Author: James Swafford
Date: 09:56:06 01/16/02
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On January 16, 2002 at 07:41:28, Graham Laight wrote: I don't have time right now to read all the previous posts, but I'd like to point out something I thought interesting when playing with TDLeaf... Temporal difference algorithms needs exactly what you mention - a probability (or a certainty factor I guess) of winning, and it needs to be in the interval -1 .. 1. Of course -1 = loss, 0 = draw, 1 = win. .9 is 'almost certainly a win', etc. You can scale the raw scores from your evaluator and plug that into a hyperbolic tangent function, and the result of that will be in that closed interval. What I think is so neat about using a hyerbolic tangent is that it predicts +5 pawns to be almost as sure to win as +9 pawns or +15 pawns. If I get a chance later and you're interested I can throw up a little chart... it's interesting when you think about it. Say a 1 pawn advantage yields a certainty factor of .74 (I'm making that up). A 2 pawn advantage might yield a cf of .89, then 3 .95, etc. The 'obviousness' starts to set it. Ok, enough rambling... I've got to get going. -- James >It has occurred to me that it is wrong to evaluate a position in terms of >relative pawns (the "de facto" standard - whereby an evaluation of 2 means that >you're approximately the equivalent of 2 pawns ahead). > >This means that many aspects of evaluation have to be squeezed into a dimension >which is not appropriate at all. > >A better way would be to evaluate "winning probability". If a position was a >draw, the value would be 0.50 (or 50%). If the player should win 3 out of 4 >times, the eval should be 75%. If the player must win from here, then the >evaluation should be 100%. > >It seems strange when you think about it that all programmers have chosen to >adopt the traditional "pawn equivalence" standard. > >-g
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