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On de Movire's solutions of the problem of duration of play 1708–1718

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Summary

I attempt to solve the enigma of how de Moivre derived his recursion formulae and the formulae for the probability of a duration of exactly n games. I believe that he obtained the latter probability by differencing Nicholas Bernoulli's formula for the probability of ruin and that he obtained the recursion formulae by a simple algebraic method and induction.

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  1. Furesøvej 87 A, DK-2830, Virum, Denmark

    A. Hald

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  1. A. Hald
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Communicated by O. Pedersen

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Hald, A. On de Movire's solutions of the problem of duration of play 1708–1718. Arch. Hist. Exact Sci. 38, 109–134 (1988). https://doi.org/10.1007/BF00348454

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