Author: Jay Scott
Date: 14:21:59 01/17/02
Go up one level in this thread
Too many of the posters to this thread do not get it. Pawns add; a pawn evaluator typically considers that winning two pawns is twice as good as winning one. Probabilities do not add; being ahead two pawns does not produce twice the probability of winning as being ahead one. The fundamental difference is that a probability evaluator, if it takes full advantage of probability theory, must account for feature interactions. In a pawn evaluator, entirely hand-made, feature interactions are handled ad hoc by the programmer saying, "Gosh, these two things are related [king safety and the endgame, say], I'd better put in a term to account for it. Hmm, let's try this value and see how it works." In a probability evaluator, whose values are filled in by collecting large amounts of statistical data, feature interactions are detected by statistical analysis and accounted for mathematically. It's principled instead of ad hoc, and as evaluators become more complicated, organizing principles for them become more important. Because of feature interaction, and because it has to be benchmarked to its own measured results, a probability evaluator is more complex to create than a pawn evaluator. The payback is that you have a mathematical theory that tells you how to extract the most information from it. If it includes all the features it needs, and you have collected enough data to accurately model the feature interactions, then it is a theorem that the evaluator will be accurate. Having math on your side can only be good. A concrete example: In an otherwise even position, it's smart to win a pawn at the cost of a positional disadvantage, unless the disadvantage is too big. Suppose you've won the pawn and accepted the disadvantage, and now you have a chance to win a second pawn at the cost of further positional damage. Everything depends on the specific position, of course, but if the one pawn is already enough to win it makes sense to consolidate your position instead of winning the second pawn. A pawn evaluator (unless it has extra smarts) compares its value of a pawn to its value of the positional disadvantage, and chooses the bigger one--whether it has already won one pawn or not. That will sometimes be a mistake. A human does not do that. A probability evaluator does not do that either: if it is correctly constructed, according to probability theory, it will understand that winning extra material produces ever-smaller increases in winning probability, and that accepting a greater positional disadvantage produces ever-greater chances of allowing a perpetual or even underestimating an attack and losing. If the probability evaluator includes good chess features and has good data on them, then it will correctly weigh the odds and choose the move that gives it the statistically best chance of winning--genuinely the best given its knowledge, according to an unimpeachable mathematical theory. You can't ask for more than that.
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