Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T11:20:04.591Z Has data issue: false hasContentIssue false
  • English
  • Français

Fair gambler’s ruin stochastically maximizes playing time

Part of: Stochastic processes

Published online by Cambridge University Press:  10 March 2022

Erol A. Peköz  and
Sheldon M. Ross
Erol A. Peköz*
Affiliation:
Boston University
Sheldon M. Ross*
Affiliation:
University of Southern California
*
*Postal address: Questrom School of Business, 595 Commonwealth Avenue, Boston, MA 02215. Email address: pekoz@bu.edu
**Postal address: Daniel J. Epstein Department of Industrial and Systems Engineering, 3650 McClintock Avenue, Los Angeles, CA 90089. Email address: smross@usc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

For the gambler’s ruin problem with two players starting with the same amount of money, we show the playing time is stochastically maximized when the games are fair.

Keywords

Stochastic inequalityplaying timegambler’s ruin

MSC classification

Primary: 60G17: Sample path properties
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 2 , June 2022 , pp. 656 - 659
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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

Coad, A., Frankish, J., Roberts, R. G. and Storey, D. J. (2013). Growth paths and survival chances: an application of Gambler’s Ruin theory. J. Business Venturing 28, 615–632.CrossRefGoogle Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. I. John Wiley, New York.Google Scholar
Harik, G., Cantu-Paz, E., Goldberg, D. and Miller, B. (1999). The gambler’s ruin problem, genetic algorithms, and the sizing of populations. Evolutionary Comput. 7, 231–253.CrossRefGoogle ScholarPubMed
Huygens, C. (1657). De Ratiociniis in Ludo Aleae. Elsevirii, Leiden.Google Scholar
Karni, E. (1977). The probability distribution of the duration of the game in the classical ruin problem. J. Appl. Prob. 14, 416–420.CrossRefGoogle Scholar
Katriel, G. (2014). Gambler’s ruin: the duration of play. Stoch. Models 30, 251–271.CrossRefGoogle Scholar
De Moivre, A. (1711). De mensura sortis, seu, de probabilitate eventuum in ludis a casu fortuito pendentibus. Phil. Trans. 27, 213–264.Google Scholar
De Moivre, A. (1718). The Doctrine of Chances: or, a Method of Calculating the Probability of Events in Play. Pearson, London.Google Scholar
Ross, S. M. (2019). Introduction to Probability Models, 12th edn. Academic Press, Amsterdam.Google Scholar
Song, S. and Song, J. (2013). A note on the history of the gambler’s ruin problem. Commun. Statist. Applications Meth. 20, 157–168.CrossRefGoogle Scholar
Zhang, Z. and Ross, S. (2021). Finding the best dueler. Preprint.Google Scholar