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Created page with "'''Home * Evaluation * Material''' FILE:Elke_Rehder_Chess_Schach_Stefan_Zweig_Schachnovelle_Royal_Game_4.jpg|border|right|thumb|link=http://www.elke-rehde..."
'''[[Main Page|Home]] * [[Evaluation]] * Material'''
[[FILE:Elke_Rehder_Chess_Schach_Stefan_Zweig_Schachnovelle_Royal_Game_4.jpg|border|right|thumb|link=http://www.elke-rehder.de/Chess_Woodcuts.htm|[https://en.wikipedia.org/wiki/The_Royal_Game The Royal Game] IV <ref>[http://www.elke-rehder.de/Chess_Woodcuts.htm Royal Game, Woodcuts Art] by [[Arts#Rehder|Elke Rehder]], [https://en.wikipedia.org/wiki/Stefan_Zweig Stefan Zweig] [https://en.wikipedia.org/wiki/The_Royal_Game The Royal Game] IV</ref> ]]
'''Material''',<br/>
a term determined by the sum of [[Point Value|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 [[Centipawns|centipawn scale]], which allows positional features of the position, worth less than a single pawn, to be evaluated without requiring fractions but a [[Score#FixedPoint|fixed point score]].
=Basic Piece Values=
Piece relative values concerning their relative strength in potential exchanges based on human experience and [[Learning|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|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 <ref>[http://www.talkchess.com/forum/viewtopic.php?t=18240 Evaluation of material imbalance (a Rybka secret?)] by [[Alessandro Scotti]] from [[CCC]], December 06, 2007</ref> .
Other factors that affect material evaluation might be:
* Bonus for the [[Bishop Pair|bishop pair]] (bishops complement each other, controlling squares of different [[Color|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|piece-square tables]] as well)
* Trade down bonus that encourages the winning side to trade pieces but no pawns <ref>[http://www.talkchess.com/forum/viewtopic.php?t=64110 trading pieces and pawns based on material balance] by [[Erin Dame]], [[CCC]], May 28, 2017</ref>
* 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)
<span id="InsufficientMaterial"></span>
=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 <ref>[http://www.open-aurec.com/wbforum/viewtopic.php?f=2&t=2112 Quark 2.35 draw claim bug] by [[Igor Korshunov]], [[Computer Chess Forums|Winboard Forum]], March 28, 2005 » [[Quark]], [[Draw]]</ref> , 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|draw evaluation]] and [[Interior Node Recognizer|interior node recognizer]].
<span id="Balance"></span>
=Material Balance=
The Material Balance is finally returned as the almost most dominating evaluation term, usually in [[Negamax]] from [[Side to Move|side to move's]] point of view, and in its pure form simply the difference of both sides material, MD:
<pre>
md := material[side_2_move] - material[side_2_move ^ 1];
</pre>
As mentioned, other material considerations, concerning [[Material#InsufficientMaterial|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 [[Material Hash Table#ApproachOfChess|hashing approach]] of [[Chess (Program)|Chess 4.5]].
=Hashing and Tables=
To save speed in the material evaluation, programs using rules often [[Hash Table|hash]] the material evaluation scores. With [[Material Tables|precomputed arrays of material values]], this is not needed.
