Author: Dann Corbit
Date: 15:19:24 12/10/02
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On December 10, 2002 at 18:02:46, Uri Blass wrote: >On December 10, 2002 at 17:55:51, Dann Corbit wrote: >>On December 10, 2002 at 17:51:40, Ingo Lindam wrote: >>>On December 10, 2002 at 17:30:47, Dann Corbit wrote: >>>>On December 10, 2002 at 13:42:36, Bernardo Wesler wrote: >>>>[snip] >>>>>THE ALGORITHM. A MATHEMATICAL FORMULA THAT , FOR EXAMPLE, ASSURE YOU THAT IF YOU >>>>>DO THE FIRST MOVE YOU ALWAYS WIN. >>>>>I MEAN TO THINK ABOUT DISCOVERING A CHESS ALGORITHM IS AN UTHOPY? >>>>Provably impossible on current hardware and software systems. >>>>Maybe in 100 years the game will be formally solved. Not in the near futre. >>>provably impossible on current hardware...? >>>are you sure? >>Absolutely sure. >> >>To solve chess you must store at least the square root of nodes of the solution >>tree. Considering the half move clock and castle rights, it easily exhausts any >>possibility of solution. > >I do not see a proof that there is no mate in 15. In order to form the proof, you will have to store the square root of the number of nodes in the tree. You might find one. But how will you prove it? >I am convinced in it I am sorry that I am not convincing. It seems completely obvious to me. >>>without assuming anything about the kind of solution? >> >>No assumptions are necessary. We pick an adversary in the tree. It's just like >>how you would prove a sort works in O(f(n)). > >No > >You do not always need a tree in order to solve problems. >I can prove that KR can beat K without a tree and without tablebases. However, until the tree is completely searched it remains possible that there is an alternative to the proposed solution. >In order to prove a mate it is enough if you divide the positions to classes and >prove that you always can go from one class to a better class when the final >class is mate positions. > >I believe that you cannot do it with the hardware of today for chess but I see >no proof. I don't want to go through the tedium of a formal proof, but I am absolutely certain that my analysis is correct.
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