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n-point, win-by-k games

Published online by Cambridge University Press:  14 July 2016

Kyle Siegrist
Kyle Siegrist*
Affiliation:
University of Alabama in Huntsville
*
∗ Postal address: Department of Mathematics and Statistics, University of Alabama in Huntsville, Huntsville, AL 35899, USA.
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Abstract

Consider a sequence of Bernoulli trials between players A and B in which player A wins each trial with probability p∈ [0, 1]. For positive integers n and k with k ≦ n, an (n, k) contest is one in which the first player to win at least n trials and to be ahead of his opponent by at least k trials wins the contest. The (n, 1) contest is the Banach match problem and the (n, n) contest is the gambler's ruin problem. Many real contests (such as the World Series in baseball and the tennis game) have an (n, 1) or an (n, 2) format. The (n, k) contest is formulated in terms of the first-exit time of the graph of a random walk from a certain region of the state-time space. Explicit results are obtained for the probability that player A wins an (n, k) contest and the expected number of trials in an (n, k) contest. Comparisons of (n, k) contests are made in terms of the probability that the stronger player wins and the expected number of trials.

Keywords

BERNOULLI TRIALSBANACH MATCH PROBLEMGAMBLER'S RUINREPLICATIONS OF A PAIRED COMPARISON
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 807 - 814
Copyright
Copyright © Applied Probability Trust 1989 

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References

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