Game Theory In Poker
As a person that loves games, I was struggling to understand game theory. So I decided to relate the concept to a game that I am somewhat familiar with: Poker. More specifically, Jingyu Li explores how game theory relates to playing heads-up no limit Texas hold’em in Exploitability and Game Theory Optimal Play in Poker. Link: https://math.mit.edu/~apost/courses/18.204_2018/Jingyu_Li_paper.pdf
For those unfamiliar with Texas holdem poker, players start off with two cards which only they can see. After this, there is a stage of betting where a player can do one of three things: check, fold, or raise. These actions are based on the two cards that were dealt. If you don’t like your hand, you can fold, meaning you won’t take part in betting anymore. If you would like to continue, you can check, or a wager on your cards. If you want to raise tension, you can raise, or increase the cost of the bet. After call bets have been matched, a call occurs, where everyone gets to see the next dealt card. This continues, with there being four stages of betting: pre-flop, flop, turn, and river. The pre-flop refers to when everyone is dealt with two cards that only they can see. Flop references the three cards that are dealt face up, turn is the fourth card, and river is the fifth card. The overall goal for the game is to form the best five-card hand using your two cards and three of the community cards (cards dealt face-up). A player wins by having the best ranking poker hand among the players that decided to not fold, or by having everyone else fold before the river.
The paper recognizes that you can have two different scenarios: one in which you know the opponents play style and one in which you don’t. When you don’t know the opponents play style, the best defense strategy is to play close to the game theory optimal play. Which as discussed in class has to do with playing the best response based on what you think the other player will choose. On the other hand, if you have past information about the opponents play style, then you should have more of an exploitative play. When it comes to betting, you have to be strategic in that you don’t want your bet to be proportional to how good of a hand you have and you don’t want to only bet when you have a good hand. Why? Because unlike the game theory we discussed in class, poker is about beating the odds over time. For instance, in class we discussed prisoner’s dilemma where you have to make one choice on whether to confess, or not. After making this decision, there are no more decisions to be made. However, in poker you have to choose from the four actions for each of the four stages in the game. Thus, there are more factors to take into consideration for poker. For that reason, the game theory optimal play is not always guaranteed to be the most profitable play, however, it will be the safest strategy to play.