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The random walk associated by the game of roulette

Published online by Cambridge University Press:  14 July 2016

James M. Hill  and
Chandra M. Gulati
James M. Hill*
Affiliation:
University of Wollongong
Chandra M. Gulati*
Affiliation:
University of Wollongong
*
∗Postal address: Department of Mathematics, University of Wollongong, Wollongong, N.S.W. 2500, Australia.
∗Postal address: Department of Mathematics, University of Wollongong, Wollongong, N.S.W. 2500, Australia.
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Abstract

The random walk arising in the game of roulette involves an absorbing barrier at the origin; at each step either a unit displacement to the left or a fixed multiple displacement to the right can occur with probabilities q and p respectively. Using generating functions and Lagrange's theorem for the expansion of a function as a power series explicit expressions are deduced for the probabilities of the player's capital at the nth step.

Keywords

RANDOM WALKROULETTEGENERATING FUNCTIONSLAGRANGE'S THEOREM
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 931 - 936
Copyright
Copyright © Applied Probability Trust 1981 

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References

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