I will try to explain some game theory concepts that apply to poker in this post. It's a whole branch of mathematics, but I'm not going into much depth here. I will cover some of the mathematics later on. The important thing for now, is that you understand the concepts/terms before reading my upcoming articles. The truth is that I'm not a game theory expert, not even much of a mathematician. I only know the concepts which apply to poker. What I want you to know after reading this post is the difference between a pure and a mixed strategy, between an optimal and an exploitative strategy, and how one strategy can dominate another.
Pure strategy
A pure strategy simply mean that you use the same action every time. That you doesn't mix it up at all. Say you got AA in the big blind and one player has gone directly all-in before it's you to act. The obvious correct strategy is to call 100% of the time in this scenario. This is a pure strategy. It's no need to fold some percentage of the time to "mix it up". This is also an example of a dominant strategy. To call dominates all other options (more profitable every time), and is both the most exploitative and optimal strategy at once.
Mixed strategy
Say you got 85s on the button. All players are 100bb deep. One player raise 3xbb from the cut-off. Against a strong player it's probably not profitable to raise or call 100% of the time here, but to do so a small percentage of the time probably is. Say you fold 60% of the time, raise 30% of the time and call 10% of the time. This would be a mixed strategy, as you doesn't take the same action every time. In this case folding isn't a dominant strategy, as (you think) it's more profitable to raise or call some percentage of the time.
Optimal strategy
An optimal strategy is maybe not quite what you expect it to be. It's usually not the most profitable strategy (unless your opponent also is using an optimal strategy), but an un-exploitable strategy. In this case it's better to use an easier game as an example. In "scissor, rock, paper" the optimal strategy will be to use each option 1/3 of the time. Your opponent simply can't beat this strategy, the best he can do is to do the same. In poker an example is to bluff at an optimal frequency versus the times you value-bet on the river, to make your opponent indifferent to what action he takes (the options are equally profitable for him).
Exploitative strategy
Say in the "scissor, rock, paper" example, that your opponent only plays paper, no matter what you do. The optimal strategy is still to use each option 1/3 of the time, but it's clearly not the most profitable. It will still beat his strategy, but you will win far more often if you always play scissor. In this case you exploit the weakness in his strategy. The problem is that if he realize what you are doing, he can now exploit your strategy. In poker an example would be to bluff far more frequently in a river spot than what's optimal if you know your opponent folds too often. Sometimes you might hear a player say a play is +EV in a vacuum. What he mean is that the play will show a profit given the conditions (your opponent will fold too often for instance), but not something you should do every single time (because you can easily be "re-exploited").
Practical use of game theory in poker
In hold'em no one plays optimally. It's a far too complex a game. What we often do though, is to make "single street games" and solve them. Meaning very simplified versions of poker, where it's possible to find the optimal strategy. They still learn us a lot and can often be applied very well to real situations.
If we feel an opponent has an edge on us in one spot, it's a good idea to play with as optimal frequencies as possible. The point being to cancel out his edge and rather exploit him in other spots. A common example would be against a player who is far too loose pre-flop, but very solid post-flop. You would generally try to get as much money in pre-flop against him as possible (with a stronger range). After the flop though, it could be an idea to mix it up as close to (what you think is) optimal as possible, instead of trying to out-play and out-guess him.
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