Material

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Material, a term determined by the sum of piece values of each side. The material value is the most influential part of the evaluation. Usually it is the sum of a constant value for each piece present, measured in units of a fraction of a pawn, for instance the common centipawn scale, which allows positional features of the position, worth less than a single pawn, to be evaluated without requiring fractions but a fixed point score.

=Basic Piece Values= Piece relative values concerning their relative strength in potential exchanges based on human experience and learning
 * Point Value
 * Pawn Advantage, Win Percentage, and Elo

=Other Material Considerations= In chess, it is known that certain material features provide an advantage, such as the bishop pair (which might be worth as much as half a pawn). A program might increase the values of rooks when there are less pawns on the board or prefer knights when there are many pawns. Larry Kaufman performed statistical tests on a variety of different material configurations to approximate their values.

Other factors that affect material evaluation might be: =Insufficient Material= Using values like these blindly can lead to bad play. Most programs uses special code or tables to detect drawn or likely drawn material combinations. For example, KB vs K is a draw, as is KN vs K and KNN vs K. There is also a class of almost-certain draws, not mentioned in the FIDE rules because of the possibility of a checkmate (KN vs KN, KB vs KN, KNN vs KB, KBN vs KB, KBN vs KR etc.) A general rule that, although not perfect, catches many likely draws is that if one side has no pawns left, it needs the equivalent of +4 pawns more material to win. For example, KRN vsv KR is usually a draw, where KRR vs KBN is usually a win for the rook side. For more details see draw evaluation and interior node recognizer. =Material Balance= The Material Balance is finally returned as the almost most dominating evaluation term, usually in Negamax from side to move's point of view, and in its pure form simply the difference of both sides material, MD: md := material[side_2_move] - material[side_2_move ^ 1]; As mentioned, other material considerations, concerning insufficient material and material imbalances (e.g. rook versus two minor pieces, queen versus two rooks or three pieces, three pawns versus piece) should be taken into account - for instance to encourage exchanging pieces but no pawns if ahead, see the hashing approach of Chess 4.5.
 * Bonus for the bishop pair (bishops complement each other, controlling squares of different color)
 * Penalty for the rook pair (Larry Kaufman called it "principle of redundancy")
 * Penalty for the knight pair (as two knights are less successful against the rook than any other pair of minor pieces)
 * decreasing the value of the rook pawns and increasing the value of the central pawns (though this can be done in the piece-square tables as well)
 * Trade down bonus that encourages the winning side to trade pieces but no pawns
 * Penalty for having no pawns, as it makes it more difficult to win the endgame
 * Bad trade penalty as proposed by Robert Hyatt, that is penalizing the material imbalances that are disadvantageous like having three pawns for a piece or a rook for two minors.
 * Elephantiasis effect as suggested by Harm Geert Muller (meaning that stronger pieces lose part of their value in presence of weaker pieces)

=Hashing and Tables= To save speed in the material evaluation, programs using rules often hash the material evaluation scores. With precomputed arrays of material values, this is not needed.
 * Material Hash Table
 * Material Tables

=See also=
 * Bishop Pair
 * Fixed Point Score
 * Influence Quantity of Pieces
 * Interior Node Recognizer
 * Material in Chess 4.5
 * Material in SOMA
 * PeSTO's Evaluation Function
 * Piece-Square Tables
 * Simplified Evaluation Function

=Related Publications=
 * Claude Shannon (1949). Programming a Computer for Playing Chess. pdf from The Computer History Museum
 * Alan Turing (1953). Chess. part of the collection Digital Computers Applied to Games, in Bertram Vivian Bowden (editor), Faster Than Thought, a symposium on digital computing machines, reprinted 1988 in Computer Chess Compendium, reprinted 2004 in The Essential Turing, google books
 * Jack Good (1968). A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares. Machine Intelligence Vol. 2
 * David Slate, Larry Atkin (1977). CHESS 4.5 - The Northwestern University Chess Program. Chess Skill in Man and Machine (ed. Peter W. Frey), pp. 82-118. Springer-Verlag, New York, N.Y. 2nd ed. 1983. ISBN 0-387-90815-3. Reprinted (1988) in Computer Chess Compendium
 * Gennady Timoshchenko (1993). Bishop or Knight? ICCA Journal, Vol. 16, No. 4
 * Larry Kaufman (1994). The Relative Value of the Pieces. Computer Chess Reports, Vol. 4, No. 2, pp. 33
 * Mark Sturman (1995). Beware The Bishop Pair. Computer Chess Reports, Vol. 5, No. 2, pp.58 » Bishop Pair
 * Mark Sturman (1996). Beware the Bishop Pair. ICCA Journal, Vol. 19, No. 2
 * Don Beal, Martin C. Smith (1997). Learning Piece Values Using Temporal Differences. ICCA Journal, Vol. 20, No. 3
 * Larry Kaufman (1999). The Evaluation of Material Imbalances. (first published in Chess Life March 1999, online version edited by Dan Heisman)
 * Sacha Droste, Johannes Fürnkranz (2008). Learning of Piece Values for Chess Variants. Technical Report TUD–KE–2008-07, Knowledge Engineering Group, TU Darmstadt, pdf
 * Christian Hesse (2011). The Joys of Chess - Heroes, Battles & Brilliancies. ISBN: 978-90-5691-355-7, New In Chess

=Forum Posts=

2000 ...

