A rule of thumb (not only) for gamblers

Andrzej S. Kozek

doi:10.1016/0304-4149(95)91546-D

A rule of thumb (not only) for gamblers

Andrzej S. Kozek^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let prize X in a game be a random variable with a cumulative distribution function F, E[X] ≠ 0, and Var(X) < ∞. In a Gambler's Ruin Problem we consider the probability P_F(A, B) of accumulating fortune A before losing the initial fortune B. Suppose our Gambler is to choose between different strategies with the same expected values and different variances. P_F(A, B) is known to depend in general on the whole cumulative distribution function F of X. In this paper we derive an approximation which implies the following rule called A Rule of Thumb (not only) for Gamblers: if E(X) < 0 then the strategy with the greater variance is superior, while in case E[X] > 0 the strategy with the smaller variance is more favorable to the Gambler. We include some examples of applications of The Rule. Moreover we derive a general solution in the Roulette case and use it to show good behavior of The Rule explicitly.

Original language	English
Pages (from-to)	169-181
Number of pages	13
Journal	Stochastic Processes and their Applications
Volume	55
Issue number	1
DOIs	https://doi.org/10.1016/0304-4149(95)91546-D
Publication status	Published - 1995

Keywords

Gambling
Martingale
Random walk
Ruin
Stopping times

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10.1016/0304-4149(95)91546-D

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