* [[Material Hash Table]]
* [[Material Tables]]
=See also=
* [[Bishop Pair]]
* [[Score#FixedPoint|Fixed Point Score]]
* [[Influence Quantity of Pieces]]
* [[Interior Node Recognizer]]
* [[Material Hash Table#ApproachOfChess|Material in Chess 4.5]]
* [[SOMA#Material|Material in SOMA]]
* [[Piece-Square Tables]]
* [[Simplified Evaluation Function]]
=Related Publications=
* [[Claude Shannon]] ('''1949'''). ''[http://www.pi.infn.it/%7Ecarosi/chess/shannon.txt Programming a Computer for Playing Chess]''. [http://archive.computerhistory.org/projects/chess/related_materials/text/2-0%20and%202-1.Programming_a_computer_for_playing_chess.shannon/2-0%20and%202-1.Programming_a_computer_for_playing_chess.shannon.062303002.pdf pdf] from [[The Computer History Museum]]
* [[Alan Turing]] ('''1953'''). '''''Chess'''''. part of the collection ''Digital Computers Applied to Games'', in [https://en.wikipedia.org/wiki/B._V._Bowden,_Baron_Bowden Bertram Vivian Bowden] (editor), [http://www.computinghistory.org.uk/cgi-bin/sitewise.pl?act=det&p=10719 Faster Than Thought], a symposium on digital computing machines, reprinted 1988 in [[Computer Chess Compendium]], reprinted 2004 in ''The Essential Turing'', [http://books.google.com/books?id=RSkxnKlv1D4C&lpg=PP882&ots=VOWmiIm_lD&dq=Turochamp%2C%20chess&pg=PP881#v=onepage&q&f=true google books]
* [[Jack Good]] ('''1968'''). ''A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares''. [http://www.doc.ic.ac.uk/~shm/MI/mi2.html 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''? [[ICGA Journal#16_4|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 <ref>[https://groups.google.com/d/msg/rec.games.chess/xFCRAQIqvjw/OVFg2ezWYTYJ Looking for Mark Sturman] by [[Mark Lefler]], [[Computer Chess Forums|rec.games.chess]], July 02, 1995</ref> » [[Bishop Pair]]
* [[Mark Sturman]] ('''1996'''). ''Beware the Bishop Pair''. [[ICGA Journal#19_2|ICCA Journal, Vol. 19, No. 2]]
* [[Don Beal]], [[Martin C. Smith]] ('''1997'''). ''Learning Piece Values Using Temporal Differences''. [[ICGA Journal#20_3|ICCA Journal, Vol. 20, No. 3]]
* [[Larry Kaufman]] ('''1999'''). ''[https://www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman The Evaluation of Material Imbalances]''. (first published in [https://en.wikipedia.org/wiki/Chess_Life 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, [[Darmstadt University of Technology|TU Darmstadt]], [http://www.ke.tu-darmstadt.de/publications/reports/tud-ke-2008-07.pdf pdf]
* [[Christian Hesse]] ('''2011'''). ''[http://www.newinchess.com/The_Joys_of_Chess-p-953.html The Joys of Chess - Heroes, Battles & Brilliancies]''. ISBN: 978-90-5691-355-7, [https://en.wikipedia.org/wiki/New_In_Chess New In Chess] <ref>[http://www.chessbase.com/newsdetail.asp?newsid=7775 The joys of chess – and the value of the pieces], [[ChessBase|ChessBase News]], December 21, 2011</ref>
=Forum Posts=
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=222033 Queen vs two rooks] by [[Benny Antonsson]], [[CCC]], April 07, 2002
* [https://www.stmintz.com/ccc/index.php?id=286659 Exceptions to (1,3,3,5,9)] by [[David Rasmussen]], [[CCC]], February 24, 2003
* [https://www.stmintz.com/ccc/index.php?id=345860 Bad trade] by [[Benny Antonsson]], [[CCC]], January 30, 2004
==2005 ...==
* [http://www.open-aurec.com/wbforum/viewtopic.php?f=2&t=2112 Quark 2.35 draw claim bug] by [[Igor Korshunov]], [[Computer Chess Forums|Winboard Forum]], March 28, 2005 » [[Quark]], [[Draw]]
* [http://www.talkchess.com/forum/viewtopic.php?t=13166 Material imbalance evaluation] by [[Alessandro Scotti]], [[CCC]], April 16, 2007
* [http://www.talkchess.com/forum/viewtopic.php?t=18240 Evaluation of material imbalance (a Rybka secret?)] by [[Alessandro Scotti]], [[CCC]], December 06, 2007
* [http://www.talkchess.com/forum/viewtopic.php?t=27387 Relative Piece Values] by [[Mark Lefler]], [[CCC]], April 09, 2009 » [[Point Value]]
