Hi CoronalDischarge,
Glad to hear the book's going well so far. I expect the answers to these sorts of questions will be very clear once you finish Ch 2, but let me give you the CliffsNotes.
If our opponent's strategy is fixed, then a
best response (or maximally exploitative) strategy is more or less what it sounds like -- it's a strategy where we choose the highest EV option in every spot. (Of course sometimes two actions might tie for highest EV.) Obviously there are no 'loss leader' type plays in a maximally exploitative strategy -- by definition we're doing the highest EV thing in every spot.
Equilibrium play occurs when both players are playing best response strategies at the same time. This is a special situation since neither player has any incentive to change his strategy -- doing so could only lower his expected profit, since he's already playing a best response. If we take one of the individual players' strategies from the equilibrium, we say it's an unexploitable or GTO strategy for the player.
So, an unexploitable strategy
is a best response strategy, when Villain is also playing GTO. Thus, in this case, it has the no-loss-leaders property of all best response strategies we noticed above.
If Villain deviates away from GTO, then some of our hands/plays could decrease in EV and others increase. However, we're guaranteed to make more (or at least as much) on average if we keep our GTO strategy since Villain decided to stop playing a best response, and any money he loses is money we gain.
So with all of that background, let's see about your question...
Quote:
Originally Posted by CoronalDischarge
My question is, do you think it's possible that, as part of a GTO strat, a play can be +EV (or at least 0EV) when made sometimes, but only because it's not made all the time? For example, we're facing a reraise preflop and are considering flatting or folding, and it turns out that flatting every time with this hand (slightly) loses money.
It can definitely be the case that a hand is played in more than one way at the equilibrium. Of course, this must mean that all of the ways it is played have the same EV, or else the plays couldn't be part of a GTO strategy. However, in this case, as long as Villain keeps his strategy fixed, beginning to play these hands all one way or all the other won't change our EV. It's only when Villain adjusts that we begin to lose EV.
Take an example -- in an over-simplified river scenario, we're in the SB with a range of hands which are all either nuts or air (but mostly air), and the BB has all bluff-catchers. So, we bet all our nuts and some bluffs, and the BB calls sometimes and folds sometimes. At the equilibrium, the BB is calling just enough so that with our bluffs, the EV of bluffing and the EV of giving up are exactly the same. (So, you might say that bluffing is 0EV, for some definition of 0EV.) Now, if Villain keeps his strategy fixed, we can start bluffing all the time or giving up all the time and it won't change our EV, but once Villain does adjust (by beginning to call a lot or fold a lot, respectively) we lose EV.
Hope this helps.