Author: Uri Blass
Date: 08:54:39 01/18/05
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On January 18, 2005 at 11:25:26, Robert Hyatt wrote: >On January 18, 2005 at 10:36:20, chandler yergin wrote: > >>Only delusional people, disconnected from reality think it can. >> >>End of discussion! >> >>Anyone want to refute this? >> >>http://stuffo.howstuffworks.com/chess1.htm >> >>In this tree, there are 20 possible moves for white. There are 20 * 20 = 400 >>possible moves for black, depending on what white does. Then there are 400 * 20 >>= 8,000 for white. Then there are 8,000 * 20 = 160,000 for black, and so on. If >>you were to fully develop the entire tree for all possible chess moves, the >>total number of board positions is about 1,000,000,000,000,000,000,000,000, >>000,000,000,000,000,000,000,000,000,000,000,000,000,000, >>000,000,000,000,000,000,000,000,000,000,000,000,000,000, >>000,000,000,000, or 10^120, give or take a few. That's a very big number. For >>example, there have only been 10^26 nanoseconds since the Big Bang. There are >>thought to be only 10^75 atoms in the entire universe. When you consider that >>the Milky Way galaxy contains billions of suns, and there are billions of >>galaxies, you can see that that's a whole lot of atoms. > >First, your numbers are wrong. We can store a chess position in about 160 bits, >which means 2^160 positions total. Way less than 10^120. Second, nothing says >we can only store one piece of information per atom. Thirdly, alpha/beta >doesn't require that we even search _every_ possible position, only about >sqrt(P) need be actually searched, which is 2^80 position. I disagree with the last point. By that logic you can solve KRB vs KR with no tablebases by only searching sqrt(P) nodes when P is the number of KRP vs KR position. Can you do it? I do not say that searching all positions is needed but I see no proof that sqrt is enough. Uri Uri
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