Abstract
This chapter is concerned with finding the probability that, in an independent sequence of identical wagers, the gambler loses L or more units (that is, he is ruined) before he wins W or more units. In Section 7.1, we treat the case of even-money payoffs by deriving an explicit formula. In Section 7.2, we consider more-general integer-valued payoffs. Formulas are available in some special cases, but in general a computational algorithm is needed. Finally, Section 7.3 allows arbitrary payoffs, and here we resort to establishing upper and lower bounds on the probability of interest.
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© 2010 Springer-Verlag Berlin Heidelberg
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Ethier, S.N. (2010). Gambler’s Ruin. In: The Doctrine of Chances. Probability and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78783-9_7
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DOI: https://doi.org/10.1007/978-3-540-78783-9_7
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78782-2
Online ISBN: 978-3-540-78783-9
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