Game theory and poker

Game theory, despite its name, isn’t about Scrabble or Monopoly, it’s actually a branch of mathematics dealing with decision-making. It has proven useful in fields as diverse as economics, political science, operations research, military science, and now poker – where the idea is to optimize a decision. Among others David Sklansky has highlighted the advantages of using Game theory in his work: “The Theory of Poker”, and has been applied and researched by poker professionals such as World Champion Chris “Jesus” Ferguson; well you would expect it from a man with a PhD in computer science, which focused on Artificial Intelligence and Game Theory. Have no fear though, you don’t to be a mathematical genius to understand or use game theory in your poker game

Here’s a hypothetical example: You are in a heads-up situation and opponent has called and you are both now waiting for the river card in Hold’em. You have never played against your opponent before, this is the first hand you’ve played, and you haven’t noticed any tells. You are drawing to an open-ended straight. Not let’s assume that your opponent knows with absolute certainty that you were on a draw for a straight. Although he cannot beat a straight, his hand is strong enough to beat you if you don’t make it.

Game theory can give you the correct frequency to bluff by; one which keep your opponent guessing. When you bluff properly – not too often and not too infrequently – it makes no difference how your opponent responds. Game theory allows you to control the outcome of your actions and optimize your results.

Bluffing using game theory: First, make sure the odds against your bluff are equal to the odds your opponent is getting from the pot. Suppose that by betting on the river, you create a situation in which your opponent will be getting 4-to-1 from the pot i.e. the pot contains $300, and by betting $100, your opponent stands to win $400 for his $100 bet. If you bluff whenever two predetermined cards come up in addition to the eight you need, you are bluffing at a frequency that precludes your opponent from taking advantage of your bluffing proclivities – regardless of what he chooses to do.

You can trigger your bluff vs. no-bluff decision by randomizing it with cards. You are looking for either a 7 or a queen to complete your straight in this case. Any one of those eight cards will do from the remaining 46 cards. Now suppose you tell yourself that you will come out bluffing if your last card is a red six instead of the desired 7 or queen. By giving yourself two bluffing cards as well as eight winning cards, in the 4-to-1 ratio of winning cards to your opponent’s pot odds, you’ve optimized your decision-making.

It’s sometimes difficult to make these kinds of calculations in the heat of the game. Bear in mind most players don’t try to calculate these situations. But you can work out common drawing situations in advance and the good thing is you don’t have to be really precise. As long as you realize that winning poker requires making mistakes at the polar extremes – neither habitually bluffing nor always checking, nor always calling your opponent’s wager or folding every time he bets – to avoid making more costly mistakes in the middle, you’re heading in the right direction.

You probably won’t use game theory too often while playing, mainly because it becomes less relevant because the more you play the better you become at reading your opponent – by putting him on a hand or picking up tells.