Author: Bruce Cleaver
Date: 08:11:42 11/27/03
Go up one level in this thread
On November 26, 2003 at 15:44:11, Dustin Moore wrote: >Are there any theoretical numbers on the number of >*reasonable* chess positions availible in a game? > >For my purposes a reasonable chess position is one >that could be reached by two good engines looking >out to about to ply 13 or so from a normal opening. > >I'm sure someone has written a paper on this at some >point. > >I wonder how impossible it would be to make a massive >hash table with all the positions likely to be reached >in a game. I'm wondering just how many hundreds of >TB it would take to store the hash table. Estimates of the number of distinct chess positions vary between 10^43 and 10^48. I know Karins Dad in this forum worked on the minimum number of bits necessary to describe a position and came up with about 160 bits. 2^160 = 10^48 positions. Now comes a leap of logic: many (most?) of the positions are nonsense full of lopsided material. I am going to conjecture that the ratio of non-ridiculous postions to all positions is the same as alpha-beta to minimax search; that is, there would be about 10^24 positions of true interest that need to be hashed. So, 160 bits (for the hash code) * 10^24 positions = 1.6*10^26 bits, or about 1.8*10^13 Terabytes! Smaller than I might have thought. The true number might be smaller yet, as some of the positions cannot be reached by legal play, or are symmetric, etc. If the number of bits necessary to describe a chess position is smaller than 160 bits, the total storage would be smaller too.
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.