[sjb]

Good show. A lot of weird "game theory" claims do show up. In support of the section "Fallacious Concept 4: An Equlibrium Strategy is a Good Strategy", let me point out that, in all forms of poker I know of (certainly HE, Omaha, and Stud, and regardless of limit structure or high/low splits) and in the absence of a rake, the EV of any Nash equilibrium strategy is exactly zero. With a rake, the EV is negative and equal to the total amount of the rake, divided by the number of players.

In any given hand, the EV would vary by position. In HE the highest EV would be on the button and decreases in earlier positions. But since each player eventually sits in each seat an equal number of times, those all average out.

The EV of the equilibrium strategy is the expectation when everyone else is playing their corresponding strategy in the equilibrium. If all players are playing optimally, then a non-zero EV comes from asymmetries in the game. In poker, that asymmetry is position. But since the button rotates, as you go from a single hand to repeated hands, that asymmetry is destroyed and the result is that everyone breaks even.

Maybe the most problematic thing about using game theory in poker is that game theory doesn't tell you how to win. Because game theory assumes all players are "rational" (that is, they play so as to maximize utility - in poker that means they play to make the most money possible) and "intelligent" (that is, they're at least as capable at analyzing the game as we are), game theory doesn't tell you how to win. It tells you how to not lose.

The EV of an equilibrium strategy represents the worst you could do. The best you could do depends on exactly how your opponents deviate from their equilibrium strategies. Game theory would still tell you how to analyze that game, but the opponent's strategy becomes part of the game and it has to be re-analyzed for each new set of opponents.

So, while game theory can make interesting contributions to poker theory, it's hardly the last word.