problem of points

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This problem was the subject of the correspondence between Fermat and Pascal that underpins the modern treatment of probability. The problem is as follows.

Two gamblers are playing a series of fair games. The winner is to be the gambler who first wins n games. However, the sequence of games is interrupted at the point where player A requires a further a wins, and player B requires a further b wins. The question is how the stake should be fairly divided.

Fermat and Pascal attacked the problem in different ways, but agreed that the answer is that the proportion of the stake that player A should be awarded is

Subjects: Probability and Statistics.

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