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From: sje@mv.mv.com (Steven J. Edwards)
Subject: Re: Chess - exhaustive searching
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Date: Thu, 13 Apr 1995 16:12:23 GMT
References: <scottecD6FAH9.2pp@netcom.com> <3ln0ol$ame@mycroft.rand.org> <D6GDIx.DM@cs.vu.nl> <3mjel3$q4e@nic.lth.se>
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hanso@dna.lth.se (Hans Olsson) writes:

>To get a strict upper bound we have to take into account whether
>en-passant is possible, and the number of moves since last pawn taken (or ...)
>This gives a total of no more than 600 such possibilities (in any
>position we can not have more than 5 en-passant possibilities and
>only one or none is possible => 1+5=6) and no more than 100 half-moves 
>is possible.

I may not fully understand what you mean by "possibility".  Note that
a position will have zero, one, or two possible en passant captures.

I am unsure of the utility of this discussion.  I hope that no one
considers state space enumeration to be a good metric for evaluation
of game complexity.  It is a trivial exercise to construct games with
arbirarily large spaces that are simple to solve.

Even two games with about the same state count can be vastly different
in complexity.  My program Spector has solved the chess endgames
classes K+Q+Q vs. K and K+B+N vs K; both have the same state count.
Yet the first is far easier to play than the second; White can mate
requiring no more than four moves in the former while the latter can
need 33.

-- Steven (sje@mv.mv.com)
