2 research outputs found
A game-theoretic analysis of baccara chemin de fer, II
In a previous paper, we considered several models of the parlor game baccara
chemin de fer, including Model B2 (a matrix game) and Model B3
(a matrix game), both of which depend on a positive-integer
parameter , the number of decks. The key to solving the game under Model B2
was what we called Foster's algorithm, which applies to additive
matrix games. Here "additive" means that the payoffs are additive in the
binary choices that comprise a player II pure strategy.
In the present paper, we consider analogous models of the casino game baccara
chemin de fer that take into account the percent commission on
Banker (player II) wins, where . Thus, the game now depends
not just on the discrete parameter but also on a continuous parameter
. Moreover, the game is no longer zero sum. To find all Nash equilibria
under Model B2, we generalize Foster's algorithm to additive
bimatrix games. We find that, with rare exceptions, the Nash equilibrium is
unique. We also obtain a Nash equilibrium under Model B3, based on Model B2
results, but here we are unable to prove uniqueness.Comment: 32 pages, 2 figure
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