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GTO Preflop Assumptions [Game Theory]

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GTO Preflop Assumptions [Game Theory]

In a common PIOsolver analysis of a hand, we typically assume that players are playing according to GTO ranges preflop. Suppose we make this assumption and then play optimally according to the solver's solution. Would that mean that our strategy is unexploitable for the whole game tree? Or is it possible that players can exploit us by changing their preflop strategy and therefore invalidating our range assumptions?

In other words: Is solving a postflop spot with the assumption of GTO preflop ranges equivalent to solving the entire game tree from scratch, including all preflop play?

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DNegs98 5 years, 3 months ago

I think the answer should be something like they lose enough EV from other areas of the game tree that changing their preflop ranges cannot exploit us, however all of GTO is predicated on perfect knowledge of the opponents strategy with the only variable being their specific hole cards. This reminds me of a Ben Sulsky video where he convinced me that playing 2 sizings in a lot of spots actually is worth your time because he showed the EV loss that your opponent suffers if they don't realise you're playing 2 sizings and they employ the solved strategy based on you only using 1 sizing at this node of the game tree. So in essence I don't think it makes a difference in solver land but in the real world where we're using solver approximations if your approximations are invalidated by a change in strategy that you were unaware of then I can imagine that you will suffer an EV loss.

BigFiszh 5 years, 2 months ago

I like extreme examples, as they demonstrate best what happens: imagine you are SB vs. BB and open from SB. Your opponent folds all but AA (that he calls). You see a flop and stick to your pre-solved strategy. It's very obvious that you'll lose EV compared to a wide preflop-defense-range from BB.

At the same time, BB will lose money preflop due to his overly tight defense strategy.

The good message: overall BB will lose more money (EV) preflop than he will win from you postflop. That is fact.

In a 6-max-game, things get more complicated though. Preflop losses are shared by five opponents (including you), which means, your postflop loss in EV could easily get bigger than the preflop win you take from his sub-optimal strategy.

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