Author: Dave Gomboc
Date: 17:09:53 01/18/02
Go up one level in this thread
Computer programs still report their assessments in centipawns, but internally they have a notion of these things. At least, as far as I can tell, the best ones do. Dave On January 17, 2002 at 17:21:59, Jay Scott wrote: >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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