Draw Evaluation

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It is important for the evaluation function to recognize the endgame positions which are likely 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. =Obvious Draws= According to the rules of a dead position, Article 5.2 b, when there is no possibility of 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

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).
 * Queen versus Rook Pawn on 7th and Queen versus Bishop Pawn on 7th
 * 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)

=See also=
 * Blockage Detection
 * Contempt Factor
 * Draw
 * Fifty-move Rule
 * Fortress
 * Insufficient Material
 * Interior Node Recognizer
 * Repetitions
 * Stalemate

=Forum Posts=

2000 ...

 * "Don't trust draw score" <=Is it true? by Teerapong Tovirat, CCC, August 08, 2001 » Repetitions, Transposition Table, Path-Dependency
 * Draw recognition by eval problems by Rafael B. Andrist, CCC, October 17, 2001 » Wrong Color Bishop and Rook Pawn
 * When can a game be declared as a draw? by Josué Forte, Winboard Forum, June 15, 2003

2010 ...

 * question on draw evaluation by liuzy, CCC, June 03, 2010
 * Re: question on draw evaluation by Robert Houdart, CCC, June 07, 2010


 * handling draw by insufficient material by Youri Matiounine, November 19, 2013 » Insufficient Material
 * evaluating tablebases draws by Uri Blass, CCC, November 23, 2013 » Endgame Tablebases
 * Discocheck 5.01: Bishop related endgame problems by Mike Scheidl, CCC, November 25, 2013 » DiscoCheck, Color of a Square, Wrong Color Bishop and Rook Pawn

2015 ...

 * Stockfish eval output by Erin Dame, CCC, August 27, 2016 » Wrong Color Bishop and Rook Pawn, Stockfish
 * draw endgame scaling by Alexandru Mosoi, CCC, December 04, 2016
 * insufficient mating material by Erin Dame, CCC, May 29, 2017
 * Marcel Duchamp endgame "splits" engines / hash phenomenon by Kenneth Regan, CCC, February 19, 2018 » Chess Problems, Compositions and Studies, Marcel Duchamp, Transposition Table
 * what to do when all depths give the exact same score? by Sander Maassen vd Brink, CCC, March 10, 2018
 * KQKP and the like by Harm Geert Muller, CCC, May 25, 2019
 * Why does stockfish randomise draw evaluations? by Vincent Tang, CCC, September 01, 2019 » Stockfish, Draw Score, Search with Random Leaf Values

2020 ...

 * Endgame woes by Tom King, CCC, February 07, 2020
 * OliThink 5.4.0 has been published with an big leap in strength for only 3 lines of code by Oliver Brausch, CCC, June 16, 2020 » OliThink
 * Alpha-beta search for drawing endgames by Emanuel Torres, CCC, June 16, 2021 » Alpha-Beta, Graph History Interaction, Repetitions

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