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### ``Winning Poker Systems''

A generalized analytic method for comparing the value of different betting decisions was presented by Norman Zadeh in his PhD thesis [104] and expanded upon in his 1974 volume ``Winning Poker Systems'' [105].

In this important book, Zadeh performs a complete mathematical analysis of several games, including Five-Card-Draw, Lowball-Draw, Stud poker with five, six or seven cards, High-Low Seven-Card-Stud, and High-Low Five-Card-Draw. In each case, he goes beyond the purely mathematical computations, offering ``best'' strategies to apply in practice. These strategies are often presented in tables, and based on a Bayesian probability analysis given the minimal strength of the opponent's hand.

He also computes the quantitative value of betting position, and incorporates this into the proposed strategy for each game. This is indicative of the completeness of this analysis, as most studies omit this complicating factor, even though it is clearly a critical factor in the actual game.

With the lessons learned from each variation, Zadeh formulates a number of generalized rules, which should serve as reliable guidelines to all poker variations. Since these conclusions are not limited to small models of poker, but to the actual play of the game, they should be of some value to researchers in computer strategic game playing. An appendix outlining some of the computational methods used for the book is also highly valuable, although somewhat brief.

& Schaeffer
Thu Feb 12 14:00:05 MST 1998