* [http://www.talkchess.com/forum/viewtopic.php?t=27616 Testing of Kaufman Material Values] by [[Mark Lefler]], [[CCC]], April 25, 2009
* [http://www.talkchess.com/forum/viewtopic.php?t=27842 Rook Pair Penalty, Knight Pair Penalty, Having a Pawn Bonus] by [[Mark Lefler]], [[CCC]], May 11, 2009
==2010 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=33035 Efficiently index material signatures and lookup] by [[Mathieu Pagé]], [[CCC]], March 03, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=34159 Stockfish - material balance/imbalance evaluation] by [[Ralph Stoesser]], [[CCC]], May 05, 2010 » [[Stockfish]]
'''2011'''
* [http://www.talkchess.com/forum/viewtopic.php?t=37592 Wrong draw claim by Naum 4.2 ?] by [[Matthias Gemuh]], [[CCC]], January 12, 2011 » [[Draw]]
* [http://www.talkchess.com/forum/viewtopic.php?t=37831 Material imbalance/bad trade and borrowing code] by [[Evert Glebbeek]], [[CCC]], January 27, 2011
'''2012'''
* [http://www.talkchess.com/forum/viewtopic.php?t=41916 Stockfish Code ( Piece Value's)] by Nolan Denson, [[CCC]], January 10, 2012 » [[Stockfish]]
* [http://www.talkchess.com/forum/viewtopic.php?t=41905 Lone minor piece penalty - What did Larry mean?] by [[Charles Roberson]], [[CCC]], January 10, 2012
* [http://www.talkchess.com/forum/viewtopic.php?t=45321 Why Knight and (lone) Bishop are so nearly equal in value] by [[Harm Geert Muller]], [[CCC]], September 25, 2012
'''2013'''
* [http://www.talkchess.com/forum/viewtopic.php?t=47713 An experiment with material imbalances and game-phase] by [[Evert Glebbeek]], [[CCC]], April 06, 2013 » [[Material Tables]]
* [http://www.talkchess.com/forum/viewtopic.php?t=49808 A balanced approach to imbalances] by [[Lyudmil Tsvetkov]], [[CCC]], October 23, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=50150 handling draw by insufficient material] by [[Youri Matiounine]], November 19, 2013 » [[Draw Evaluation]]
* [http://www.talkchess.com/forum/viewtopic.php?t=50504 Lonely queen] by [[Lyudmil Tsvetkov]], [[CCC]], December 15, 2013
* [http://macechess.blogspot.de/2013/12/queen-vs-3-minors.html Queen vs 3 minors] by [[Thomas Petzke]], [http://macechess.blogspot.de/ mACE Chess], December 18, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=50550 Accessing Material Imbalance Information?] by [[Steve Maughan]], [[CCC]], December 19, 2013 » [[Material Tables]]
* [http://macechess.blogspot.de/2013/12/queen-vs-3-minors-part-2.html Queen vs 3 Minors part 2] by [[Thomas Petzke]], [http://macechess.blogspot.de/ mACE Chess], December 21, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=50601 Trading penalty with imbalances] by [[Lyudmil Tsvetkov]], [[CCC]], December 22, 2013
'''2014'''
* [http://www.talkchess.com/forum/viewtopic.php?t=52757 Scaling eval with material on the board] by [[Lyudmil Tsvetkov]], [[CCC]], June 25, 2014
* [http://www.talkchess.com/forum/viewtopic.php?t=52775 Obligatory scaling] by [[Lyudmil Tsvetkov]], [[CCC]], June 27, 2014 » [[Rook Endgame]]
==2015 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=56142 Rook vs 2 minor pieces with pawns on the board] by [[Shawn Chidester]], [[CCC]], April 27, 2015
* [http://www.talkchess.com/forum/viewtopic.php?t=56168 Piece weights with regression analysis (in Russian)] by [[Vladimir Medvedev]], [[CCC]], April 30, 2015 <ref>[http://habrahabr.ru/post/254753/ Определяем веса шахматных фигур регрессионным анализом / Хабрахабр] by [[Vladimir Medvedev|WinPooh]], April 27, 2015 (Russian)</ref> » [[Point Value]], [[Automated Tuning]]
* [http://www.talkchess.com/forum/viewtopic.php?t=62687 Another way of evaluating material imbalances] by [[Volker Annuss]], [[CCC]], January 01, 2017 » [[Arminius]]
* [http://www.talkchess.com/forum/viewtopic.php?t=64110 trading pieces and pawns based on material balance] by [[Erin Dame]], [[CCC]], May 28, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=64115 insufficient mating material] by [[Erin Dame]], [[CCC]], May 29, 2017 » [[Draw Evaluation]]
