Game Theory and Poker (Part I)

See also Game Theory and Poker (Part II)

Game Theory in poker is primarily about two goals:

1. The study and understanding of the opposition.
2. The development of an efficient strategy to dominate the competition.

To be of maximum value, this study and understanding must be translated into effective action, and these actions must be the antithesis of everything a poker opponent thinks or does.

The difference between an antithesis and a correct response defines the utility of Game Theory in poker. An opponent makes an obvious bluff. You are certain that your hand will not even beat the bluff. A correct response in poker is to fold your hand when you know you are beat. The antithesis is to raise or re-raise and make your opponent fold his.

This is an example of a move. In an environment of ever-increasing odds and stakes such as a poker tournament, good hands just don't come along often enough for a player to make it on the strength of his hand alone. A winning player must make moves and the study and application of the principles of Game Theory can help him to know

1. When and where to make the move.
2. How likely the move is to succeed.

Expressed in the specific terminology of advanced theorists, poker can be defined as an asynchronous, non-cooperative, constant-sum (zero-sum), dynamic game of mixed strategies.

While the game is played in an atmosphere of common knowledge and no player possesses complete knowledge, some players are better able to process this common knowledge into a more complete knowledge than are their opponents. A player is most able to make the best-reply dynamic (sometimes referred to as the Cournot adjustment) and earn a cardinal payoff after using the process of backward induction to construct and deploy a dominant strategy.

In poker, beyond a certain set of rules, players do not cooperate with each other because each is trying to win at the expense of all others (zero-sum). Moreover, they will repeatedly change their strategies at different intervals and for different reasons (therefore, asynchronously).

While information about stakes, pot-size, board-cards and players' actions and reactions is available as common knowledge to all players at the table, no player has complete knowledge of such factors as the other players' cards or intentions.

The one characteristic common to most outstanding players is their ability to better process and better use — that is, they get more value from — the information that is commonly available to everyone else at the table.

Two of the most basic assumptions of Game Theory are that all players:

1. Have equal common knowledge.
2. Will act in a rational manner.

But in poker, while all players at any given table have access to the same common information, not all of them are smart enough to do something with it. Players who know more about odds and probabilities, and whose instincts and keen observation enable them to better process the common knowledge around them, will take far better advantage of this information and will have correspondingly higher positive expectations.

So while all the players at the table have access to the same common knowledge, some players are able to base their actions on knowledge that is more complete. That all players in all games will always act rationally is never a safe assumption in poker.

Equilibrium versus Evolution.
According to the "Nash Equilibrium" a game is said to be in a state of equilibrium when no player can earn more by a change in strategy. It has been argued that, using the process of backward induction, players will evolve their strategies to the point of equilibrium.

In poker, the astute players strategy will always be in a state of evolution so that his opponents, in order not to be dominated, will also be compelled to modify their strategies.

In a real game of poker there is constant evolution and therefore hardly ever a point of absolute equilibrium.