I was wondering if there is a statistical or probabilistic (at least approximate) way of looking at a score of a chess position of a certain fixed engine, say "crafty version 5" for example.

i.e. maybe +2 could be interpreted as "if the engine keeps on playing, 60% wins white, 30% black and 10% draw. I know this isn't the purpose of the score, but maybe it can be translated to approximate probabilities, maybe someone has done a statistical test with hundreds of games to see the correlation. And the amount of draw maybe depends on the "sharpness" of the position.

1 Answer 1


On the website of Houdini, one of the best chess engines (see for instance CCRL or CEGT), the author writes

Houdini 4 uses calibrated evaluations in which engine scores correlate directly with the win expectancy in the position. A +1.00 pawn advantage gives a 80% chance of winning the game against an equal opponent at blitz time control. At +2.00 the engine will win 95% of the time, and at +3.00 about 99% of the time. If the advantage is +0.50, expect to win nearly 50% of the time.

The Chess Programming Wiki mentions a study where data from more than 400 000 computer games have been used to find a relation between pawn advantage (P) and winning percentage (W).

W = 1 / (1+10^(-P/4))

  • Amazing that only one pawn gives so much advantage. Aug 29, 2016 at 21:32
  • True, the 80% winning percentage for P=1 in case of Houdini is quite high. Especially when compared to other engines: according to the formula, for P=1, W=0.64. But, as you correctly mention in your question, the score has a different purpose and it is not necessarily related to the winning percentage.
    – Maxwell86
    Aug 30, 2016 at 7:39
  • 2
    P=4 and W = 91% seems rather low
    – jf328
    Aug 30, 2016 at 10:01
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    Also check "Peter Österlund’s Texel Tuning" in Andrew Grant, Evaluation & Tuning in Chess Engines", which you can locate under Andrew Grant wiki entry were you will get his work on relating the engine evaluation to the winning percentage.
    – djnavas
    Nov 23, 2020 at 6:35

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