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Poker and Game Theory

Game theory optimal essentially focuses on the ability to craft an unexploitable strategy to ensure long term profitability in an unbelievably complex game such as No Limit Texas Hold’em. Another important concept that most poker players employ while deciding whether to call an opponent’s bet is the mathematical idea of Pot Odds.

A simple way to calculate pot odds involves calculating the bet made by the opponent with respect to the amount of money already in the pot. For example, if the pot contains 100 dollars after the opponent bet 20 dollars into the pot, then your pot odds are 5:1. This means that in order to achieve long term profitability, the hand that you hold and are calling with, needs to win once every five times. This is a simple technique that can be used in order to justify a call, when a player is on the fence or confused about his opponent’s range.

However, there are times when this technique can be ignored, if a player pays attention to game theory and attempts to understand the strategies employed by his opponent. We can take a simple example in poker wherein we are playing heads up against another player. This relates to the prisoner’s dilemma example studied in class where two prisoners had to decide what was the best move for them in order to maximize their payoff.

In our case, let’s assume that the player we are playing heads up against is extremely tight in his approach. He typically bets on the river with a strong hand, which he believes beats his opponents range. He almost never bluffs on the river when he has a busted flush or straight draw. Further, he is happy to check on the river even if he has a weak pair with little to no showdown value. So now that we understand the strategy that our opponent employs on the river, we can start making decisions based on this that may sometimes go against basic pot odds.

For example, if we have reached the river card with a weak pair on the river and we are in position. If our opponent decides to fire out a bet of 7 dollars into a 193 dollar pot, then our pot odds are about 29:1. This means that we only need to win with a marginal hand about once in every 29 hands! This seems like an obvious call as it should lead to long term profitability. However, if we inspect our opponent’s strategy then we know that he is not a very creative player and that this small bet is most certainly a value bet. Hence, although mathematically, we should be calling and paying off his value bet, through game theory, we can see that we have a greater pay off if we fold to that bet size 100% of the time.

This is a simple application of game theory in poker and it can be expanded to involve a plethora of scenarios pertaining to one or more players and their respective playing styles.


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September 2018