 * Queen vs two rooks by Benny Antonsson, CCC, April 07, 2002
 * Exceptions to (1,3,3,5,9) by David Rasmussen, CCC, February 24, 2003
 * Bad trade by Benny Antonsson, CCC, January 30, 2004

2005 ...

 * Quark 2.35 draw claim bug by Igor Korshunov, Winboard Forum, March 28, 2005 » Quark, Draw
 * Material imbalance evaluation by Alessandro Scotti, CCC, April 16, 2007
 * Evaluation of material imbalance (a Rybka secret?) by Alessandro Scotti, CCC, December 06, 2007
 * Relative Piece Values by Mark Lefler, CCC, April 09, 2009 » Point Value
 * Testing of Kaufman Material Values by Mark Lefler, CCC, April 25, 2009
 * Rook Pair Penalty, Knight Pair Penalty, Having a Pawn Bonus by Mark Lefler, CCC, May 11, 2009

2010 ...
2011 2012 2013 2014
 * Efficiently index material signatures and lookup by Mathieu Pagé, CCC, March 03, 2010
 * Stockfish - material balance/imbalance evaluation by Ralph Stoesser, CCC, May 05, 2010 » Stockfish
 * Wrong draw claim by Naum 4.2 ? by Matthias Gemuh, CCC, January 12, 2011 » Draw
 * Material imbalance/bad trade and borrowing code by Evert Glebbeek, CCC, January 27, 2011
 * Stockfish Code ( Piece Value's) by Nolan Denson, CCC, January 10, 2012 » Stockfish
 * Lone minor piece penalty - What did Larry mean? by Charles Roberson, CCC, January 10, 2012
 * Why Knight and (lone) Bishop are so nearly equal in value by Harm Geert Muller, CCC, September 25, 2012
 * An experiment with material imbalances and game-phase by Evert Glebbeek, CCC, April 06, 2013 » Material Tables
 * A balanced approach to imbalances by Lyudmil Tsvetkov, CCC, October 23, 2013
 * handling draw by insufficient material by Youri Matiounine, November 19, 2013 » Draw Evaluation
 * Lonely queen by Lyudmil Tsvetkov, CCC, December 15, 2013
 * Queen vs 3 minors by Thomas Petzke, mACE Chess, December 18, 2013
 * Accessing Material Imbalance Information? by Steve Maughan, CCC, December 19, 2013 » Material Tables
 * Queen vs 3 Minors part 2 by Thomas Petzke, mACE Chess, December 21, 2013
 * Trading penalty with imbalances by Lyudmil Tsvetkov, CCC, December 22, 2013
 * Scaling eval with material on the board by Lyudmil Tsvetkov, CCC, June 25, 2014
 * Obligatory scaling by Lyudmil Tsvetkov, CCC, June 27, 2014 » Rook Endgame

2015 ...
2017 2018
 * Rook vs 2 minor pieces with pawns on the board by Shawn Chidester, CCC, April 27, 2015
 * Piece weights with regression analysis (in Russian) by Vladimir Medvedev, CCC, April 30, 2015 » Point Value, Automated Tuning
 * Another way of evaluating material imbalances by Volker Annuss, CCC, January 01, 2017 » Arminius
 * trading pieces and pawns based on material balance by Erin Dame, CCC, May 28, 2017
 * insufficient mating material by Erin Dame, CCC, May 29, 2017 » Draw Evaluation
 * list of material combinations requiring specialized eval ? by Mahmoud Uthman, CCC, July 11, 2017
 * Trading Pieces When Ahead In Material by Daniel Anulliero, CCC, October 03, 2017
 * Magic end-game material hash? by Harm Geert Muller, CCC, November 30, 2017
 * 'ab-initio' piece values by Harm Geert Muller, CCC, March 30, 2018 » Piece-Square Tables
 * The Xiphos Material Evaluator by Dennis Sceviour, CCC, November 05, 2018 » Xiphos

2020 ...

 * Imbalance by Vivien Clauzon, CCC, February 01, 2020
 * Trading gradient: to trade or not to trade? by Harm Geert Muller, CCC, February 18, 2021

=External Links=
 * The Evaluation of Material Imbalances by Larry Kaufman
 * Statistics of material imbalances in chess games by Alessandro Scotti » Match Statistics
 * Chess piece relative value from Wikipedia
 * About the Values of Chess Pieces by Ralph Betza
 * The joys of chess – and the value of the pieces, ChessBase News, December 21, 2011

=References=

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