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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 09:40:09 GMT
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Jim Gillogly <jim@acm.org> writes:

>The smallest estimate I've seen is in the neighborhood of 10^67 possible
>positions, based on a efficient method of encoding the board in 201 bits.
>People have estimated the number of possible games as 10^120... they are two
>different questions.

For my Ph.D. thesis, in which I discuss a number of popular thinking games,
I have created programs which calculate the state-space complexity 
(the number of legal positions) and the game tree complexity (related to
the number of possible games) for 15 games.

For chess, I have found that the state-space complexity is not larger than
10^53, and 10^50 is probably an accurate measure. I believe that quotes
in the literature of 10^43 are too low.

The estimate of 10^120 for the number of games is based on two assumptions:
1. The branching factor (average number of moves per positions) is 35.
2. The average game length is 80 ply (i.e. 40 moves).
This last average is in my opinion not so relevant as a measure of the
complexity of the game. It says something about the current practice
in human expert play.

For some background on these matters, see chapter 6 of my thesis:
	http://www.cs.vu.nl/~victor/thesis.html

Victor Allis.
