Author: chandler yergin
Date: 22:57:38 01/12/05
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On January 13, 2005 at 01:52:52, Uri Blass wrote: >On January 13, 2005 at 00:48:10, chandler yergin wrote: > >>Yes! From Your LINK! >> >>It's worth Quoting! >>"Subject : Re: The total number of possible chess positions? WT >> >>Posted by : Robert Hyatt on September 01, 2000 at 23:41:29 >> >>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. So will we (or someone or something) be able to work them out, >>effectively retro-analysing the 32-piece endgame chess represents? >> >>Again the answer is no, but not on principle grounds but for practical reasons. >>A computer processing a billion positions per second would require about 10^38 >>years to solve the game. If you use a billion computers in perfect >>multi-processing you will still have to wait 10^29 years for the answer (and if >>you are not careful with the program it might simply produce ?42?). >> >>But there is still a major problem. You cannot store the tables on CDs or DVDs. >>As John Nunn explained to me we will need the matter from many millions of >>galaxies to store the information that is generated. So solving the game using >>the method of exhaustive analysis is theoretically possible, but one wonders >>what Greenpeace would say if we started dismantling galaxies in order to store >>chess positions. >> >> >>This is way too simplistic an estimate, unless the 50 move rule and 3-fold >>repetition rules are discarded. In reality there are nearly an infinite number >>of positions, because each position is unique to the path leading to it. Just >>because the same piece configuration has been reached in two or more positions, >>the positions are not guaranteed to be equal. How many different pathways can >>be spanned to reach those identical positions? And how do those pathways >>affect the 50 move and repetition rules? >> >>When you take a single position with the 32 pieces (or fewer) placed on the >>board in a legal configuration, and then try to enumerate all the pathways >>from the original position which can lead to these two identical positions, >>the number of pathways is absolutely enormous. And each "identical" position >>would be different because the moves played _after_ each of these positions >>would inherit different 50 move counters and different repetition lists. >> >>I think you could safely say that the game is nearly infinite... or at least >>so large that the difference between the real number and infinity is not >>easy to interpret. >> >> NOw.. Programmers... Yu think ya can 'get smart' with me; but.. >>You want to REFUTE Dr. Hyatt, DR. John Nunn & Frederick Friedel? >>STOP YOUR NONSENSE! > >I do not see where Dr. John nunn is involved there. > >Frederick Friedel did not claim that it is impossible but only that you need to >store many positions and I agree with it. > >I think that his number is too high and I proved less than 10^47 positions so >10^53-10^55 is only upper bound. > >I do not agree with Hyatt's words there >Hyatt said there about the practical problems pf solving chess: > >"because each position is unique to the path leading to it." > >This is relevant only for playing programs but it is totally irrelevant for >tablebases. > >Tablebases do not consider the path and there is no problem with them except the >50 move rule and the 50 move rule problem can be corrected by having special >tables of distance to conversion instead of distance to mate(program may miss >the shortest mate but it is not important because it is important only to find >mate when there is a mate and they will prefer conversion in 2 and mate in 43 >and not conversion in 3 and mate in 30). > >repetition is not important because engine that always play the best move will >get no repetition. > >Uri And... with 1 pV your Hard drive will spin til "Hell Freezes Over"! Give it up Uri!
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