On the three-person game baccara banque

Baccara banque is a three-person zero-sum game parameterized by $\theta\in(0,1)$. A study of the game by Downton and Lockwood claimed that the Nash equilibrium is of only academic interest. Their preferred alternative is what we call the independent cooperative equilibrium. But this solution exists only for certain $\theta$. A third solution, which we call the correlated cooperative equilibrium, always exists. Under a "with replacement" assumption as well as a simplifying assumption concerning the information available to one of the players, we derive each of the three solutions for all $\theta$.Comment: 22 pages, 4 figures, and a 54-page appendix; new figure and minor corrections in v

Teaching a University Course on the Mathematics of Gambling

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a course on the mathematics of gambling

On the Three-Person Game Baccara Banque

Baccara banque is a three-person zero-sum game parameterized by (thetain(0,1)). A study of the game by Downton and Lockwood claimed that the Nash equilibrium is of only academic interest. Their preferred alternative is what we call the independent cooperative equilibrium. However, this solution exists only for certain (theta). A third solution, which we call the correlated cooperative equilibrium, always exists. Under a \u27\u27with replacement\u27\u27 assumption as well as a simplifying assumption concerning the information available to one of the players, we derive each of the three solutions for all (theta)