Poker Theory''The Theory of Poker'' by David Sklansky remains the single most important book ever written on poker. Completed in 1987, it was the first book to correctly recognized many of the underlying strategic principles of poker. These concepts are illustrated with examples from Seven-Card-Stud, Texas Hold'em, Five-Card-Draw, Seven-Card-Lowball, and Lowball-Draw, but they are as much applicable to all variants of poker.
Sklansky's Basic Theorem of Poker:
Every time you play a hand in a different manner from the way you would have played it if you could check all your opponents' cards, they are the gainers; and every time you play your hand the similar way you would have played it if you could see all their cards, then they lose. In contrast, every time the players play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you surely lose.
This basic theorem is explained in common language, but has an exact mathematical interpretation. The expected value of every decision made during an actual game can be compared to the expectation of the correct decision, based on perfect information. Every player's long term expectation is calculated precisely by the relative frequency and severity of these ``misplays''. On an average, a player who makes fewer misplays than her opponents will be a winning player. The theorem may seem to state the obvious, but has many subtle implications to poker strategy, some of which are illustrated in the text.
Other more fundamental concepts discussed in this book include the value of deception, ``odds'' (=pot odds, implied odds and reverse implied odds effective odds,), the danger of the free card, the semi-bluff, and the importance of position. Each of these notions can be included into a theoretical framework for understanding the game, and could prove to be major strengths for a computer algorithm.
Issues of practical importance are also addressed in the book, such as reading hands, understanding the psychology of poker, and evaluating the profitability of a game. While these topics may be of a less theoretical nature, they are among the many abilities required for play at the highest levels. It is unclear to what degree a computer algorithm can excel at these ``human'' aspects of the game, or whether it is even necessary to attain world class strength.
Note that this classic book does not attempt to give a step-by-step procedure for playing each game, but instead teaches the person how to think in the right manner about each situation that may arise. This requires a lot of effort on the part of the student, but once the principles are fully understood, they are much more dependable, and can be applied to any form of poker, regardless of the particular characteristics or game conditions.