* [http://www.talkchess.com/forum/viewtopic.php?t=64576 list of material combinations requiring specialized eval ?] by [[Mahmoud Uthman]], [[CCC]], July 11, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=65364 Trading Pieces When Ahead In Material] by [[Daniel Anulliero]], [[CCC]], October 03, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=65870 Magic end-game material hash?] by [[Harm Geert Muller]], [[CCC]], November 30, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=66966 'ab-initio' piece values] by [[Harm Geert Muller]], [[CCC]], March 30, 2018 » [[Piece-Square Tables]]
=External Links=
* [https://www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman The Evaluation of Material Imbalances] by [[Larry Kaufman]]
* [http://walkofmind.com/programming/chess/mat_stats.html Statistics of material imbalances in chess games] by [[Alessandro Scotti]] » [[Match Statistics]]
* [https://en.wikipedia.org/wiki/Chess_piece_relative_value Chess piece relative value from Wikipedia]
* [http://www.chessvariants.com/d.betza/pieceval/index.html About the Values of Chess Pieces] by [[Ralph Betza]]
* [http://www.chessbase.com/newsdetail.asp?newsid=7775 The joys of chess – and the value of the pieces], [[ChessBase|ChessBase News]], December 21, 2011 <ref>[[Christian Hesse]] ('''2011'''). ''[http://www.newinchess.com/The_Joys_of_Chess-p-953.html The Joys of Chess - Heroes, Battles & Brilliancies]''. ISBN: 978-90-5691-355-7, [https://en.wikipedia.org/wiki/New_In_Chess New In Chess]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=41556 Interesting article about the value of the pieces] by Aloisio Ponti, [[CCC]], December 22, 2011</ref>
=References=
<references />
'''[[Evaluation|Up one level]]'''
[[Category:Elke Rehder]]
[[FILE:Elke_Rehder_Chess_Schach_Stefan_Zweig_Schachnovelle_Royal_Game_4.jpg|border|right|thumb|link=http://www.elke-rehder.de/Chess_Woodcuts.htm|[https://en.wikipedia.org/wiki/The_Royal_Game The Royal Game] IV <ref>[http://www.elke-rehder.de/Chess_Woodcuts.htm Royal Game, Woodcuts Art] by [[Arts#Rehder|Elke Rehder]], [https://en.wikipedia.org/wiki/Stefan_Zweig Stefan Zweig] [https://en.wikipedia.org/wiki/The_Royal_Game The Royal Game] IV</ref> ]]
'''Material''',<br/>
a term determined by the sum of [[Point Value|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 [[Centipawns|centipawn scale]], which allows positional features of the position, worth less than a single pawn, to be evaluated without requiring fractions but a [[Score#FixedPoint|fixed point score]].
=Basic Piece Values=
Piece relative values concerning their relative strength in potential exchanges based on human experience and [[Learning|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|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 <ref>[http://www.talkchess.com/forum/viewtopic.php?t=18240 Evaluation of material imbalance (a Rybka secret?)] by [[Alessandro Scotti]] from [[CCC]], December 06, 2007</ref> .
Other factors that affect material evaluation might be:
* Bonus for the [[Bishop Pair|bishop pair]] (bishops complement each other, controlling squares of different [[Color|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|piece-square tables]] as well)
* Trade down bonus that encourages the winning side to trade pieces but no pawns <ref>[http://www.talkchess.com/forum/viewtopic.php?t=64110 trading pieces and pawns based on material balance] by [[Erin Dame]], [[CCC]], May 28, 2017</ref>
* 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)
<span id="InsufficientMaterial"></span>
=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 <ref>[http://www.open-aurec.com/wbforum/viewtopic.php?f=2&t=2112 Quark 2.35 draw claim bug] by [[Igor Korshunov]], [[Computer Chess Forums|Winboard Forum]], March 28, 2005 » [[Quark]], [[Draw]]</ref> , 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|draw evaluation]] and [[Interior Node Recognizer|interior node recognizer]].
