Quote:
Originally Posted by pasita
I could use some help here: p. 45
"Why is it that Hero's GTO strategy cannot involve either always checking or always leading here with all his near-nut hands?"
What's the difference of this scenario compared to the full street [0,1] game from MoP, where Hero just bets out with a fixed portion of his range, then check calls some and check folds some?
Quote:
Originally Posted by MrPete
I think it just has to do with the implications of hero's checking range if villain is betting all his nuts, and near nuts, then checking only weak hands. Villain will start to value bet very thin and hero can then increase his EV by checking a stronger hand. I'm wondering why then hero also cannot play a mixed strategy with his pure nut hands?
Quote:
Originally Posted by pasita
Logically, that could make sense, but unless I missed something obvious, MoP solved the same game using a pure strategy, i.e. predefined and fixed bet, chcall, chfold action regions.
So, I'm not quite sure what game from MoP you're talking about, but I found it useful to look at the game I'm talking about in more detail later in the book, and I stuck a full solution in Appendix 13.10 (p240).
That TestYourself question is mostly just meant to get you to go over the same line of reasoning given on the previous page, and I guess you can do that, but maybe you don't see how it applies to this game, since you think BB is always leading with his strongest hands at the equilibrium of this game?
On pg 44, I said what I mean by "near-nut" hands -- a hand strong enough that we'll always try to get all-in, and whenever Villain has a better hand, he'll always try to get all-in too. Basically, it just means that whenever we have such a hand and Villain has better, we're guaranteed to go broke.
This applies to a full 1/3 of the BB's range in this game (in the symmetric distributions case, with B=S=P). The top 1/3 of BB's range is actually indifferent between leading and check-calling at equilibrium, and indieed, he sometimes leads and sometimes checks with hands in this region. And SB puts in the same amount of money, exactly, versus both actions.
In the way the solution is normally structured, BB leads with his strongest hands and check-calls some weaker ones, but that solution isn't actually unique. Other structures (which can involve check-calling with the nuts) are co-optimal. I talk about this and this game more in one of my videos.