Poker Theory

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Poker Game Theory

Poker and The Prisoner's Dilemma

by Jesse Knight
The Prisoners Dilemma

Poker and Economics

Prisoner's DillemaIf you are a poker player, you are already a game theorist, whether you realize it or not. Improving your understanding of game theory, and how it applies to logical reasoning, will help you improve your poker game as well. In game theory, a model of a competitive situation is called a game. The game which is most frequently used to introduce game theory is called “The Prisoner’s Dilemma.” The following is how the prisoner’s dilemma is modeled in its most basic form. It is important to note that in this game, and in game theory in general, each actor cares only about his own best interest and does not care about the benefits or consequences of his actions to anyone else.

Two partners in crime are arrested and detained by the police in separate interrogation rooms. The police only have enough evidence to prosecute each for a misdemeanor. They want felony charges, and need at least one of the criminals to testify against the other in order to get them. The police are willing to plea bargain with one or both of the criminals, and have no preference which one they do business with. Each prisoner (we will call them prisoner “A” and prisoner “B”) is visited by their lawyer who explains the situation to them. If prisoner “A” agrees to testify against prisoner “B,” he will be set free immediately, and Prisoner “B” will be sent to jail for ten years, but only if prisoner “B” refuses to testify. The same deal is also offered to prisoner “B.” If he testifies against prisoner “A,” he will be set free immediately, and prisoner “A” will be sent to jail for ten years, but only if “A” refuses to testify. If both testify against each other, they will split the sentence and each receives five years in jail. If both refuse to testify against the other, they will each be charged with misdemeanors and receive one year sentences. Since they are both in separate interrogation rooms, neither will know what the other has chosen to do until after they have each made their decision. Each cares only about minimizing his own jail time and does not care at all about the other. Assuming that each prisoner operates in a logical, self interested manner, what will each prisoner choose to do?

The way to approach this is to realize that each prisoner has two choices; they can each agree to testify or remain silent and accept the consequences. Each knows that if the other agrees to testify, he will receive the maximum ten year sentence if he chooses to remain silent. Because each cares only about minimizing his own jail time, each will have to make it a priority to take the necessary steps to prevent their own ten year sentence. That means each will agree to testify against the other. What is notable about this is that both of them testifying is in neither prisoner’s best interest. Had they both remained silent, they both could have walked after one year. The problem is, it would have required collusion between them, which was not possible because they had been separated at the police station. Even if they were able to communicate with each other, and made an agreement not to testify, it wouldn’t help. Such an agreement would only increase the incentive for each to go back on his word and testify, as each would gain immediate freedom if he did so. There is no way out for these prisoners, each must agree to testify, even though doing so will lead to a five year sentence for each rather than a one year sentence.

This game can be altered by changing the model in any number of ways. The rules could be changed giving one player an advantage over the other. The length of sentences could be changed, or new conditions could be imposed which could alter the incentives of one or both of the prisoners. Each change to the model may or may not change the outcome depending upon the incentives it creates.

Like the prisoner’s dilemma, a poker game is a near perfect model for applying the principles of game theory. This is because a poker game is a competitive event, with static rules, and all players theoretically doing their best to act in their own best interest. Each time a player is faced with a decision, they must do so within the confines of the rules, and base their decision upon the likely action of their opponents. The more that you know about the game, and about your opponents tendencies and thought processes, the more deeply strategic your actions become. The more adept you are with game theory, the more prepared you are to handle these strategic decisions. This necessarily leads to more positive outcomes over the long run. In a nutshell, you outplay your opponents, and become a better poker player, by adding an understanding of game theory to your analytical tool kit.

For more about Poker Game Theory, read Game Theory Modeling and Poker.

Principles of Poker

Other Articles by Jesse Knight:
Pot Limit Omaha - The Action Game
Omaha Poker Tips: Transitioning from Hold'em to Omaha
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Prisoner Dilema


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