Author: Robert Hyatt
Date: 15:18:19 01/18/05
Go up one level in this thread
On January 18, 2005 at 11:54:39, Uri Blass wrote: >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 OK. My math was wrong. There is a difference in the number of positions that can be produced and the number of positions that have to be searched. But _whatever_ the number, it is finite because chess is finite. And if the size is finite, it can be searched in finite time, which means not "infinite"...
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