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Subject: Re: Board games and mathematical complexity: a poll

Author: James Swafford

Date: 14:38:42 12/11/02

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On December 11, 2002 at 16:42:35, Dann Corbit wrote:

>On December 11, 2002 at 15:33:36, James Swafford wrote:
>[snip]
>
>>    chess         10^46
>
>Where does this figure come from?
>10^48 is the lowest bound I have ever seen demonstrated.


H.J. ven den Herik et al., in Schaeffer's "Chips Challenging Champions".
It says the state space complexity of chess is 10^46, with a 10^123
game tree complexity.

His references are:

L.V. Allis, Searching for solutions in games and artificial intelligence,
PhD Thesis, University of Limburg, Maastricht, 1994

and

S. Chinchalkar, An upper bound for the number of reachable positions,
ICCA J. 19 (3) (1996) 181-183.

--
James



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