<span id="Balance"></span>
=Material Balance=
The Material Balance is finally returned as the almost most dominating evaluation term, usually in [[Negamax]] from [[Side to Move|side to move's]] point of view, and in its pure form simply the difference of both sides material, MD:
<pre>
md := material[side_2_move] - material[side_2_move ^ 1];
</pre>
As mentioned, other material considerations, concerning [[Material#InsufficientMaterial|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 [[Material Hash Table#ApproachOfChess|hashing approach]] of [[Chess (Program)|Chess 4.5]].
=Hashing and Tables=
To save speed in the material evaluation, programs using rules often [[Hash Table|hash]] the material evaluation scores. With [[Material Tables|precomputed arrays of material values]], this is not needed.
* [[Material Hash Table]]
* [[Material Tables]]
=See also=
* [[Bishop Pair]]
* [[Score#FixedPoint|Fixed Point Score]]
* [[Influence Quantity of Pieces]]
* [[Interior Node Recognizer]]
* [[Material Hash Table#ApproachOfChess|Material in Chess 4.5]]
* [[SOMA#Material|Material in SOMA]]
* [[Piece-Square Tables]]
* [[Simplified Evaluation Function]]
=Related Publications=
* [[Claude Shannon]] ('''1949'''). ''[http://www.pi.infn.it/%7Ecarosi/chess/shannon.txt Programming a Computer for Playing Chess]''. [http://archive.computerhistory.org/projects/chess/related_materials/text/2-0%20and%202-1.Programming_a_computer_for_playing_chess.shannon/2-0%20and%202-1.Programming_a_computer_for_playing_chess.shannon.062303002.pdf pdf] from [[The Computer History Museum]]
* [[Alan Turing]] ('''1953'''). '''''Chess'''''. part of the collection ''Digital Computers Applied to Games'', in [https://en.wikipedia.org/wiki/B._V._Bowden,_Baron_Bowden Bertram Vivian Bowden] (editor), [http://www.computinghistory.org.uk/cgi-bin/sitewise.pl?act=det&p=10719 Faster Than Thought], a symposium on digital computing machines, reprinted 1988 in [[Computer Chess Compendium]], reprinted 2004 in ''The Essential Turing'', [http://books.google.com/books?id=RSkxnKlv1D4C&lpg=PP882&ots=VOWmiIm_lD&dq=Turochamp%2C%20chess&pg=PP881#v=onepage&q&f=true google books]
* [[Jack Good]] ('''1968'''). ''A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares''. [http://www.doc.ic.ac.uk/~shm/MI/mi2.html 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''? [[ICGA Journal#16_4|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 <ref>[https://groups.google.com/d/msg/rec.games.chess/xFCRAQIqvjw/OVFg2ezWYTYJ Looking for Mark Sturman] by [[Mark Lefler]], [[Computer Chess Forums|rec.games.chess]], July 02, 1995</ref> » [[Bishop Pair]]
* [[Mark Sturman]] ('''1996'''). ''Beware the Bishop Pair''. [[ICGA Journal#19_2|ICCA Journal, Vol. 19, No. 2]]
* [[Don Beal]], [[Martin C. Smith]] ('''1997'''). ''Learning Piece Values Using Temporal Differences''. [[ICGA Journal#20_3|ICCA Journal, Vol. 20, No. 3]]
* [[Larry Kaufman]] ('''1999'''). ''[https://www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman The Evaluation of Material Imbalances]''. (first published in [https://en.wikipedia.org/wiki/Chess_Life 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, [[Darmstadt University of Technology|TU Darmstadt]], [http://www.ke.tu-darmstadt.de/publications/reports/tud-ke-2008-07.pdf pdf]
* [[Christian Hesse]] ('''2011'''). ''[http://www.newinchess.com/The_Joys_of_Chess-p-953.html The Joys of Chess - Heroes, Battles & Brilliancies]''. ISBN: 978-90-5691-355-7, [https://en.wikipedia.org/wiki/New_In_Chess New In Chess] <ref>[http://www.chessbase.com/newsdetail.asp?newsid=7775 The joys of chess – and the value of the pieces], [[ChessBase|ChessBase News]], December 21, 2011</ref>
