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Subject: Re: Mathematical question regarding chess

Author: Gordon Rattray

Date: 08:38:15 08/01/01

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On August 01, 2001 at 09:58:27, Uri Blass 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
>
>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

I have to disagree that such an evaluation function is "random".  I agree that
it would have some element of randomness and therefore "pseudo-random" or
"semi-random" or some other term that denotes partial randomness may be used,
but not just plain "random".

If I have an evaluation function with material, etc. and then add a random value
between 0.0000001 and 0.0000005, can I call that "random" too?  It certainly
wouldn't play very randomly.  Ok, I admit that it wouldn't be entirely
deterministic either, so I won't describe it as "random" or "deterministic", as
neither would be an accurate enough description.

By-the-way, if I said that I was choosing moves at random, and then later told
you that I actually meant playing a random pawn move, if possible, and if not
any other random move, would you think that my initial statement was too vague?
I would.

Gordon



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