Poker Theory

Probably the single most important book ever written on poker is ``The Theory of Poker'' by David Sklansky Written in 1987, it was the first book to correctly identify many of the underlying strategic principles of poker. These concepts are illustrated with examples from Texas Hold'em, Seven-Card-Stud, Five-Card-Draw, Seven-Card-Lowball, and Lowball-Draw, but they are equally applicable to all variations of poker.

While it is beyond the scope of this essay to present a complete overview of poker theory, a few examples of essential concepts will be given for context. First, after explaining the nature of mathematical expectation, Sklansky states the overriding principle of the game, which he calls ``The Fundamental Theorem of Poker''.

Sklansky's Fundamental Theorem of Poker:

Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents 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 lose.

The Fundamental Theorem is stated in common language, but has a precise mathematical interpretation. The expected value of each decision made during an actual game can be compared to the expectation of the correct decision, based on perfect information. Each player's long term expectation is determined precisely by the relative frequency and severity of these ``misplays''. On average, a player who makes fewer misplays than her opponents will be a winning player. The theorem may appear to state the obvious, but has many subtle implications to poker strategy, some of which are illustrated in the text.

Other fundamental concepts introduced in this book include ``odds'' (pot odds, effective odds, implied odds and reverse implied odds), the value of deception, the danger of the free card, the semi-bluff, and the importance of position. Each of these notions can be encorporated into a theoretical framework for understanding the game, and could prove to be substantial 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 player how to think correctly about each situation that may arise. This requires considerable effort on the part of the student, but once the principles are fully understood, they are much more reliable, and can be applied to any form of poker, regardless of the particular characteristics or game conditions.

Sklansky also includes a chapter on game theory, as it applies to bluffing and calling. This is done largely for the sake of completeness, and to show that he is aware of such views. He then goes on to explain some of the limitations of such a system, and justifies the more pragmatic approach to bluffing, described in a separate chapter.