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'''[[Main Page|Home]] * [[Evaluation]] * [[Game Phases]] * [[Endgame]] * Draw Evaluation'''
It is important for the evaluation function to recognize the endgame positions which are likely [[Draw|drawn]], even though one side has a nominal advantage. This page is devoted to listing some of them. More of that kind of knowledge can be found in the [[KPK]] section.
<span id="immediate"></span>
=Obvious Draws=
According to the rules of a dead position, Article 5.2 b, when there is no possibility of [[Checkmate|checkmate]] for either side with any series of legal moves, the position is an immediate draw if
* both sides have a bare king
* one side has a king and a minor piece against a bare king
* both sides have a king and a bishop, the bishops being the same color
=Simple Heuristics=
The bishops of different colors are not counted as an immediate draw, because of the possibility of a helpmate in the corner. Since this is unlikely given even a four ply search, we may introduce another class of drawn positions: those that cannot be claimed, but can be evaluated as draws:
* two knights against the bare king
* both sides have a king and a minor piece each
* the weaker side has a minor piece against two knights
* two bishops draw against a bishop
* two minor pieces against one draw, except when the stronger side has a [[Bishop Pair|bishop pair]]
Please note that a knight or even two knights against two bishops are not included here, as it is possible to win this ending.
'''Implementation note:''' When a program uses heuristics of that kind, it is of utmost importance to be consistent. For example, if KBN vs KB is scored as a draw, the same must be done with KBN vs KBP. A possible idea is to divide a score by a large constant, such as 16 or 32, when the side nominally ahead has the wrong piece combination.
=Complex Heuristics=
* If the stronger side has a pawn and a bishop against the minor piece, the position is almost certainly drawn if the weaker side's king occupies a square on the path of a pawn that is inaccessible to the enemy bishop (the degenerate cases like trapping the minor piece are best left for search).
* [https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame KQKP] with [https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame#Rook_pawn rook pawn] or [https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame#Bishop_pawn bishop pawn] on its seventh rank supported by own king threatening [[Stalemate|stalemate]], other king far enough away <ref>[http://www.talkchess.com/forum/viewtopic.php?t=66640 Marcel Duchamp endgame "splits" engines / hash phenomenon] by [[Kenneth Wingate Regan|Kenneth Regan]], [[CCC]], February 19, 2018 » [[Chess Problems, Compositions and Studies]], [[Arts#Duchamp|Marcel Duchamp]], [[Transposition Table]]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=66798 what to do when all depths give the exact same score?] by [[Sander Maassen vd Brink]], [[CCC]], March 10, 2018</ref>
* [[Wrong Color Bishop and Rook Pawn]]
=One-sided Heuristics=
There are some heuristics that tells us only that one of the players cannot win the endgame
* a single minor piece should not win against any number of pawns (again, there is a special case of a smothered mate in the corner, but it is search issue, not to be taken into account by the [[Evaluation Function|evaluation function]])
=See also=
* [[Blockage Detection]]
* [[Contempt Factor]]
* [[Draw]]
* [[Fifty-move Rule]]
* [[Fortress]]
* [[Material#InsufficientMaterial|Insufficient Material]]
* [[Interior Node Recognizer]]
* [[Repetitions]]
* [[Stalemate]]
=Forum Posts=
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=182927 "Don't trust draw score" <=Is it true?] by [[Teerapong Tovirat]], [[CCC]], August 08, 2001 » [[Repetitions]], [[Transposition Table]], [[Path-Dependency]]
* [https://www.stmintz.com/ccc/index.php?id=193257 Draw recognition by eval problems] by [[Rafael Andrist]], [[CCC]], October 17, 2001 » [[Wrong color Bishop and rook pawn]]
==2010 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=34673 question on draw evaluation] by liuzy, [[CCC]], June 03, 2010
: [http://www.talkchess.com/forum/viewtopic.php?t=34673&start=8 Re: question on draw evaluation] by [[Robert Houdart]], [[CCC]], June 07, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=50150 handling draw by insufficient material] by [[Youri Matiounine]], November 19, 2013 » [[Material#InsufficientMaterial|Insufficient Material]]
* [http://www.talkchess.com/forum/viewtopic.php?t=50194 evaluating tablebases draws] by [[Uri Blass]], [[CCC]], November 23, 2013 » [[Endgame Tablebases]]
* [http://www.talkchess.com/forum/viewtopic.php?t=50223 Discocheck 5.01: Bishop related endgame problems] by [[Michael Scheidl|Mike Scheidl]], [[CCC]], November 25, 2013 » [[DiscoCheck]], [[Color of a Square]], [[Wrong color Bishop and Rook Pawn]]
==2015 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=61250 Stockfish eval output] by [[Erin Dame]], [[CCC]], August 27, 2016 » [[Wrong color Bishop and rook pawn]], [[Stockfish]]
* [http://www.talkchess.com/forum/viewtopic.php?t=62380 draw endgame scaling] by [[Alexandru Mosoi]], [[CCC]], December 04, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=64115 insufficient mating material] by [[Erin Dame]], [[CCC]], May 29, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=66640 Marcel Duchamp endgame "splits" engines / hash phenomenon] by [[Kenneth Wingate Regan|Kenneth Regan]], [[CCC]], February 19, 2018 » [[Chess Problems, Compositions and Studies]], [[Arts#Duchamp|Marcel Duchamp]], [[Transposition Table]]
* [http://www.talkchess.com/forum/viewtopic.php?t=66798 what to do when all depths give the exact same score?] by [[Sander Maassen vd Brink]], [[CCC]], March 10, 2018
=References=
<references />
'''[[Endgame|Up one Level]]'''
It is important for the evaluation function to recognize the endgame positions which are likely [[Draw|drawn]], even though one side has a nominal advantage. This page is devoted to listing some of them. More of that kind of knowledge can be found in the [[KPK]] section.
