Author: Robert Hyatt
Date: 08:25:26 01/18/05
Go up one level in this thread
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. 2^80 is a big number, still. But it is a _finite_ number and given enough time, todays computers could search it. Or given enough time, faster computers will be developed that might search it in real-time. But it _can_ be searched when it is finite, and 2^80 is clearly finite by any math dictionary you care to use... So the game is finite and a finite tree can be searched in finite time, provably. This discussion is pointless... > > That number is dwarfed by the number of possible chess moves. > > Chess is a pretty intricate game! >No computer is ever going to calculate the entire tree. What a chess computer >tries to do is generate the board-position tree five or 10 or 20 moves into the >future. Assuming that there are about 20 possible moves for any board position, >a five-level tree contains 3,200,000 board positions. A 10-level tree contains >about 10,000,000,000,000 (10 trillion) positions. > > > Any "garbage" about the 50 move rule is smoke & mirrors, the number of >possible legal moves in the 1st 10 Moves of a game exceeds the number of >molecules in the observable Universe. > Poor math. There are about 35^20 possible different positions after the first ten moves by black and white. There are more atoms in the observable universe than that. And since alpha/beta would only need to search 35^10, it is even smaller... Please do some math and stop quoting made up numbers... The Canadian winter is clouding your ability to think... > > >A few people here been nippin on the juice or something... And some are just plain stupid...
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