Author: Jay Scott
Date: 14:25:38 02/26/98
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On February 26, 1998 at 05:15:06, Amir Ban wrote: >I thought this question would come up. I don't think there is any >problem in defining the probability. For a single position, talking >about probability is meaningless (that's usually the case with >probabilities), but for many positions, it does. Here's a precise though >theoretical definition: Take all the positions that you evaluate as x, >lookup their game-theoretic value in your 32-piece tablebase, and >average. This is the true outcome expectation (or probability) of your >x-evaluation, and it should be compared to what your probability mapping >says for x, that is, what you thought an x score means. E.g. you may >think a value of +4 means you score 98%, but looking at all positions >that you value +4, you find that they really score only 93%. Another way to look at it is by individual evaluation terms. Your passed pawn evaluation will take certain features into account and ignore most of what's going on in the position. You can partition the set of chess positions into equivalence classes where each class must get the same passed pawn score, simply because the passed pawn evaluator can't tell them apart. You can do the same analysis for any subset of evaluation terms up to and including the whole evaluator. The difference from your definition is that the set of chess positions is partitioned by evaluation features used, rather than by score. Different partitions may get the same score, under this scheme. It's a "white box" view that might be more useful for real-life tuning. Here's one complication: For a given program, it doesn't matter whether the program mis- evaluates a position that it will never see. If your program battles like a maniac to avoid closed positions, then it won't make any difference whether it understands them or not. Conversely, if it's hell-bent on kingside attacks then it had better evaluate them accurately if it wants to win. So for a more useful :-) measure, you could define a probability distribution over the set of chess positions, saying how likely the program is to reach or to care about each position. >Practically, this can be approximated by scanning game databases. If you are careful, yes, I think so too. Jay
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