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 [2] . 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 [3]:

A theoretical attempt to evaluate the pieces was made by H. M. Taylor in 1876 [4] , reported by Coxeter (1940, pp. 162-165 [5]). 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 [6]. 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.

Source Year Pawn Knight Bishop Rook Queen
H. S. M. Coxeter [7] 1940 300 350 550 1000
Max Euwe and Hans Kramer [8] 1944 100 350 350 550 1000
Claude Shannon [9] 1949 100 300 300 500 900
Alan Turing [10] 1953 100 300 350 500 1000
Mac Hack [11] 1967 100 325 350 500 975
Chess 4.5 [12] 1977 100 325 350 500 900
Tomasz Michniewski [13] 1995 100 320 330 500 900
Hans Berliner [14] [15] 1999 100 320 333 510 880
Larry Kaufman [16] 1999 100 325 325 500 975
Fruit and others [17] 2005 100 400 400 600 1200
Larry Kaufman [18] 2012 100 350 350 525 1000

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

See also

Publications

Forum Posts

1993 ...

2000 ...

2005 ...

2010 ...

2015 ...

Re: Pawn value estimation by Larry Kaufman, CCC, May 09, 2015

External Links

References

  1. Wassily Kandinsky, Points, 1920, Ohara Museum of Art, Google Art Project, Wassily Kandinsky from Wikipedia
  2. Claude Shannon (1949). Programming a Computer for Playing Chess. Philosophical Magazine, Ser. 7, Vol. 41, No. 314 - March 1950
  3. Jack Good (1968). A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares. Machine Intelligence Vol. 2
  4. H. M. Taylor (1876). On the Relative Values of the Pieces in Chess. Philosophical Magazine, Series 5, Vol. 1, pp. 221-229
  5. H. S. M. Coxeter (1940). Mathematical Recreations and Essays. from the original by W. W. Rouse Ball, Macmillan
  6. Influence Quantity of Pieces - Fibonacci Spiral
  7. see Theoretical Attempt {12, 14, 22, 40} * 25 = {300, 350, 550, 1000}
  8. Max Euwe, Hans Kramer (1944, 1977). Het middenspel, deel 1-4. Spectrum, Utrecht
  9. Claude Shannon (1949). Programming a Computer for Playing Chess. Philosophical Magazine, Ser. 7, Vol. 41, No. 314 - March 1950
  10. 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
  11. Richard Greenblatt, Donald Eastlake, Stephen D. Crocker (1967). The Greenblatt Chess Program. Proceedings of the AfiPs Fall Joint Computer Conference, Vol. 31, pp. 801-810. Reprinted (1988) in Computer Chess Compendium, pdf from The Computer History Museum or as pdf or ps from DSpace at MIT
  12. David Slate, Larry Atkin (1977). CHESS 4.5 - The Northwestern University Chess Program. Chess Skill in Man and Machine, reprinted (1988) in Computer Chess Compendium
  13. Simplified Evaluation Function
  14. Hans Berliner (1999). The System: A World Champion's Approach to Chess. Gambit Publications, ISBN 1-901983-10-2
  15. Chess piece value, the Hans Berliner's system from Wikipedia
  16. Larry Kaufman (1999). The Evaluation of Material Imbalances. (first published in Chess Life March 1999, on-line version edited by Dan Heisman)
  17. Re: 2005 National Computer Chess Championships by Shaun Press, Chess Chat, July 17, 2005 » NC3 2005
  18. Re: What is the correct value of the pieces? by Larry Kaufman, CCC, October 10, 2012
  19. Christian Hesse (2011). The Joys of Chess - Heroes, Battles & Brilliancies. ISBN: 978-90-5691-355-7, New In Chess
  20. Interesting article about the value of the pieces by Aloisio Ponti, CCC, December 22, 2011

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