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Subject: Re: positions in chess <= 10^40?

Author: Sune Fischer

Date: 01:22:47 11/30/02

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On November 29, 2002 at 17:01:39, Uri Blass wrote:
>>P.S: I hope I will be able to prove exactly that there are less than 10^42 or
>>even less than 10^40 positions. This requires a combination of techniques from
>>operations research with classic tree search algorithms and combinatorics
>>theory.
>>
>>P.S.2: Please correct me if I express sthg in the wrong way - english is not my
>>primary language.
>
>I do not know the number and it is only a guess but my guess is that you are
>going to be unable to prove that there are less than 10^40 position for the
>simple reason that there are more than 10^40 positions.

I think you are right. We discussed this a long time ago (perhaps it's in the
archieves). My first upper bound estimates were about 10^36 IIRC, but I didn't
consider that it is possible to generate 14 promoted pieces, something which you
were quick to remind me of :)
This blew the counting to over 10^40 because promoting to knights, bishops and
rooks beside queens, give a very large variaty of piece combination on the
board.
I think if there weren't a promotion rule, then it would be less than 10^40, but
I don't remember the (rather long) equation anymore.

-S.



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