### Abstract

In a two-person red-and-black game, each player holds an integral amount of chips. At each stage of the game, each player can bet any integral amount in his possession, winning the chips of his opponent with a probability which is a function of the ratio of his bet to the sum of both players’ bets and is called a win probability function. Both players seek to maximize the probability of winning the entire fortune of his opponent. In this paper we propose two new models. In the first model, at each stage, there is a positive probability that two players exchange their bets. In the second model, the win probability functions are stage dependent. In both models, we obtain suitable conditions on the win probability functions such that it is a Nash equilibrium for the subfair player to play boldly and for the superfair player to play timidly.

Original language | English |
---|---|

Pages (from-to) | 97-108 |

Number of pages | 12 |

Journal | Journal of Applied Probability |

Volume | 47 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2010 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Applied Probability*,

*47*(1), 97-108. https://doi.org/10.1239/jap/1269610819

}

*Journal of Applied Probability*, vol. 47, no. 1, pp. 97-108. https://doi.org/10.1239/jap/1269610819

**Two new models for the two-person red-and-black game.** / Chen, May Ru; Hsiau, Shoou Ren.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Two new models for the two-person red-and-black game

AU - Chen, May Ru

AU - Hsiau, Shoou Ren

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In a two-person red-and-black game, each player holds an integral amount of chips. At each stage of the game, each player can bet any integral amount in his possession, winning the chips of his opponent with a probability which is a function of the ratio of his bet to the sum of both players’ bets and is called a win probability function. Both players seek to maximize the probability of winning the entire fortune of his opponent. In this paper we propose two new models. In the first model, at each stage, there is a positive probability that two players exchange their bets. In the second model, the win probability functions are stage dependent. In both models, we obtain suitable conditions on the win probability functions such that it is a Nash equilibrium for the subfair player to play boldly and for the superfair player to play timidly.

AB - In a two-person red-and-black game, each player holds an integral amount of chips. At each stage of the game, each player can bet any integral amount in his possession, winning the chips of his opponent with a probability which is a function of the ratio of his bet to the sum of both players’ bets and is called a win probability function. Both players seek to maximize the probability of winning the entire fortune of his opponent. In this paper we propose two new models. In the first model, at each stage, there is a positive probability that two players exchange their bets. In the second model, the win probability functions are stage dependent. In both models, we obtain suitable conditions on the win probability functions such that it is a Nash equilibrium for the subfair player to play boldly and for the superfair player to play timidly.

UR - http://www.scopus.com/inward/record.url?scp=79957477461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957477461&partnerID=8YFLogxK

U2 - 10.1239/jap/1269610819

DO - 10.1239/jap/1269610819

M3 - Article

AN - SCOPUS:79957477461

VL - 47

SP - 97

EP - 108

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 1

ER -