Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T11:09:29.959Z Has data issue: false hasContentIssue false
  • English
  • Français

TWO-PERSON RED-AND-BLACK GAME WITH LOWER LIMIT

Published online by Cambridge University Press:  02 November 2010

May-Ru Chen
May-Ru Chen
Affiliation:
National Sun Yat-sen University, Kaohsiung 80424, Taiwan, Republic of China E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article we consider a two-person red-and-black game with lower limit. More precisely, assume each player holds an integral amount of chips. At each stage, each player can bet an integral amount between a fixed positive integer ℓ and his possession x if x ≥ ℓ; otherwise, he bets all of his own fortune. He might win his opponent's stakes with a probability that is a function of the ratio of his bet to the sum of both players' bets and is called a win probability function. The goal of each player is to maximize the probability of winning the entire fortune of his opponent by gambling repeatedly with suitably chosen stakes. We will give some suitable conditions on the win probability function such that it is a Nash equilibrium for the subfair player to play boldly and for the superfair player to play timidly.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 1 , January 2011 , pp. 119 - 133
Copyright
Copyright © Cambridge University Press 2011

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

1.Chen, M.-R. (2009). Proportional three-person red-and-black games. Probability in the Engineering and Informational Sciences 23: 37–50.CrossRefGoogle Scholar
2.Chen, M.-R. & Hsiau, S.-R. (2006). Two-person red-and-black games with bet-dependent win probability functions. Journal of Applied Probability 43: 905–915.CrossRefGoogle Scholar
3.Chen, M.-R. & Hsiau, S.-R. (2010). Two new models of two-person red-and-black game. Journal of Applied Probability 47: 97–108.CrossRefGoogle Scholar
4.Dubins, L. E. & Savage, L. J. (1976). Inequalities for stochastic processes: How to gamble if you must, 2nd ed.New York: Dover.Google Scholar
5.Maitra, A. P. & Sudderth, W. D. (1996). Discrete gambling and stochastic games. New York: Springer-Verlag.CrossRefGoogle Scholar
6.Pontiggia, L. (2005). Two-person red-and-black with bet-dependent win probability. Advances in Applied Probability 37: 75–89.CrossRefGoogle Scholar
7.Pontiggia, L. (2007). Nonconstant sum red-and-black games with bet-dependent win probability function. Journal of Applied Probability 44: 547–553.CrossRefGoogle Scholar
8.Ross, S. M. (1974). Dynamic programming and gambling models. Advances in Applied Probability 6: 598–606.CrossRefGoogle Scholar
9.Secchi, P. (1997). Two-person red-and-black stochastic games. Journal of Applied Probability 34: 107–126.CrossRefGoogle Scholar