Author: Alvaro Polo
Date: 02:58:11 09/01/00
Go up one level in this thread
On August 31, 2000 at 16:41:22, Uri Blass wrote: >On August 31, 2000 at 15:54:16, Frederic Friedel wrote: > >>On August 31, 2000 at 15:01:18, Vincent Lejeune wrote: >> >>>If I remember well I red in a magasin some years ago that there is 10^80 >>>possible positions and there is 10^120 different playable games (no >>>demonstration was given). >> >>There are 10^112 possible games lasting 40 moves. This is considerably more than >>the 10^82 elementary particles in the universe. It is clear that, for principle >>reasons, all possible games will not be reconstructed (generated and stored) in >>the course of this universe. >> >>But we don’t need to do that in order to solve chess (in the Thompson endgame >>sense). The number of possible legal chess positions is far smaller: between >>10^53 and 10^55. > >The number of possible legal positions is really smaller and my counting program >found that it is smaller. > >3.7010630121207222927827147741452119115968e46 is the upper bound that my program >found(not considering side to move and castling or en passant rule). >Ratko v.tomic improved it to a smaller bound but not clearly smaller. > >I guess that the real number of positions is between 10^43 and 10^45. > >It is possible to get an estimate for this number by the following steps. >1)counting the exact number of pseudo-legal positions(I will call it x). >2)generating 10000 of random pseudo-legal positions. >3)counting the number of the real legal positions out of the 10,000 pseudo-legal >positions(I will call it L). >4)get the estimate x*L/10000. > >We must be careful that x will not be too big(otherwise we may get a very small >number in step 3 and in this case the estimate cannot be trusted). >An extreme case is the case when L=0 and the estimate in step 4 is 0. > >If we get L>30 we can know that we found a good estimate. > >This is a hard work to do it and I am not going to try it unless I find somebody >to pay me for this job(at least 10000$). >Checking the 10000 positions is a hard work(If I need 6 minutes to decide for >every position if it is legal then I need 1000 hours only to do step 3). > >I do not believe that I will find somebody who wants to pay for this job so I am >not going to try to do this job. > >Uri What I would like to know is how many of the possible positions are "reasonable" positions. IE, I assume that the vast majority of the possible positions are "crazy" positions that wouldn't arise in a chess game or positions where one side has huge advantage over the other (for example, white having 8 pieces against black lone king). The "unreasonable" positions could be ignored, and perhaps the new number is computable within a "reasonable" time. Alvaro
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.