Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T22:03:04.383Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, L. R. and Fontenot, R. A. (1980) On the gain ratio as a criterion for betting in casino games. J. R. Statist. Soc. A 143, 33–40.Google Scholar
Downton, F. and Holder, R. L. (1972) Banker's games and the Gaming Act 1968. J. R. Statist. Soc. A 135, 336–364.Google Scholar
Epstein, R. A. (1967) The Theory of Gambling and Statistical Logic. Academic Press, New York.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications , Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Whittaker, E. T. and Watson, G. N. (1963) A Course of Modern Analysis. Cambridge University Press.Google Scholar