Fundamental Theorem of Poker

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Poker professional and author David Sklansky gets full credit for expressing the Fundamental Theorem of Poker in lay terms. It describes a way of thinking and approaching the game, as follows:

“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.”

Obviously, it is not possible to actually see the opponents’ cards, so the next best thing is to be able to read opponents so well that it is possible to put them on a narrow range of hands and play accordingly. In this regard, the players who have the most information have the advantage and will win the most.

Applying the Theorem

All of the players at a Poker table begin with the same disadvantage—partial information. They must make decisions about calling, raising, and folding for each hand pre-flop, with little to go by other than the actions of the players ahead of them. How is it possible to know with any certainty what choice will satisfy the conditions of the theorem—the play that would not be different if all cards were visible?

Fortunately, there is an answer. Decisions about how to play hands can be evaluated based upon a mathematical concept known as “expected value” (EV). Given any situation, EV expresses the average payoff of a decision when such a decision is replicated many times. The best decision will always be the one that provides the highest EV.

At first glance, it may seem impossible to know with any certainty what course of action will produce the highest EV, but fortunately one’s opponents will be in the same boat. The players who come closest to getting it right will be the most successful, and those who miss the mark widely will end up on the losing side of the equation the majority of the time.

That explains why one of the most important goals in Poker is to get opponents to misread hands and make mistakes. Strategies such as range balancing can induce opponents to make poor decisions based on incorrect evaluations of EV. Even if a Player has difficulty determining the EV for decision, he or she gains the advantage if the opponents are doing an even worse job of it.

An Exception to the Theorem

It is said that exceptions prove rules, and there is one aspect of Poker play that can’t be covered by the Fundamental Theorem. When playing heads up against a single opponent, the theorem always applies. But for multi-way pots, the decision-making process is slightly different and the theorem sometimes fails.

An instance of this is when two or more opponents each make a poor decision. For example, a player with a strong hand bets after the flop and two opponents call with weaker hands, chasing the draw, even though folding was warranted for one or both of them. This “mistake” actually improves the opponents’ odds of catching a lucky card and winning. This case is known as “implicit collusion”—a collective decision that works against the player. The opponents’ “two wrongs” end up making a “right.”

Like all aspects of Poker, proper application of the Fundamental Theorem requires knowledge, skill, and experience. It does, however, provide an excellent way of thinking about the game in countless varieties of circumstances.

Published on: 30/12/2010

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