Author: Robert Hyatt
Date: 21:30:39 05/14/01
Go up one level in this thread
On May 15, 2001 at 00:13:13, Uri Blass wrote: > >If you have enough memory 2^3000 is not relevant because the relevant number is >the number of logical chess positions that is less than 10^50 and in this game >even smaller than chess. First, we argue that everything is O(1) (in theory). Now we are on what are logical positions and what are not (again in theory). But in reality, or in practice, we are not able to discern the difference between logical and illogical moves. Which is why we have to do a tree search in the first place. We will _never_ be able to exclude illogical moves from the tree, any more than we will ever be able to search to the end of the game and find out whether it is a forced win or a draw. > >If you try to construct the 32 piece tablebases in the game when it is illegal >to play moves that give the opponent a simple win then it is enough. How would you determine that? IE how can you determine a position is a "simple win" without searching to see that result? > >You can also ignore the 50 move rule for the case that you prove that chess is a >draw. > >In this case proving that there is no win in 6500 without the 50 move rule is >enough to prove that there is no mate in chess with the 50 move rule because >every game of 13000 plies is a draw by the 50 move rule. > >In this case the number of iterations is not a problem. >I believe that chess even without the 50 move rule is a draw. > >My idea to solve chess in 2050 or 2100 is the following idea: > >1)Generate all the leagl positions in the game when the sides have no right to >let the opponent a win without doubt(you should construct an evaluation to >define a win without doubt and it should be something that you can compute in a >relatively short time like 0.01 seconds on today's hardware > >In order to do it you generate all the possible positions in games of x plies >when x<13000(the number can be even slightly smaller than 13000 but I am lazy to >calculate or to find it) > >I do not know if the number of these positions is smaller or bigger than 10^25 >It may be 10^30 and may be 10^20. For a full game, W averages 38. Which means your W^13000 is simply beyond imagination. Even storing one gigabyte per atom in universe matter. > >It means that if you are optimistic you may get 10^20 possible numbers when >everyone of them is of 192 bits or even less bits if there is a simple way to >represent chess positions by numbers. I don't see any possible way to get 10^20 that would mean that there is a forced win inside 15 plies or so. I don't believe it. > >You can sort all these numbers so it will be easy to find the place of every >position in your array. > > >2)Calculate tablebases for all the positions that you found. >The tablebases will give you for every position if it is a win in n moves for >n<6500. >A win in n moves does not mean mate in chess but mate in the game similiar to >chess when it is illegal to play moves when the opponent gets a position that is >evaluated as a win without doubt. > >Uri
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