Game Theory in Poker
While poker is a complex game with many variables and strategies, one aspect can be modeled as a mixed-strategy game: bluffing. This article from the Kellogg School of Management at Northwestern University discusses optimal bluffing strategy through the lens of game theory. Say a player has 2 options: bluff or don’t bluff, in which the probability of bluffing is some constant p between 0 and 1. The player wants p at a probability such that he can bluff effectively – i.e., he can maintain a reputation for being truthful while also taking full advantage of that reputation. “If I bluffed all the time, obviously my bluffing would be ineffective. But it’s not effective to under-bluff, either, because then I’m not making enough use of my reputation as a non-bluffer. If you never bluff, or bluff very rarely, you can use this reputation to bluff more effectively and increase your long-term winnings.” This strategy is a way of manipulating the trust of opponents.
This is similar to what we discussed in class on the game theory of soccer penalty kicks – each strategy is most effective when mixed with other strategies. If a player always shoots left, the goalie will be able to block his shot; if he mixes up his shots in the right balance the goalie will have a hard time predicting his shot. As the article says, “…each move ideally [serves] to maximize unpredictability.”
Article: http://insight.kellogg.northwestern.edu/article/to-bluff-or-not-to-bluff