, June 27, 2017
 * Mate scores in TT (a new?... approach) by Vince Sempronio, CCC, April 09, 2018
 * Yet another Mate scores in TT thread by Andrew Grant, CCC, April 12, 2018 » Score, Transposition Table
 * mate test positions by Uri Blass, CCC, July 29, 2018 » Test-Positions
 * A mate suite to test multi-pv and new engines by Uri Blass, CCC, August 06, 2018
 * Trying to find a weird mate in 1... by Martin Bryant, CCC, July 22, 2019 » Fieberg's mate-in-1

2020 ...

 * Correct way to store and extract mate scores by Ian Mitchell, CCC, July 08, 2020 » Score, Transposition Table
 * mate suite for chess engines by Uri Blass, CCC, July 30, 2021

Leonid's Positions
=External Links=
 * Checkmate from Wikipedia
 * Checkmate pattern from Wikipedia
 * Checkmate/Stalemate Scoring from Bruce Moreland's Programming Topics
 * Handling Mate Scores from Bruce Moreland's Programming Topics

=References= Up one Level