Newsgroups: comp.ai.games
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From: victor@cs.vu.nl (Victor Allis)
Subject: Re: Chess - exhaustive searching
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Date: Mon, 3 Apr 1995 09:57:09 GMT
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aws@monaco.cs.brown.edu (Adam Smith) writes:

>As I understand it, the problem with chess is not storage space, but
>search time.  Whether or not you store or re-generate all the
>positions is almost immaterial next to the time that it takes to do a
>search from the current board position to find a winning mate
>position.  The branching factor is very high since there are as many
>as 32 pieces on the board, and in the large majority of game positions at
>least half of these will be left, or 16.  With that sort of
>complexity, and full search to 4 levels inspects around 65,000 board
>positions, and a search to 8 levels would see about 4.3 billion
>situations.  Even with a computer capable of checking a position for a
>mate every microsecond (including computing each new position), this
>means that an 8-move full search would take 4300 seconds (1.2 hours)!

I disagree.

If you want to SOLVE chess (which is purely a hypothetical question),
i.e. determine the outcome of chess with optimal play by both players
and determine a strategy to obtain that outcome, then the memory
is the main bottleneck. Without memory, we will computer the value of
the same position many times, since the same position occurs in a large
number of different variations.

As an example, Nine men's morris has been solved almost two years ago
by Ralph Gasser. It has been solved through complete enumeration of the
middle and endgame, which was the major part of the work. Had there not
been enough memory available to store the 10^10 positions of the middle
and endgame, Nine men's morris would not have been solved today.
Doing just a forward search is bound to fail.

I believe the same holds for chess. Thus, solving it through complete
enumeration is easier than solving it through forward search, and thus,
memory is the most important part.

Back to reality: both are impossible, one is just more impossible than the
other.

Victor Allis.
