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Subject: Re: likelihood instead of pawnunits? + chess knowledge

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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