Author: Uri Blass
Date: 13:41:22 08/31/00
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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
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