Author: Les Fernandez
Date: 22:52:23 01/17/02
Go up one level in this thread
On January 18, 2002 at 01:39:45, Chris Hull wrote: >On January 18, 2002 at 01:25:18, Les Fernandez wrote: > >>Every so often this subject gets brought up and I have a thought. Lets say that >>the current estimated number of unique positions is designated by N. When we >>say number of positions we need also to take into account some symmetries that >>exist. If symmetry is found in more then 1 position then we actually do not >>have N number of unique positions. With this is mind examine the following 4 >>diagrams which were generated by my Permutator application: >> >>[D]k1K4R/8/8/8/8/8/8/8 w - - >>acd 4; acn 91; acs 1; ce 32762; pv Rg8; id "-XTDa.1-"; >> >>[D]R4K1k/8/8/8/8/8/8/8 w - - >>acd 4; acn 91; acs 1; ce 32762; pv Rb8; id "-XTDb.1-"; >> >>[D]8/8/8/8/8/8/8/K1k4r b - - >>acd 4; acn 91; acs 1; ce 32762; pv Rg1; id "-XTDc.1-"; >> >>[D]8/8/8/8/8/8/8/r4k1K b - - >>acd 4; acn 91; acs 1; ce 32762; pv Rb1; id "-XTDd.1-"; >> >>These 4 diagrams, although symmetrically different, are in fact the identical >>position and contain the identical solution. This being true implies that when >>estimates for N are performed we need to apply the following 2 rules for >>arriving at a much closer estimate. #1 N/2 applies for positions that have any >>type of castling rights and #2 N/4 for positions that have no castling rights. >> >>Although N remains still fairly large we are much closer to the right number >>then how it has been estimated in the past. Whether dividing N by 2 or 4 will >>atleast cut the estimate by 1/2 and I suspect there are many more positions with >>no castling rights then with. Perhaps other symmetries exist that we have not >>found yet, and yes I do have some in mind <s>. >> >>Les > > >Actually there is 8-fold symmetry in this positions (can you find the other 4?). I think I can but do those other 4 symmetries exist for all chess positions including pawns?? <S>. I was not aware that the estimates took symmetries into account. Thanks for the info. BTW what is the current estimate out of curiosity? >Also, the estimated number of unique chess position already take into account >this reduction due to symmetry. > >Chris
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