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Subject: Re: Mathematical question regarding chess

Author: Uri Blass

Date: 11:05:18 08/01/01

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On August 01, 2001 at 11:53:55, José de Jesús García Ruvalcaba wrote:

>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
>>
>
>Even with a pure random non-constant evaluation, deeper search helps (but I
>would assume that checkmates and other ways to end the game are recognised and
>properly evaluated). The reason is that even a random evaluation will favour
>moves which increase the own mobility (as long as the search depth is bigger
>than two)

Why?
If the evaluation is a random number I see no reason for prefering moves that
increase the mobility.

If you assume that the program evaluates checkmates correctly then it s clear
that it plays better than rabdom moves because it is going to never miss a
simple forced mate so you do not need to use mobility.

Uri



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