Computer Chess Club Archives


Search

Terms

Messages

Subject: Re: Exact number of positions in the game of chess... Please help.

Author: Russell Reagan

Date: 21:01:45 11/28/02

Go up one level in this thread


Generally the number of chess positions is estimated at about 10^40, but it is
not possible (currently) to know exactly how many there are. It will probably
not be possible within our lifetime to know exactly how many there are, and
quite possibly never possible at all.

Even a search, such as perft, couldn't determine this piece of data. You would
need to store every position, and make sure you don't count duplicates that
arise in the search more than onces, which means you would have to store all of
the positions.

If you take the approach of generating endgame tablebases, you might have some
positions that are not actually possible to reach in a legal game of chess, so
that number could be wrong.

So now we're back to doing one giant search and storing each position we come
across in a giant array capable of storing every possible chess position (both
legal and illegal) and then seeing which ones you can find.

Perhaps set each array element to 1 if the position is found, and initialize the
array with 0's. Then count the number of 1's in the array, and you have your
answer. So you would need a computer capable of doing this giant search (and
none is even close to existing) and you'd need some medium capable of storing
such an array, using a godel number (I think that's what it's called) as the
index into that array. So you could do this computation needing only 1-bit per
position, but, that number is not terribly useful even if you could compute it,
and I don't know of anyone that has 10^40 bits laying around. You would need
about 1,164,153,218,269,348,144,531,250,000,000 gigabytes of memory. I only have
20 gigs, but my birthday is coming up, so maybe someone will give me a new hard
drive with this much storage :)



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.