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Subject: Re: Mathematical question regarding chess

Author: Uri Blass

Date: 06:58:27 08/01/01

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On August 01, 2001 at 09:08:08, Gordon Rattray wrote:

>On July 31, 2001 at 22:35:26, Christophe Theron wrote:
>
>>On July 31, 2001 at 19:18:36, Roy Eassa wrote:
>>
>>>On July 31, 2001 at 15:26:08, Ed Panek wrote:
>>>
>>>>On July 31, 2001 at 15:24:48, Roy Eassa wrote:
>>>>
>>>>>On July 31, 2001 at 15:21:17, Ed Panek wrote:
>>>>>
>>>>>>Lets say I have a move generator that selects a random move every time it is its
>>>>>>turn. What are the odds against it drawing/winning a game? Is it less likely
>>>>>>than winning a game of Keno with all the correct numbers picked?
>>>>>>
>>>>>
>>>>>Is the opponent Kramnik or Deeper Blue?  Or a human rated 400?  Or another such
>>>>>"random" program?  I think this matters.
>>>>
>>>>Lets try a random opponent first...and then Kramnik
>>>>
>>>>Ed
>>>
>>>
>>>Obviously, the chance of beating another random-playing program is 50% (not
>>>counting draws).
>>
>>
>>It depends how is programmed the random opponent.
>>
>>If the opponent just picks a move at random, odds are 50%.
>>
>>If the opponent is a program that does some sort of of alpha beta on a tree
>>where the leaves receive random numbers, this opponent will win very often.
>>
>>That means: a random evaluation function is much stronger than a program
>>choosing a move at random.
>
>Do you assume that a move leading immediately to checkmate, stalemate, etc.
>returns a meaningful (non-random) value?  If not, I don't understand why your
>claim holds true?  I assume a "random evaluation function" to be random for
>*all* positions.
>
>Gordon

I agree with christophe that the question is what randomness means.

If the evaluation is the material evaluation +some random number between
+2 pawns and -2 pawns then the program clearly does not play random moves and
you can describe it as random evaluation.

Uri



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