In poker, there rarely are any pure strategies; almost all equilibriums are composed of mixed strategies. The question that must be asked is: how do you strategically play a hand with so little information? If poker was a game of perfect information, it would be very bland. For instance, if you knew exactly what cards would be dealt, and more importantly, what every other player was holding, nobody would ever play a hand. There are several solutions to dealing with the imperfect information. The first and most obvious answer is bet when you have a good hand and fold when you don’t. However, even bad hands sometimes can strike it big if the right cards come on the board. Likewise, the best hands can get occasionally busted by a lucky opponent. This leaves you with the idea of the odds of winning a hand (which the best poker players can calculate quickly in their heads). But knowing the odds still does not give you an idea of how to play the hand. That answer comes in two parts: psychology and game theory.

The psychology part is pretty simple: if you can read your opponent’s body language to better gauge what hand he is holding, whether he is strong or weak, or whether he is scared or confident, you will have more of an idea how to strategically play the hand. For instance, if he seems scared, you may try bluffing him out of the hand. Vice versa, if he seems confident, he may be trying to bluff you out of the hand. So while being able to “read” your opponent is perhaps the most important aspect of poker strategy, it is not the only way to make decisions.

Game theory has several advantages in poker. Say, for instance, your strategy consists of this: bet when you have a straight or better, and fold when you have three of a kind or worse. Once your opponent discovers this, he will fold whenever you bet, and bet whenever you don’t in order to force you to fold. However, say that one out of ten times you were going to fold, you bet instead. Your opponent would most likely fold every time until he realized you changed your strategy. By mixing up your play, you are actually increasing your odds of winning the hand. Game theory would suggest that if your odds of winning a hand are exactly 50%, your optimal strategy would be to play exactly the same way: fold half of the time and bet half of the time. This way, not only will you give yourself a chance to win with the odds, but also a chance to win by mixing up your opponent and having him play improper strategy. The same reasoning applies if you are a 90% favorite or even a 1% underdog. If you are able to perfectly vary your behavior according to your stated odds, game theory is actually your optimal strategy, especially against experts who would be able to figure you out otherwise.

It may be hard to believe, but the moral of the story is that even if you are an overwhelming favorite, you are not best off by playing a pure strategy. Jason Swanson, a math expert examines a simplified version of poker and after much in-depth analysis, mathematically reaches the same conclusion: “You cannot win with the optimal strategy.” By playing a mixed strategy in which you randomize your situations to play in and your situations to fold, you will be able to maximize your expected payout and become a winner in the long run.

http://swansonsite.com/W/instructional/game_theory.pdf