=Forum Posts=
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=222033 Queen vs two rooks] by [[Benny Antonsson]], [[CCC]], April 07, 2002
* [https://www.stmintz.com/ccc/index.php?id=286659 Exceptions to (1,3,3,5,9)] by [[David Rasmussen]], [[CCC]], February 24, 2003
* [https://www.stmintz.com/ccc/index.php?id=345860 Bad trade] by [[Benny Antonsson]], [[CCC]], January 30, 2004
==2005 ...==
* [http://www.open-aurec.com/wbforum/viewtopic.php?f=2&t=2112 Quark 2.35 draw claim bug] by [[Igor Korshunov]], [[Computer Chess Forums|Winboard Forum]], March 28, 2005 » [[Quark]], [[Draw]]
* [http://www.talkchess.com/forum/viewtopic.php?t=13166 Material imbalance evaluation] by [[Alessandro Scotti]], [[CCC]], April 16, 2007
* [http://www.talkchess.com/forum/viewtopic.php?t=18240 Evaluation of material imbalance (a Rybka secret?)] by [[Alessandro Scotti]], [[CCC]], December 06, 2007
* [http://www.talkchess.com/forum/viewtopic.php?t=27387 Relative Piece Values] by [[Mark Lefler]], [[CCC]], April 09, 2009 » [[Point Value]]
* [http://www.talkchess.com/forum/viewtopic.php?t=27616 Testing of Kaufman Material Values] by [[Mark Lefler]], [[CCC]], April 25, 2009
* [http://www.talkchess.com/forum/viewtopic.php?t=27842 Rook Pair Penalty, Knight Pair Penalty, Having a Pawn Bonus] by [[Mark Lefler]], [[CCC]], May 11, 2009
==2010 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=33035 Efficiently index material signatures and lookup] by [[Mathieu Pagé]], [[CCC]], March 03, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=34159 Stockfish - material balance/imbalance evaluation] by [[Ralph Stoesser]], [[CCC]], May 05, 2010 » [[Stockfish]]
'''2011'''
* [http://www.talkchess.com/forum/viewtopic.php?t=37592 Wrong draw claim by Naum 4.2 ?] by [[Matthias Gemuh]], [[CCC]], January 12, 2011 » [[Draw]]
* [http://www.talkchess.com/forum/viewtopic.php?t=37831 Material imbalance/bad trade and borrowing code] by [[Evert Glebbeek]], [[CCC]], January 27, 2011
'''2012'''
* [http://www.talkchess.com/forum/viewtopic.php?t=41916 Stockfish Code ( Piece Value's)] by Nolan Denson, [[CCC]], January 10, 2012 » [[Stockfish]]
* [http://www.talkchess.com/forum/viewtopic.php?t=41905 Lone minor piece penalty - What did Larry mean?] by [[Charles Roberson]], [[CCC]], January 10, 2012
* [http://www.talkchess.com/forum/viewtopic.php?t=45321 Why Knight and (lone) Bishop are so nearly equal in value] by [[Harm Geert Muller]], [[CCC]], September 25, 2012
'''2013'''
* [http://www.talkchess.com/forum/viewtopic.php?t=47713 An experiment with material imbalances and game-phase] by [[Evert Glebbeek]], [[CCC]], April 06, 2013 » [[Material Tables]]
* [http://www.talkchess.com/forum/viewtopic.php?t=49808 A balanced approach to imbalances] by [[Lyudmil Tsvetkov]], [[CCC]], October 23, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=50150 handling draw by insufficient material] by [[Youri Matiounine]], November 19, 2013 » [[Draw Evaluation]]
* [http://www.talkchess.com/forum/viewtopic.php?t=50504 Lonely queen] by [[Lyudmil Tsvetkov]], [[CCC]], December 15, 2013
* [http://macechess.blogspot.de/2013/12/queen-vs-3-minors.html Queen vs 3 minors] by [[Thomas Petzke]], [http://macechess.blogspot.de/ mACE Chess], December 18, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=50550 Accessing Material Imbalance Information?] by [[Steve Maughan]], [[CCC]], December 19, 2013 » [[Material Tables]]
