Author: Amir Ban
Date: 10:06:36 02/25/98
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On February 25, 1998 at 11:29:06, Don Dailey wrote: >>I have wondered why programs evaluations are measured in pawns intead of >>probablilities of winning. Has no one done this? Has anyone ever taken >>the evaluations in Informant as probabilities of winning and regressed >>them against explanatory variables such as material, space, etc. to fit >>this function. >> >>George Essig > >I'm actually working on this! This is how I think of >evaluation and it would be natural to convert the program >to this system. However I'm not sure it's any more useful >than simply finding the right function to convert a score >to a probability. But most of it's usefulnes is just >thinking in these terms (whether you actually implement >it or not.) For instance, I believe having an advanced >passed pawn should not affect your probability of winning >too much if you are already a piece up, but should have >more impact on the score if you are down a piece. A simple >linear bonus for this passed pawn might not be quite right. > >In general, I believe many positional terms should change >in value when material is not close to zero. Another way >of viewing this is to say "don't be as eager to hunt pawns >if you are already have extra material." It's the same >concept. > > >- Don I've also done some work on this. It seems that the most natural probability mapping is: 1 / (1 + exp(-x/c)), where x is your eval and c a suitable positive constant for scaling. It meets the necessary boundary conditions and symmetry requirements. I don't think I agree with your statement on needing to change positional terms according to the base score. Actually with this function it makes perfect sense for them to be simple additives. If you see how it behaves, you will see that a small fixed increment will change 50% to 60%, but 99% to only 99.2% and 0.8% to 1% (just offhand examples). I.e. they don't affect the expected outcome seriously unless it's reasonably even. Looking at it another way: There must be some mapping where simple addition of terms makes sense. Since this is what you currently do, then after so many years of tuning you can expect that your evaluation would be a close approximation of it. Amir
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