I drafted a thread that had 9 questions about GTO strategy, some of which may generate a lot of responses, making the thread a bit complicated to follow. So I decided to make separate threads for each question or group of related questions (assuming there is interest). Here goes:

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We know the definition of GTO as being the same as Nash equilibrium, where heads up, if both play GTO neither has any incentive to unilaterally deviate.

But we don’t know, at least for now, just what that strategy is. So this and future threads present some questions for heads up play that, for me at least, can clear up some things:

Q1. Is my definition correct?

Q2. Does the following make sense for a way to describe and implement a GTO strategy?

We define an information set as all the factors known to a player at some decision point (everything except villain’s cards). We then describe a GTO strategy as a rule book stating what action is to be taken for every possible information set.

Q3. Assume a poker game only allows a small number of bet sizes. Is GTO still applicable? If so, if you ran enough solvers a long enough time, with lightning speed computers, you could eventually achieve such a rule book. True or false?

GT is the branch of mathematics that studies games and we informally use GTO as a way to refer to the nash eq of poker yeah.
No. 2 is also correct yes
No. 3 is correct too, and limiting betsizes makes a GTO solition simpler and easier to find

I agree with your definition and believe it's correct in general game theory.

I think this is limited depending on what constitutes a unique information set and what the out put action looks like.

I am specifically thinking of situations where actions (check, bet, raise, call, fold) for the same information set (specifically same hand) because two actions (check, bet, raise, call, fold) might occur with mixed frequencies because they have the same EVs otherwised known as a mixed strategy.

If your definitions allow for this then I see nothing wrong with the way you choose to describe these things, though, some game theory terminology already in use may be more beneficial since it is accepted outside of poker.

I am going to take some liberty with your question and assume that you don't mean "is a nash equillibrium possible with limited number of bet sizes" and what you are asking "is the nash equillibrium of a poker game with limited bet sizes equivalent to the nash equilibrium of the game with variable bet sizing".

I don't know that this question is answered or not.

There is work in subgame equillibriums but that seems to be relevant only to perfect information games.

I would have to err on the side of caution and say the solutions would be different.

True - I think some academics and maybe even commercial solvers are doing this.

Thanks for the two replies so far.

In response to j_g:


Q2. Does the following make sense for a way to describe and implement a GTO strategy?

We define an information set as all the factors known to a player at some decision point (everything except villain’s cards). We then describe a GTO strategy as a rule book stating what action is to be taken for every possible information set.

What I meant by information set is the actual actions taken by an opponent in the hand in question, so mixed strategy is not involved even though villain’s action may be the result of a mixed strategy.


Q3. Assume a poker game only allows a small number of bet sizes. Is GTO still applicable?

I actually did mean to ask if limiting bet sizes to a discrete number is still GTO. Don’t know why it wouldn’t be. The question was asked in order to make the follow-up question about developing the complete strategy through computer analysis meaningful

I guess I was more refering to reading our action from the book. I wasn't sure if we were limited to only a pure strategy of check, bet, raise, call, or fold as I believe in some spots you could take multiple actions with all relevant information up to that point.

I assumed you knew it would have to have a nash equillibrium as limiting bet sizes shouldn't effect the game to such a degree that it makes equillibrium impossible, which is why I thought your question meant something else.