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I'm reading The Unfinished Game by Keith Devlin and it made me think about this:
Pacioli, the man who first wrote about the problem, considered a version in which the game is played until one player has won six rounds, but play is abandoned when the score is 5 to 2. He suggested that the solution is to divide the pot according to the current state of play, namely 5 to 2, but this reasoning is incorrect. The flaw in Pacioli's reasoning was demonstrated in 1539 by the next person to try to solve the problem, his countryman Gerolamo Cardano.
Cardano noted, correctly, that the appointment of the pot depended not on how many rounds each player had already won (as Pacioli thought) but on how many each player must still win in order to win the contest.
[pages 16 to 17]
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