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More on n-point, win-by-k games

  • John Haigh (a1)

Abstract

When Siegrist (1989) derived an expression for the probability that player A wins a game that consists of a sequence of Bernoulli trials, the winner being the first player to win n trials and have a lead of at least k, he noted the desirability of giving a direct probabilistic argument. Here we present such an argument, and extend the domain of applicability of the results beyond Bernoulli trials, including cases (such as the tie-break in lawn tennis) where the probability of winning each trial cannot reasonably be taken as constant, and to where there is Markov dependence between successive trials.

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Postal address: School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK.

References

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Feller, W. (1969) An Introduction to Probability Theory and its Applications. Vol. 1, 3rd edn. Wiley, New York.
Mohan, C. (1955) The gambler's ruin problem with correlation. Biometrika 42, 486–193.
Proudfoot, A. D. and Lampard, D. G. (1972) A random walk problem with correlation. J Appl. Prob. 9, 436440.
Renshaw, E. and Henderson, R. (1981) The correlated random walk. J. Appl. Prob. 18, 403414.
Siegrist, K. (1989) n-point, win-by-k-games. J. Appl. Prob. 26, 807814.

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