Betfair Official Blog

The prisoner's dilemma

The prisoner's dilemma is a problem that is frequently discussed as an example of game theory. It is a simple problem that has some key consequences on poker. Game theory is extremely useful for analysing certain aspects of poker, and the prisoner's dilemma is a great example of a problem which can demonstrate why the principles of game theory are so useful to poker strategy.

The prisoner's dilemma is structured like this:

You have been arrested along with a friend for a crime. You are offered a deal by the police. If you decide to snitch on your friend, and they don't snitch on you, you will get out of jail, but they will get ten years in prison. If both of you snitch on each other, then you both get five years in jail. If you stay silent, but your friend snitches on you, you get ten years in prison. If you both stay silent then you will each get just six months in prison.

The common consensus about this problem is that in the single case, you are always better of snitching, as by doing this you avoid the prospect of getting ten years in prison (the worst case scenario), while also possibly giving yourself a shot at getting out of jail (the best scenario). So in the single case, you are usually better off snitching.

However, complications with this problem arise when the possibility of it being repeated numerous times are thought about. In these situations, a long term strategy of staying silent can be argued to become optimal, as it ensures that on average you both do the shortest amount of time possible each time you are arrested (which is no doubt why career criminals have such a low opinion of snitches).

Here the comparison with poker becomes important. What is optimal in one hand is not necessarily optimal when considered in the context of many others. This can have a range of manifestations, ranging from not calling a bet with the second nuts because you know a specific player is so tight that they can have no other hand, to avoiding low edge confrontations early in tournaments in the hope of surviving.

What looks to be the obvious path in one hand, may actually be a key mistake when considered in the context of the history or future of the game. By trying to analyse each situation on both the past and future you will be able to make much better decisions, and you can boost your profits as quickly as the prisoners can cut their time.

• Poker
• Marcus Bateman