Author: Ricardo Gibert
Date: 19:38:01 01/16/02
Go up one level in this thread
On January 16, 2002 at 16:01:52, Robert Hyatt wrote: >On January 16, 2002 at 15:01:38, Ricardo Gibert wrote: > >>On January 16, 2002 at 14:06:37, Robert Hyatt wrote: >> >>>On January 16, 2002 at 12:58:13, James Swafford wrote: >>> >>>>On January 16, 2002 at 11:43:59, Robert Hyatt wrote: >>>> >>>>>On January 16, 2002 at 07:41:28, Graham Laight wrote: >>>>> >>>>>>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 >>>>> >>>>> >>>>>It is harder to do otherwise. IE KPP vs K is winning, except for some rare >>>>>cases, while KR vs KB is drawn. >>>>> >>>>>It would be very hard to translate some sort of material imbalance into a >>>>>winning percentage. As a general rule, the more material you are ahead, the >>>>>better your chances, with some exceptions that many engines know about... >>>> >>>>Right, but the gains are not linear, and raw scores from an evaluator >>>>typically are. Winning probability is not a linear function of material >>>>+ positional advantages. >>>> >>>>-- >>>>James >>> >>> >>>It could be linear. But perhaps the slope of the straight line is not 45 >>>degrees... >> >>Hmmm...an even position has about a 50% WE (=Win Expectation). It has been >>estimated statistically that a pawn advantage has about a 75% WE on average. Now >>how will you fit all the larger positive advantages in the remaining 75% to 100% >>and maintain a staight line? > >First, I am not sure I believe the pawn advantage wins 3 of every 4 games. >That seems high. I would expect a 2-pawn advantage to be closer to that kind >of winning percentage. But if we plot this on some special graph, I could >certainly envision a straight line result that connects material/positional >score advantage to some reasonable winning percentage estimate. Special graph? You said, "It could be linear" *and* you said it would be a "straight line", so resorting to using soemething like a graph with a logarithmic (or whatever) scale on one side does help. You would still need to redefine the terms "linear" or "straight line" to make what you said to work. As for whether it is 2 or 1 pawns that is equivalent to a 75% WE, I'll let you take your pick. It makes no difference. But it would >be a pointless exercise, because if that can be done, then it would say that >one could be derived from the other, and therefore the original score is >"good enough"...
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