Author: Uri Blass
Date: 12:48:50 10/01/01
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On October 01, 2001 at 15:14:07, Slater Wold wrote: >I am not a math expert, and I know a lot of you (Uri) out there are. So I ask >all you experts to solve this problem: > > *How many legal positions are their in chess?* My counting positions program found that 3.7010630121207222927827147741452119115968e46 is an upper bound when I considered only the squares of the pieces and did not consider side to move,en passant rule and rights to castle. The way that my program calculated the upper bound was simply by calculating the number of possible pseudo legal positions for every possible material structure and calculating the sum of these numbers. I did not use data structure that gives me the possibility to get all the digits after 3 and Dann corbit translated my program to do this job but the original program also could get the number 3.701...e46 I remember that retko v.tomic found a better upper bound by finding that part of the material structures that I used are not possible but his number was still bigger than 1e46. I have an idea how to calculate even a lower upper bound but my conclusion was that a program may need many days to calculate the better upper bound and I did not consider it as important(my original program needs few minutes of run time to find the upper bound that is posted and finding a better upper bound demands more design time and more run time). > >Also, please take into account that the king will always be present on the >board. both kings were present in the board in all my positions. There were other limitations Examples: positions when white has 9 queens and 3 rooks were not considered. positions with 32 pieces when the side have not the original pieces were not considered as legal. positions with 31 pieces when the number of promoted pawns was too big also were not considered. Uri
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