Centipawns

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Centipawns, (Centi-pawns) a score unit which corresponds approximately to one hundredth of a pawn unit. Fixed point representation with centipawn fractions allows a smooth relation of all piece values with a reasonable granularity to distinguish positional scores. 16 or even 15 bits are sufficient to store signed centipawn ranges in hash tables, while sign extension to the common 32-bit integer range is convenient to avoid overflows in scaling terms like in the tapered eval, even with an internal finer granularity used inside the evaluation.

=Quotes=

Robert Hyatt
Robert Hyatt on score grain in Crafty : Having done all three, my take on the issue is this:

Aske Plaat
Aske Plaat's implementation tip on MTD(f) : The coarser the grain of eval, the less passes MTD(f) has to make to converge to the minimax value. Some programs have a fine grained evaluation function, where positional knowledge can be worth as little as one hundredth of a pawn. Big score swings can become inefficient for these programs. It may help to dynamically increase the step size: instead of using the previous bound, one can, for example, add an extra few points in the search direction (for failing high, or searching upward, adding the bonus, and for failing low, or searching downward, subtracting the bonus) every two passes or so. (Don Dailey found that a scheme like this works well in a version of Cilkchess.) At the end, if you overshoot the minimax value, you have to make a small search in the opposite direction, using the previous search bound without an extra bonus, to make the final convergence. Also, it can be quite instructive to experiment with different evaluation function grain sizes. Sometimes coarse grain functions work better than fine grain, both for NegaScout and MTD(f).

=See also=
 * Millipawns
 * Pawn Advantage, Win Percentage, and Elo
 * Point Value

=Forum Posts=

2000 ...

 * Performance of MTD(f) versus eval granularity? by Werner Mühlpfordt, CCC, November 01, 2001 » MTD(f)
 * Centipawns and Millipawns by Ricardo Gibert, CCC, September 08, 2009
 * Winning percentage and centipawns by Luca Hemmerich, CCC, November 18, 2009

2010 ...

 * xboard protocol and centipawn by Joshua Shriver, CCC, October 17, 2010
 * Evaluations in centipawns and symbols by Marek Soszynski, CCC, October 23, 2012
 * Is centipawn the right unit for measuring the score? by Karol Majewski, CCC, August 09, 2016

2020 ...

 * Centipawns vs Millipawns with NNUE by Madeleine Birchfield, CCC, October 23, 2020 » NNUE

=External Links=
 * Centipawn - WikiChess
 * centi- - Wiktionary
 * Centi- from Wikipedia
 * Fixed-point arithmetic from Wikipedia
 * Granularity from Wikipedia
 * Resolution from Wikipedia
 * Rounding from Wikipedia
 * Centipede - Septober Energy, 1971 (edited), YouTube Video
 * feat. Keith Tippett, Ian Carr, Karl Jenkins, John Marshall, Roy Babbington, ...

=References= Up one level