Author: Bob Durrett
Date: 07:56:06 11/03/02
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On November 03, 2002 at 05:20:31, Omid David wrote: > >The game of chess can never ever be solved: > >There are about 10^128 potential chess positions. If we start searching with a >supercomputer with the speed of 100 million nodes per second (10^8 NPS), it will >take about 10^113 years to process all possible positions! What is the speed you >can imagine in the next 100 years? Let's say 100 million million nodes per >second (10^14 NPS); then it will take "only" 10^107 years to solve the game of >chess! > >And even if we process all 10^128 possible positions, we will have one little >problem: where to store the data?! Even if we manage to store a position in an >atom, there won't be enough atoms for that, since there are "only" 10^80 atoms >in the entire universe...! Maybe a more indirect method of proof is needed than the brute force search of all possible lines. For example, if it could be proven [somehow] that a certain first move for white is the best possible move in the initial position, then the next step would be to find the best response for Black. If, then, it could be proven that the chosen move is the best possible response, then the best second move for white should be found. Then if it could be proven that that second move for White is the best possible move for White in that position, the next step would be to find the best possible second move for black and to prove that it is the best possible move in that position. This process could be continued until the game concludes. IF the game concludes, it would be a simple matter to determine the outcome. Suppose white won in that line. Then one might conclude that "with best play on both sides, White wins." If there are two or more equally good moves in a position, then a tree might result, but it would be a "small" tree, presumably. But what if the sequence of best possible moves goes on forever? Well, forever is a long time. What to do? Just say "we quit"? Suppose it could NOT be proven, beyond any possible doubt, that a particular move is the best move in one of the positions occurring in the above process. In that case, the process could be continued until a conclusion is reached. Then the questionable move might be changed to another move. Then the process would be repeated. The results would be compared and the obvious conclusion reached. Of course, if it were impossible to prove that any move was the best possible move in ANY position, then the entire method of proof would have to be discarded. Bob D.
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