Author: Vincent Vega
Date: 20:44:39 08/31/00
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On August 31, 2000 at 16:41:22, Uri Blass wrote: >On August 31, 2000 at 15:54:16, Frederic Friedel wrote: > >>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. It is easy to see that the number of legal positions is less than 10^51 with just a few simple rules (1 king per side, at most 16 pieces per side, no pawns on 1st or 8th row). > >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. I think this estimate is probably close to the truth. En passant and castling won't add a significant number of positions because they require very specific board setups. > >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 Why do you think that the process of checking if a pseudo-legal position is legal can't be automated? I think one could devise an algorithm that would look at all the things a human could possibly check.
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