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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
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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
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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