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

May Ru Chen, Shoou Ren Hsiau

Research output: Contribution to journalArticle

3 Citations (Scopus)

### 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 97-108 12 Journal of Applied Probability 47 1 https://doi.org/10.1239/jap/1269610819 Published - 2010 Jan 1

### Fingerprint

Probability function
Person
Game
Chip
Nash Equilibrium
Model
Maximise
Entire
Dependent
Integral

### All Science Journal Classification (ASJC) codes

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

### Cite this

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title = "Two new models for the two-person red-and-black game",
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.",
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In: Journal of Applied Probability, Vol. 47, No. 1, 01.01.2010, p. 97-108.

Research output: Contribution to journalArticle

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

AU - Chen, May Ru

AU - Hsiau, Shoou Ren

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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.

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