Game Theory in Poker
https://math.mit.edu/~apost/courses/18.204_2018/Jingyu_Li_paper.pdf
Poker is a very well known game, and one that takes years to master. Just like any game that has a high ceiling for learning, poker does not only require the player to have luck in their favor, but also takes quite some bit of strategy. Although there are many types of strategies a player could use, for example folding and waiting for the right hand, the strategy incorporating game theory seems to be one that will achieve the most beneficial pay off. In this blog post, I would like the discuss the usage of exploitation in conjunction with game theory.
A common term thrown around in the poker scene is the bluff. A bluff could be defined as “pretending” or “faking” in order to deceive your opponent into thinking they know your hand by possibly over-bidding or under-bidding. Some could think that never bluffing (playing-it-safe) or over-bluffing could offer the maximum payoff, and these strategies would work if the other player always called or always folded, however, that is not the case. Through the process of analyzing the river (the cards shown) a player can minimize their loses by exploiting their opponents. From the example given in the article, (paraphrased) if player A has three of a kind is afraid of player B getting a flush, if player A knows that player B would only bet when they got a flush, they could simply fold when player A bets or bet more when player A doesn’t either minimizing loss or winning the pot. This scenario can be shown to exemplify the importance of game theory when there are pure strategies in play, but if we take another example, (also paraphrased) from the article, and say that player A is not as transparent and assume they have around 20% of a getting a flush but bets anyways, we can calculate the optimal strategy by setting the expected value of player B’s calling frequency equal to their folding frequency. With this we can calculate the frequency in which player A could bluff with player B being indifferent to calling or folding, finding the optimal bluffing strategy for player A. These cases from the article show both sides of pure strategy and mixed strategy optimal returns, illustrating the importance of game theory on poker games.