Thanks for your thoughtful response.
Quote:
Originally Posted by Matthew Janda
Basically, the "balance" you see a GTO player play is a byproduct of always taking the line with the highest expectation.
I'm not following, sorry.
I feel like the "mistake", is that what we ought to be doing is comparing different strategies, NOT comparing individual spots in that strategy. The claim is we are trying to approximate a total GTO strategy and claim that this strategy is not beatable. It is tempting to say that GTO strategy is taking the most +EV line in any spot, as you suggest, but this isn't true. If one fixes an unchanging opponent strategy this is the definition of the maximally exploitive counterstrategy, but it is not the definition of the GTO strategy.
The basic reason is that when we do GTO, the opponent's strategy is not fixed, and is allowed to vary. In particular, it can adjust to what we do. So speaking about taking the maximally +EV line in any spot just doesn't make sense because to compute that we need to know the opponents strategy, and the opponents strategy depends on what we do in other spots as they are allowed to adjust.
I think my example still applies where we open shove everything pre. With that strategy, villian will adjust by calling with the top x% of hands by equity. So open shoving with AA is massively +EV, given our strategy. But if we fold everything and open shove with AA, then villian adjusts by folding everything but AA. And so open shoving has an EV of 0, given our strategy. So we can't just say we are taking the maximally +EV line in every spot, because what the maximally +EV line is depends on the villian's counterstrategy which depends on how we play the other hands. As in, we have to take it as a strategy holistically.
Quote:
Originally Posted by Matthew Janda
The point of that statement is you are never taking a line with a lower EV for "balance" (many people used to think you should do this and recommended bluffing even if it was -EV to make value hands more +EV).
I'm sorry, I still don't see why this is wrong. If we change from strategy A to strategy B, some lines will go up in EV (against "standard" villian counter strategies) and some will go down. We ask whether strategy A or strategy B is more profitable, but there can certainly be trade offs where different components within the larger strategy go up or down but that the net effect is positive.
Quote:
Originally Posted by Matthew Janda
Everyone I know that talks poker theory is constantly talking about EV as well as the opponent's strategy and possible counter-strategy. If we don't talk about these things then I think poker theory won't be very useful. Honestly, I don't even see how it'd be possible to talk about poker theory or GTO without having some idea of the different EV of different lines (even if they're estimations) or some idea of how the opponent should play.
Sure fair enough. The way I think about it is that in order to
discover something that is close to GTO, we need to give our opponents various strategies and then we can compute EV against those strategies to shape our GTO approximation, even if a priori GTO solution is blind to an opponents strategy and thus can't make any mention of EV. It would just strike me as weird to try and define GTO as that which maxes EV in every spot.