posted March 23, 2009 at 18:15 EST in Poker School Tips & Strategies
Game Theory and Poker Part 1 - Introduction
by BetUS Staff
Game Theory Part 1: Introduction
This is the first part in a series of articles dedicated to the complicated topic of game theory and its uses in poker. Game theory only becomes relevant at advanced levels of play against excellent opposition. However, any player with an understanding of game theory is at a huge advantage: they will be able to answer questions others can’t and their development as players will really accelerate.
What is game theory?
Game theory is a branch of mathematics developed by John von Neumann in the 1940s. It deals with strategic situations where the actions of one “player” affect the decisions of the other players. Game theory is important in many fields, especially economics, military strategy and the social sciences. Of course, the field we’re all interested in is poker theory, and game theory has a lot to say here as well.
Equilibria – optimal strategies
The goal of most work in game theory is the development of “equilibria.” An equilibrium is sort of like a perfect strategy. It’s perfect in the sense that even if you revealed your poker strategy, your opponents would still not be able to profit at your expense. This may seem crazy or impossible; that’s exactly why game theory is so interesting and useful. In poker, equilibria are called optimal strategies. An optimal strategy cannot be exploited no matter what our opponent knows or does. We’ll expand greatly on this in the later articles in this series.
What can game theory do for me?
Game theory is used in poker, to even things up against players that are better hand readers than you are. Have you ever played with someone who just seems to have your number? They always seem to call you down when you’re bluffing and they never pay you off when you have a big hand. It’s so frustrating. Game theory will teach you techniques to limit the ability of others to outplay you. You will take their hand reading and decision making strength away from them. Game theory cannot teach you how to extract extra profit from weaker players, it cannot teach you to make money against players that are better than you. All it can do is reduce and/or eliminate the advantage that those better players have.
How does it all work?
This is obviously a big, complicated question. In poker, there are really two steps to using game theory. The first, and by far the most difficult is the creation of a mathematically balanced strategy. Then, you must implement this strategy by using randomization. I realize this is all too theoretical, but we’ll get to the practical stuff soon. For now, here’s an example of the process taken from a game that’s simpler than poker: rock, paper, scissors.
Rock, Paper, Scissors
You’re playing rock, paper, scissors, but unfortunately, you’re playing against someone with amazing intuition about what you’re going to choose. Because he recognizes that he’s got an edge, he agrees to give you 2:1 odds. When he wins you pay him $10, and when you win he pays you $20.
The first thing to do is construct a mathematically balanced strategy. Here’s an example of an unbalanced strategy: always picking rock. Someone playing “paper” at a high frequency can exploit that strategy. It should be fairly obvious that the best strategy is to play each option 1/3 of the time. With this strategy, no matter what strategy our opponent plays, we will win 1/3 of time, lose 1/3 of the time and tie 1/3 of the time. Normally, this would mean that we break even, but remember that our opponent has offered you 2:1 odds. If we can successfully implement our balanced strategy, we will make $10 every three rounds (win $20, lose $10, tie) on average.
But, you might ask, how can we get around the fact that he knows what we’re going to do before we do it? That’s where randomization comes in. Instead of deciding what we’re going to do, we leave it up to chance. Take three pieces of paper and write the number 1,2 and 3 on them. 1 will be rock, 2 paper and 3 scissors. Now turn them over and shuffle them up. Whenever you have to decide what to pick, you just randomly choose a piece of paper. Your strategy is now completely impossible to exploit; it’s so optimal that you can tell your opponent what you’re going to do (I’m going to pick one of the three papers … ) and there’s nothing he can do about it.
