Poker tournaments are a place where game theory is relevant, but how exactly can it be used? Well, thinking like a game theorist in poker involves reducing the game itself to a series of mathematical problems that can be ’solved’, either with a definite solution like ‘fold’ or ‘move all-in’ or a balance of the possible options that creates the best outcome. A simple example of this can be limping in with Aces 20% of the time under the gun and raising the other 80%.
The correct play in any given situation, of course, depends on how your opponents play, and mixing it up with aces would only be sensible against intelligent opponents. If they were raising all-in every hand anyway you would always just call. The latter is called an exploitative strategy, and there are also many plays in poker that are mathematically unexploitable and therefore always correct. For example, on the bubble in a sit & go a very big stack can profitably move all-in from the small blind with virtually any hand when the blinds get big and everyone has already folded because of the prize-structure implications.
This is the simple side of game theory in poker, but against skilled opposition, who play near perfectly, you would need to employ an optimal strategy – making winning impossible even if they knew what you were doing or try simple game like transylvanian beauty slots. For example, suppose you are playing a game where there is $200 in a heads-up pot by the river, you have a 20% chance of hitting your hand and the optional bet is $50. Given all these factors and the fact that your opponent is getting 5/1 on a call ($50 to win $250) you should bluff another 4% of the time, duplicating the odds that your opponent gets on the call into your bluffing strategy, which makes his decision equally bad either way.
Similarly, when you are facing top-class opposition you need to mix up your play throughout a hand to make it difficult for your opponents to read you. Limping with aces a certain predetermined amount of the time is one simple example, but against the best this needs to be carried through into the rest of your play. For example, when most cautious players flop a set they check in the hope of inducing action, but more aggressive players will tend to bet out with it in the hopes of disguising the hand and winning a big pot.