As we saw in the last edition of +plus, mathematical techniques have been applied very successfully to analysing certain types of games. The two examples that we looked at were the simple subtraction game Nim, and the much more complex case of chess endgames. The next step is to see how computers, which are no more than automated maths machines, are being programmed to actually play chess themselves. It is theoretically possible to play chess perfectly, but neither humans nor machines will probably ever accomplish this. Computers have, however, already practically achieved perfection in draughts, and soon may be said to have ‘solved’ the game.
Although it may be inevitable that computers will become unbeatable in the near future, human Grandmasters are still holding their own against the machines today. How is it then that the human brain, with a mere fraction of a computerís number-crunching ability, is still able to put up a fair fight? The answer, as we will see, lies in the difference between human and artificial methods of reckoning, and a smart player knowing how to best exploit a computer’s weaknesses.
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This article has also been translated into Italian and reprinted by the mathematics department of the University of Milan.