Author: Sune Fischer
Date: 00:30:17 10/26/02
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On October 25, 2002 at 19:08:02, Rodney Topor wrote: >On October 25, 2002 at 16:34:40, Robert Hyatt wrote: > >>On October 25, 2002 at 14:29:59, Uri Blass wrote: >> >>>You can translate pawn to expected result but not to probabilities. >>> >>>The expected result is the same in the following 2 cases: >>>probability 1% win for white and 98% draw >>>probability 40% win for white and 20% draw. >>> >>>The probabilities are not the same. >>> >>>Uri >>> >>And I would hope the scores are not the same for those two cases either. >> >>The 40% win probability should (IMHO) have a higher score than a position >>with a 1% win/98% draw score... >> >>The latter should be near to 0.00 > >I guess Uri was trying to suggest that the second position was somehow >unstable, with white and black both equally likely to win but a draw >being relatively unlikely. I guess such a situation might occur in a wild >tactical position. In this case, the 3 probabilities might describe the >position better than a single expected value. But I have no idea whether >this would be useful or not. >Rodney Topor I don't follow this with the tre scores, why would you need three? The game has a only three posible outcomes, white wins +1, white draws 0, white loses -1. That is a closed interval [-1;1] and you can transform that to [0;1] without problems if you want. If you go by the first interval -0.97 would be like -7.34 pawns and 0 would be 0 and +0.56 might be like +2.3 pawns. There is probably a nice (but slow) trigonometric fit to this transformation. I think the point is it doesn't change anything in the alpha-beta algorithm as long as the transformation is injective on the domain (a!=b => T(a)!=T(b)), otherwise things would get real spooky. -S.
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