Point Value

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Point Value, a piece relative value concerning its relative strength in potential exchanges based on human experience and learning. Common rule of thumb are the {1, 3, 3, 5, 9} point values for pawn (1), knight, bishop, rook and queen, also proposed by Claude Shannon in his 1949 paper Programming a Computer for Playing Chess. In the evaluation of a chess program, the balance of material, the aggregated point values for both sides, is usually the most influential term. =Theoretical Attempt= Jack Good in his Five-Year Plan for Automatic Chess, Appendix F : A theoretical attempt to evaluate the pieces was made by H. M. Taylor in 1876, reported by Coxeter (1940, pp. 162-165 ). The value of a piece is taken as proportional to the average number of squares controlled, averaged over all 64 positions of the piece on the board. This argument leads to the relative values of N, B, R and Q: 3, 5, 8 and 13. Coxeter (or Taylor) goes on to modify the argument by asking instead for the probability of 'safely' giving check, that is, without being en prise to the king, if the piece and king are both placed on the board at random. This gives the ratios 12, 14, 22 and 40. These values are good, but this modification of the argument is artificial. =Basic values= Measured in units of a fraction of a pawn, for instance the common centipawn scale, allows positional features of the position, worth less than a single pawn, to be evaluated without requiring fractions but a fixed point score. Sample point values from various sources over the time, most were used in concrete chess programs.

The king value is often assigned a large constant such as 10000 centipaws, which is important to avoid king captures in certain implementations of SEE. =Reciprocal piece values= Concerning a piece controlling a square, its value of attack might be considered as inverse proportional to its point value, which is an issue in aggregating of mobility or square control terms of different pieces.

=Samples=
 * Material in SOMA
 * Piece Coding in Gambiet
 * Point Values in Komodo
 * Point Values in LL Chess
 * Point Values in MicroChess
 * Point Values in Turochamp

=See also=
 * Experiments with Chess by Jens Christensen and Richard Korf
 * Fixed Point Score
 * Influence Quantity of Pieces
 * Material
 * Piece-Square Tables
 * Point Value by Regression Analysis by Vladimir Medvedev
 * Simplified Evaluation Function by Tomasz Michniewski

=Publications=
 * H. M. Taylor (1876). On the Relative Values of the Pieces in Chess. Philosophical Magazine, Series 5, Vol. 1, pp. 221-229
 * Max Euwe, Hans Kramer (1944, 1977). Het middenspel, deel 1-4. Spectrum, Utrecht
 * Claude Shannon (1949). Programming a Computer for Playing Chess. Philosophical Magazine, Ser. 7, Vol. 41, No. 314 - March 1950, 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
 * Jens Christensen, Richard Korf (1986). A Unified Theory of Heuristic Evaluation functions and Its Applications to Learning. Proceedings of the AAAI-86, pp. 148-152, pdf
 * Larry Kaufman (1994). The Relative Value of the Pieces. Computer Chess Reports, Vol. 5, No. 2, pp. 33
 * Don Beal, Martin C. Smith (1997). Learning Piece Values Using Temporal Differences. ICCA Journal, Vol. 20, No. 3
 * Hans Berliner (1999). The System: A World Champion's Approach to Chess. Gambit Publications, ISBN 1-901983-10-2
 * Sacha Droste, Johannes Fürnkranz (2008). Learning of Piece Values for Chess Variants. Technical Report TUD–KE–2008-07, Knowledge Engineering Group, TU Darmstadt, pdf
 * Sacha Droste, Johannes Fürnkranz (2008). Learning the Piece Values for three Chess Variants. ICGA Journal, Vol. 31, No. 4
 * Kunihito Hoki, Tomoyuki Kaneko (2011). The Global Landscape of Objective Functions for the Optimization of Shogi Piece Values with a Game-Tree Search. Advances in Computer Games 13 » Shogi

=Forum Posts=

1993 ...

 * deriving piece values from mobility by Barney Pell, rgc, August 09, 1993
 * Value of the pieces by Joost de Heer, rgc, February 01, 1995 » Influence Quantity of Pieces
 * Chess in BASIC? by William H. Rogers, CCC, August 28, 1998 » Basic

2000 ...

 * A Piece Value Question by laocmo, rgcc, January 12, 2000
 * piece values by Toni, CCC, December 30, 2003
 * Piece Values in the Endgame by Guy Haworth, CCC, February 11, 2004 » Endgame

2005 ...

 * Re: 2005 National Computer Chess Championships by Shaun Press, Chess Chat, July 17, 2005 » NC3 2005
 * Relative Piece Values by Mark Lefler, CCC, April 09, 2009

2010 ...

 * Stockfish Code ( Piece Value's) by Nolan Denson, CCC, January 10, 2012
 * Why Knight and (lone) Bishop are so nearly equal in value by Harm Geert Muller, CCC, September 25, 2012
 * What is the correct value of the pieces? by Roberto Munter, CCC, October 10, 2012
 * The value of a pawn by Evert Glebbeek, CCC, March 28, 2013

2015 ...

 * Piece Value - Human vs. Computer by Sean Evans, CCC, April 19, 2015
 * Piece weights with regression analysis (in Russian) by Vladimir Medvedev, CCC, April 30, 2015 » Point Value by Regression Analysis
 * Pawn value estimation by Dann Corbit, CCC, May 04, 2015
 * Re: Pawn value estimation by Larry Kaufman, CCC, May 09, 2015


 * Larry Kaufman, Math and "The Development of Chess Style by Charles Roberson, CCC, May 19, 2015
 * Xiangqi piece value model by Evert Glebbeek, CCC, May 29, 2016 » Xiangqi
 * Approximating Stockfish's Evaluation by PSQTs by Thomas Dybdahl Ahle, CCC, August 23, 2017 » Regression, Piece-Square Tables, Stockfish
 * '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 » Schooner, Xiphos

2020 ...

 * Estimating piece strength by grandmastermac, CCC, April 26, 2020
 * How to calculate piece weights with logistic regression? by Maksim Korzh, CCC, October 01, 2020 » Regression, Point Value by Regression Analysis

=External Links=
 * Chess piece relative value from Wikipedia
 * Centipawn - WikiChess
 * 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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