Author: James Swafford
Date: 06:08:27 11/01/01
Go up one level in this thread
On November 01, 2001 at 08:35:46, Simon Finn wrote: >On October 31, 2001 at 18:17:39, James Swafford wrote: > >>On October 31, 2001 at 18:14:41, James Swafford wrote: >> >>> >>>I'm playing around with a hyperbolic tangent function in order >>>to predict a reward [-1 ... 1] based on my raw evaluation score >>>of the principal variation. >>> >>>I've come up with predicted_reward = tanh(pawn_adv/300), where >>>a pawn advantage of 1 pawn ---> pawn_adv=100. >>> >>>The following table shows the relationship between pawn_adv and >>>predicted_reward: >>> >> >>Actually, that's pawn_adv/100 vs. predicted_reward... >> >> >>>pawn_adv predicted_reward >>>.1 .033 >>>.25 .083 >>>.33 .11 >>>.4 .133 >>>.5 .165 >>>.75 .245 >>>1 .32 >>>2 .58 >>>3 .76 >>>4 .87 >>>5 .93 >>>6 .964 >>>7 .981 >>>8 .990 >>>9 .995 >>>10 .9975 >>>12 .9993 >>>15 .9999 >>> >>>So... a 1 pawn advantage yields a predicted reward of .32. >>> >>>Has anybody done research, or know of research, that can tell me >>>how close those figures are? i.e. if your program obtains a >>>1 pawn advantage, do you know how likely it is to win? >>> >>>Tridgell and Baxter's paper says they give a one pawn advantage >>>a predicted reward of .25, but it doesn't say why they chose >>>that number. Maybe they pulled it out of thin air, I don't know. >>> >>>Comments? Anybody know of a better function than tanh() to >>>do this? > >How does predicted reward convert into the expected percentage? > >Is it 50 + 50 * predicted_reward? No.. I don't know where you got that. I have no method of converting predicted reward into expected percentage, because I don't know any real numbers to work with. That's why I'm asking if anybody has any solid numbers stating: "when my program gets a 1 pawn advantage it wins X% of the time" and so on. > >If so, the predicted reward for small advantages seems a bit small. Maybe, but shouldn't it be small? If you have a 5 pawn advantage, aren't you almost as sure to win as if you had a 10 or 15 pawn advantage? There is a lot of uncertainty with small advantages. I guess this could be thought of as a certainty factor, or a measure of belief. That's not the same as a probability. If I could find a way to convert from this certainty factor to a winning probability, I would do it. But I'd like some numbers to work with. > >White is generally expected to score roughly 55%. > >On the above formula, this corresponds to a predicted reward of 0.1, >but I don't think you would find many takers for the proposition >that White's initial advantage is more than 0.25 pawns. I don't necessarily believe white has any measurable initial advantage in terms of the formula I gave. > >Simon > > > > >>> >>>-- >>>James
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