Author: J. Wesley Cleveland
Date: 18:27:15 05/09/01
Go up one level in this thread
On May 09, 2001 at 14:27:03, Dann Corbit wrote: >On May 09, 2001 at 13:33:21, Uri Blass wrote: >[snip] >>>Suppose we find there is a forced mate in 150000 plies? And none sooner? >> >> >>In this case the loser can ask for a draw during the game because of the 50 move >>rule so the mate is not relevant for deciding that the position is drawn. >> >> >>>Can you prove there isn't? >> >>I can prove for a bigger constant that there is not. >>The shortest mate is of less than 10^100 plies because every game of 10^100 >>plies include repetitions and if there is a mate there is a shorter mate with no >>repetitions. > >It does not matter if the limit in plies is 5000 or 150000 because chess is >exponential. Neither of those will ever be computable. That's the whole reason >we bother to find out. > >Let's simplify. We ask this question: > >Given some depth in plies n of my search, what happens to the time when I search >n+1 plies? > >The only thing that can solve this problem is an infinitely fast computer. > >An internet of millions of petaflop computers will never solve it. > >If that is what O(1) means, then tell me what value that definition is. If we have enough memory to represent every possible position, we can use the endgame tablebase algorithm, which is O(n), where n is the maximum number of plies (and O is about 10^50).
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