Game Theory and Strategy In Poker Matt Matros

 We have covered many number crunching ways of assessing the strength of of a hand and its chances of winning the pot such as pot odds, outs, expected value and dynamic hand value.

This article is about the amazing strategies of Game Theory and how they apply to Poker. Game Theory is the mathematical modelling of situations in which several parties have competing interests and explains the way they make decisions and predicts the Optimum Strategy.

Former World Champion Chris “Jesus” Ferguson was probably the first poker player to apply Game Theory to Poker. Chris says that he didn't learn Poker by masses of practice but by studying the game academically and calculating the best strategies in any given situation.

This may sound odd at first but wouldn't you prefer your surgeon to study first before trying to pick it up as they went along?

Game Theorists regard Poker in purely mathematical terms with an optimal action for a desired outcome. Players who follow a different approach will say that always following a set of strict criteria will make you predictable and easy to beat at a higher level but Game Theory actually allows for the same hand to be played in different ways depending on the situation, a so called mixed strategy.  For instance imagine you have an King and a  Queen and that all the players have folded before you on the button the trick here is to also fold half the time and go all-in the rest of the time -  a mixed strategy. The opposite strategy - where you do play the same way with a particular hand every time is called a pure strategy.
So Game Theory accounts for pure and mixed play allowing you to 'play the odds' without becoming predictable.

Game Theory as applied to Poker has two strategies which are considered correct, optimal strategy and exploitative.
An Optimal Strategy is one where even if you told your opponent what you were doing there would be nothing that he could do to affect the outcome. Although for instance you would never tell him what cards you had you could warn him that you will bluff sometimes and he wouldn't know when. If you could play Poker to an Optimal Strategy without giving away any tells you would win in the long run and if you and your opponents were all playing an Optimal Strategy you would gradually lose to the house.

Is it then just a matter of playing Optimal Strategy to become a Champion?. Say your playing Texas Hold'em No Limit against a calling station who always wants to see the flop before folding. Your Hole cards are a pair of Aces, Optimal Strategy would be a small raise to both build the pot and disguise your hand. However if you already know that he will call you , you should go all-in to take advantage of his predictability in an Exploitative Strategy. The Optimal Strategy would still have won but against this poor player not as much as the Exploitative Strategy. In other words the Optimal Strategy is a safer bet against good players but use the Exploitative Strategy where possible against the poorer ones.

As always do not just consider how you can use a strategy but also how it may be used against you by other players -  are you open to an Exploitative Strategy? For instance is your play always to raise to a Big Blind playing Texas Hold'em with a medium pair or Ace, King? Do you have a set play for a narrow range of hands? Good players will pick up on that and use an Exploitative Strategy on you.
Imagine your Hole Cards are a pair of Eights and your chips are low. If a player makes a standard raise you could go all-in but if they make a large raise you could fold. If they were holding a pair of Tens they would have bust you with the standard raise and led you to fold with the large raise losing out on your chips.

Jerrod Ankenman and Bill Chen have just finished their book called The Mathematics of Poker, which will go into more depth should you need it.