Game Theory Optimal and Exploitative Play

 

Game Theory Optimal and Exploitative Play

 

Most students of HUSNGs are at least aware of the Nash Equilibrium charts for endgame play, which solves shortstacked strategy if the small blind is only allowed to go all-in or fold preflop. In equilibrium, neither opponent has any incentive to change their strategy – any adjustment will have worse expectation. Thus, perfect poker players would actually play the endgame the same way for eternity against each other.

What fewer people know is that Nash Equilibrium as a concept is not just limited to shove-or-fold endgame play. At any stack depth, there is a complex Nash Equilibrium that says what perfect poker players would do against each other to break even with each unable to profitably deviate. John Nash’s work proving this (heads up poker is a game that falls into conditions he set proving it about various games) helped him earn a Nobel Prize. However, don’t feel bad if you were unaware about this aspect of Nash Equilibrium – Tom “durrrr” Dwan recently argued with a great deal of conviction that this conclusion is false. If Dwan can prove it, he will likely become the first professional poker player to become a Nobel Laureate.

The takeaway knowledge here is that it is possible to play a static, mixed strategy, and for no opponent to be able to profit against you. In fact, opponents will always have negative expectation against you unless they too are playing Game Theory Optimally (GTO). It can be very worthwhile thinking about what this solution might look like, especially because every non-GTO strategy is one that is readily available to be exploited.

While the entire GTO strategy is very difficult to compute, you can learn more about it by working through balanced ranges in common situations. Because of the power of position, the GTO small blind strategy is likely very aggressive, putting constant pressure on the big blind and making as many bluffs as possible without becoming unbalanced. This tells you that when you play against a tough opponent, you have to be very careful about getting exploited by having ranges that are too value-oriented from the small blind. Likewise, when you check/raise the flop and bet the turn and river, it seems reasonable that in equilibrium you would include as many bluffs as you can get away with given all the value hands in your range.

It can be very tempting for poker players, upon knowing that it is possible to be unexploitable with balanced frequencies, to stick to strategies that seem like they might be close to GTO. The allure of it being impossible for your opponent to beat you can be very strong. However, every time you try to be unexploitable, you pass up on an opportunity to maximally exploit your opponent’s frequencies, and GTO strategies are really made to play against other GTO strategies. If your goal is to make as much money as possible in your games (and I’m assuming it is), seeking to be unexploitable is not really a coherent approach – for the most part, playing GTO guarantees that you’ll be throwing away boatloads of expectation. Again, you are playing DogLoverAA, not Phil Ivey. Be wary of biases that can lead you to play fancier, prettier poker, instead of poker that makes the most money.

Of course, it is not so easy as to just “decide to play GTO”, anyway. Nobody really has that much of a sense of what GTO poker 75bb deep would even look like, so saying, “OK, I’ll decide to play perfect poker now” is not really an option. Because of this, the vast majority of specific advice in this ebook will be exploitative advice, taking advantage of the general exploitable tendencies of opponents and the ways you can make the most from players with other styles. This means that a lot of the strategies I advocate for are exploitable - that’s not something to be afraid of. Since your opponents are not playing GTO, what makes the most money will absolutely be exploitable. You will have to adapt if your opponent adjusts. Still, after tens of thousands of games, I am consistently reminded of just infrequently opponents optimally adjust against exploitative frequencies.

Well-reasoned, exploitative play is also exploitable play. Embrace this reality. From the start off the match, go after frequencies that you think you can exploit. Learning about the game theory of poker will help you in adjusting your tendencies against different opponents, but beware the fancy play syndrome that results from putting more emphasis on being balanced than on making money.

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