Author: Dann Corbit
Date: 12:13:24 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? The problem is that you must have optimal ordering. This is difficult to achieve. But it is theoretically possible. If it is nearly optimal, then you can still do quite well. There is also a constant of proportionality which is greater than or equal to one. This may be important in practice. >I do not say that searching all positions is needed but I see no proof that sqrt >is enough. You realize that only one position must be solved to solve chess (the opening one). We would therefore make the analogy to solving a single KRBkr position.
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