<span id="immediate"></span>
=Obvious Draws=
According to the rules of a dead position, Article 5.2 b, when there is no possibility of [[Checkmate|checkmate]] for either side with any series of legal moves, the position is an immediate draw if
* both sides have a bare king
* one side has a king and a minor piece against a bare king
* both sides have a king and a bishop, the bishops being the same color
=Simple Heuristics=
The bishops of different colors are not counted as an immediate draw, because of the possibility of a helpmate in the corner. Since this is unlikely given even a four ply search, we may introduce another class of drawn positions: those that cannot be claimed, but can be evaluated as draws:
* two knights against the bare king
* both sides have a king and a minor piece each
* the weaker side has a minor piece against two knights
* two bishops draw against a bishop
* two minor pieces against one draw, except when the stronger side has a [[Bishop Pair|bishop pair]]
Please note that a knight or even two knights against two bishops are not included here, as it is possible to win this ending.
'''Implementation note:''' When a program uses heuristics of that kind, it is of utmost importance to be consistent. For example, if KBN vs KB is scored as a draw, the same must be done with KBN vs KBP. A possible idea is to divide a score by a large constant, such as 16 or 32, when the side nominally ahead has the wrong piece combination.
=Complex Heuristics=
* If the stronger side has a pawn and a bishop against the minor piece, the position is almost certainly drawn if the weaker side's king occupies a square on the path of a pawn that is inaccessible to the enemy bishop (the degenerate cases like trapping the minor piece are best left for search).
* [https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame KQKP] with [https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame#Rook_pawn rook pawn] or [https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame#Bishop_pawn bishop pawn] on its seventh rank supported by own king threatening [[Stalemate|stalemate]], other king far enough away <ref>[http://www.talkchess.com/forum/viewtopic.php?t=66640 Marcel Duchamp endgame "splits" engines / hash phenomenon] by [[Kenneth Wingate Regan|Kenneth Regan]], [[CCC]], February 19, 2018 » [[Chess Problems, Compositions and Studies]], [[Arts#Duchamp|Marcel Duchamp]], [[Transposition Table]]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=66798 what to do when all depths give the exact same score?] by [[Sander Maassen vd Brink]], [[CCC]], March 10, 2018</ref>
* [[Wrong Color Bishop and Rook Pawn]]
=One-sided Heuristics=
There are some heuristics that tells us only that one of the players cannot win the endgame
* a single minor piece should not win against any number of pawns (again, there is a special case of a smothered mate in the corner, but it is search issue, not to be taken into account by the [[Evaluation Function|evaluation function]])
=See also=
* [[Blockage Detection]]
* [[Contempt Factor]]
* [[Draw]]
* [[Fifty-move Rule]]
* [[Fortress]]
* [[Material#InsufficientMaterial|Insufficient Material]]
* [[Interior Node Recognizer]]
* [[Repetitions]]
* [[Stalemate]]
=Forum Posts=
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=182927 "Don't trust draw score" <=Is it true?] by [[Teerapong Tovirat]], [[CCC]], August 08, 2001 » [[Repetitions]], [[Transposition Table]], [[Path-Dependency]]
* [https://www.stmintz.com/ccc/index.php?id=193257 Draw recognition by eval problems] by [[Rafael Andrist]], [[CCC]], October 17, 2001 » [[Wrong color Bishop and rook pawn]]
==2010 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=34673 question on draw evaluation] by liuzy, [[CCC]], June 03, 2010
: [http://www.talkchess.com/forum/viewtopic.php?t=34673&start=8 Re: question on draw evaluation] by [[Robert Houdart]], [[CCC]], June 07, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=50150 handling draw by insufficient material] by [[Youri Matiounine]], November 19, 2013 » [[Material#InsufficientMaterial|Insufficient Material]]
* [http://www.talkchess.com/forum/viewtopic.php?t=50194 evaluating tablebases draws] by [[Uri Blass]], [[CCC]], November 23, 2013 » [[Endgame Tablebases]]
* [http://www.talkchess.com/forum/viewtopic.php?t=50223 Discocheck 5.01: Bishop related endgame problems] by [[Michael Scheidl|Mike Scheidl]], [[CCC]], November 25, 2013 » [[DiscoCheck]], [[Color of a Square]], [[Wrong color Bishop and Rook Pawn]]
==2015 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=61250 Stockfish eval output] by [[Erin Dame]], [[CCC]], August 27, 2016 » [[Wrong color Bishop and rook pawn]], [[Stockfish]]
* [http://www.talkchess.com/forum/viewtopic.php?t=62380 draw endgame scaling] by [[Alexandru Mosoi]], [[CCC]], December 04, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=64115 insufficient mating material] by [[Erin Dame]], [[CCC]], May 29, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=66640 Marcel Duchamp endgame "splits" engines / hash phenomenon] by [[Kenneth Wingate Regan|Kenneth Regan]], [[CCC]], February 19, 2018 » [[Chess Problems, Compositions and Studies]], [[Arts#Duchamp|Marcel Duchamp]], [[Transposition Table]]
* [http://www.talkchess.com/forum/viewtopic.php?t=66798 what to do when all depths give the exact same score?] by [[Sander Maassen vd Brink]], [[CCC]], March 10, 2018
=References=
<references />
'''[[Endgame|Up one Level]]'''
