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By Mike James (Auth.)

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Even the wildest imagination will find it difficult to cope with more than one universe in which to repeat the event! There are many ways round this difficulty but the easiest is to abandon the direct interpretation of probability as an indication of how often something would occur. Of course, once you do this you can only use probability as a vague measure of how certain you are of something and this cannot be verified in the same way as the proportion of times that an event happens; it is in this sense subjective.

It is possible to play chess using a heuristic and completely ignore the importance of any moves your opponent may make but you are unlikely to w i n ! It is clear that to extend the heuristic method to competitive games - the simplest of which are two-person games we have to find a way of taking into account not only the advantage resulting from the next move but how our opponent's next move wil affect it. A simple two-person game: noughts and crosses It is difficult to find problems that will serve as an adequate example.

Evaluation After playing a few games against this simple program, you might be surprised at how good it is! This is rather more a reflection of how simple a game noughts and crosses is rather than how powerful the method we are using is. However, there is at least one game that the program loses and it is only by studying examples where the program fails that it can be improved. If 'X' plays 1,1 the program responds with 2,2. If then 'X' plays the rather odd move 3,3 the program responds with 3,1 resulting in the following position and all is lost because X then plays 1,3.

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