Author: Dann Corbit
Date: 15:08:55 02/02/99
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Actually, you could say that chess is already reduced to a mathematical equation. Unfortunately, the algorithm that implements that equation is: ouch = O(exp(n)) Which is not good for solving things. Even with Alpha/Beta and all the other clever searching techniques applied, the algorithm is still: ouch = O(exp(n)) but with a smaller multiplier. In other words, the difficulty is not in reducing the problem to a mathematical model. The problem is in finding an algorithm which is faster than exponential. If you could discover a linear equation to solve chess positions, you could find a solution for practically any position almost instantly. Even a quadratic equation in the number of plies would be solvable since the longest game is about 6000 moves that would give k*144,000,000, which would take a few seconds or perhaps minutes to solve, depending on k and how advanced the hardware you are using is. The Hakmem page lists a simple way to solve the game of chess. Ennumerate all of the board positions. Any position generator that produces legal moves could do that. Unfortunately, there are more than 10^40 of them. So it would take longer than it hurts even to imagine.
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