A little background - I was a SS cash player pre-BF whilst studying mathematics at university. Got back into the game recently but was always reluctant due to the endless 'poker is dead' and GTO threads, and expected tables full of perfectly balanced 'GTO' opponents. To my surprise, the games are as good as I remember (could be due to lockdowns) which got me interested in the current GTO approach.
I have been reading a few papers and have some (probably basic) questions about this theoretical approach to the game.
1) Is there a formal definition (in mathematical terms) of GTO? Discussions in the forum seem to conflate a number of concepts (Nash equilibria, unexploitability). It seems that most players take GTO to just mean an unexploitable strategy that will not lose to any other strategy (although not necessarily be most profitable against a specific strategy).
This paper defines GTO poker as 'non-exploitable'. This seems incomplete to me, as the Nash Equilibrium is composed of a
pair of strategies (in a HU game). As I understand it, a NE approximation was found for HULHE by having a bot play itself and constantly adjust its strategy until equilibrium was approached. So there may be more than one NE strategy pairs? I think the confusion arises by making analogues to simple games like RPS, in which an unexploitable strategy is obvious (play 1/3 of each at random), whereas the situation is more like the
Coordination game, in which there are multiple NE strategies, depending on the other player's strategy.
2) A Nash Equilibrium exists for HUNL due to the fixed-point theorem and the fact that NL with discrete bet sizes is a finite game (durrrr seems to be arguing against this in
this thread?) Could there be multiple NE strategies for HUNL?
3) How do solvers like PIOSolver work on a technical level? I have watched videos and understand
how they are used but how exactly do they work? I know that they calculate the EV of every possible choice in the game tree (given the parameters and the estimated ranges). Is this basically like a PokerStove calculation but applied to an entire game tree rather than a single node?