POKER MATHEMATICS III
GAME THEORY AND APPLICATIONS
On this page you will find a second installment written by Thomas S. Ferguson. Thomas S. Ferguson is a Professor in the Department of Mathematics and the Department of Statistics at the University of California at Los Angeles. Once again this paper is by no means light reading and is not for the cranially challenged. It is however, from the parts i could understand, a very interesting read and i wish to pass it on to my valuable visitors! Enjoy!
GAME THEORY AND APPLICATIONS
On this page you will find a second installment written by Thomas S. Ferguson. Thomas S. Ferguson is a Professor in the Department of Mathematics and the Department of Statistics at the University of California at Los Angeles. Once again this paper is by no means light reading and is not for the cranially challenged. It is however, from the parts i could understand, a very interesting read and i wish to pass it on to my valuable visitors! Enjoy!
FREEROLL
HAVEN
HAVEN
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On the Borel and von Neumann Poker Models
Chris Ferguson, Bright Trading, Westwood, California
Thomas S. Ferguson, University of California, Los Angeles
1. Introduction and Summary.
The study of two-person zero-sum poker models with independent uniform
hands goes back to Borel and von Neumann. Borel discusses a form of poker
in Chapter 5, “Le jeu de poker” of his 1938 book, Applications aux Jeux des
Hazard. Von Neumann presents his analysis of a similar form of poker in the
seminal book on game theory — Theory of Games and Economic Behavior
by von Neumann and Morgenstern (1944). Section 19 of the book is
devoted to certain mathematical models of poker, with both discrete and
continuous hands, and with both simultaneous bets and alternating bets.
Extensions of the model of Borel may be found in the work of Bellman and
Blackwell (1949), Bellman (1952), and Karlin and Restrepo (1957).
In these models, Player I is dealt a random hand X ? [0, 1] where X has a
uniform distribution over the interval [0, 1]; the prior probability that X is in
any subinterval of [0, 1] is the length of the subinterval. Similarly, Player II
independently receives a random hand, Y , according to a uniform distribution
on [0, 1]. Throughout the play, both players know the value of their own
hand, but not that of the opponent. The structure of the betting in the two
models is the same. Each player antes one unit. Player I first decides
whether or not to bet. If Player I bets, then Player II decides whether to call
or to fold. If Player II folds, Player I wins one unit (the ante) from Player II. If
Player II calls, the hands are compared and the player with the higher hand
wins an amount B +1 from the
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Chris Ferguson, Bright Trading, Westwood, California
Thomas S. Ferguson, University of California, Los Angeles
1. Introduction and Summary.
The study of two-person zero-sum poker models with independent uniform
hands goes back to Borel and von Neumann. Borel discusses a form of poker
in Chapter 5, “Le jeu de poker” of his 1938 book, Applications aux Jeux des
Hazard. Von Neumann presents his analysis of a similar form of poker in the
seminal book on game theory — Theory of Games and Economic Behavior
by von Neumann and Morgenstern (1944). Section 19 of the book is
devoted to certain mathematical models of poker, with both discrete and
continuous hands, and with both simultaneous bets and alternating bets.
Extensions of the model of Borel may be found in the work of Bellman and
Blackwell (1949), Bellman (1952), and Karlin and Restrepo (1957).
In these models, Player I is dealt a random hand X ? [0, 1] where X has a
uniform distribution over the interval [0, 1]; the prior probability that X is in
any subinterval of [0, 1] is the length of the subinterval. Similarly, Player II
independently receives a random hand, Y , according to a uniform distribution
on [0, 1]. Throughout the play, both players know the value of their own
hand, but not that of the opponent. The structure of the betting in the two
models is the same. Each player antes one unit. Player I first decides
whether or not to bet. If Player I bets, then Player II decides whether to call
or to fold. If Player II folds, Player I wins one unit (the ante) from Player II. If
Player II calls, the hands are compared and the player with the higher hand
wins an amount B +1 from the
READ MORE
Back to Online Poker Strategy Articles
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