* [http://macechess.blogspot.de/2013/12/queen-vs-3-minors-part-2.html Queen vs 3 Minors part 2] by [[Thomas Petzke]], [http://macechess.blogspot.de/ mACE Chess], December 21, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=50601 Trading penalty with imbalances] by [[Lyudmil Tsvetkov]], [[CCC]], December 22, 2013
'''2014'''
* [http://www.talkchess.com/forum/viewtopic.php?t=52757 Scaling eval with material on the board] by [[Lyudmil Tsvetkov]], [[CCC]], June 25, 2014
* [http://www.talkchess.com/forum/viewtopic.php?t=52775 Obligatory scaling] by [[Lyudmil Tsvetkov]], [[CCC]], June 27, 2014 » [[Rook Endgame]]
==2015 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=56142 Rook vs 2 minor pieces with pawns on the board] by [[Shawn Chidester]], [[CCC]], April 27, 2015
* [http://www.talkchess.com/forum/viewtopic.php?t=56168 Piece weights with regression analysis (in Russian)] by [[Vladimir Medvedev]], [[CCC]], April 30, 2015 <ref>[http://habrahabr.ru/post/254753/ Определяем веса шахматных фигур регрессионным анализом / Хабрахабр] by [[Vladimir Medvedev|WinPooh]], April 27, 2015 (Russian)</ref> » [[Point Value]], [[Automated Tuning]]
* [http://www.talkchess.com/forum/viewtopic.php?t=62687 Another way of evaluating material imbalances] by [[Volker Annuss]], [[CCC]], January 01, 2017 » [[Arminius]]
* [http://www.talkchess.com/forum/viewtopic.php?t=64110 trading pieces and pawns based on material balance] by [[Erin Dame]], [[CCC]], May 28, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=64115 insufficient mating material] by [[Erin Dame]], [[CCC]], May 29, 2017 » [[Draw Evaluation]]
* [http://www.talkchess.com/forum/viewtopic.php?t=64576 list of material combinations requiring specialized eval ?] by [[Mahmoud Uthman]], [[CCC]], July 11, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=65364 Trading Pieces When Ahead In Material] by [[Daniel Anulliero]], [[CCC]], October 03, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=65870 Magic end-game material hash?] by [[Harm Geert Muller]], [[CCC]], November 30, 2017
* [http://www.talkchess.com/forum/viewtopic.php?t=66966 'ab-initio' piece values] by [[Harm Geert Muller]], [[CCC]], March 30, 2018 » [[Piece-Square Tables]]
=External Links=
* [https://www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman The Evaluation of Material Imbalances] by [[Larry Kaufman]]
* [http://walkofmind.com/programming/chess/mat_stats.html Statistics of material imbalances in chess games] by [[Alessandro Scotti]] » [[Match Statistics]]
* [https://en.wikipedia.org/wiki/Chess_piece_relative_value Chess piece relative value from Wikipedia]
* [http://www.chessvariants.com/d.betza/pieceval/index.html About the Values of Chess Pieces] by [[Ralph Betza]]
* [http://www.chessbase.com/newsdetail.asp?newsid=7775 The joys of chess – and the value of the pieces], [[ChessBase|ChessBase News]], December 21, 2011 <ref>[[Christian Hesse]] ('''2011'''). ''[http://www.newinchess.com/The_Joys_of_Chess-p-953.html The Joys of Chess - Heroes, Battles & Brilliancies]''. ISBN: 978-90-5691-355-7, [https://en.wikipedia.org/wiki/New_In_Chess New In Chess]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=41556 Interesting article about the value of the pieces] by Aloisio Ponti, [[CCC]], December 22, 2011</ref>
=References=
<references />
'''[[Evaluation|Up one level]]'''
[[Category:Elke Rehder]]
