Let us for the fun of it assume that we actually have 40% equity when called. How often does villain then need to fold for a shove to be +EV?
Let x = villain folds
1-x = villain calls
36(x) + (1-x)[(32)(0.4) - (32)(0.6)] = 0
36x + (1-x)(12.8 - 19.2) = 0
36x + (1-x)(-6.4) = 0
36x - 6.4 + 6.4x = 0
42.4x = 6.4
x = 15%
We don't necessarily have to bet though to win the $36 already in the pot.
This. When you're not going to get bluffed out of the pot then it's like being in position, that $36 is already yours vs hands you beat; And if there's no bluff equity (you won't fold out better hands) you don't actually gain anything from the times he folds. It's the classic value bets need to be 50% or more to work because your only gain is the amount you bet so don't include the money already in the pot in EV calculations - or if you do, also do the EV of checking vs a 60% equity range and compare.
Now, you can say that those are big assumptions to make, to me a much bigger one is that a seemingly passive guy could call 2 barrels in a 3bet pot then bluff-shove a TT76x board when checked to - or that he would shove 88 after 4 hands. Maybe I'm wrong here, but do you see that situation often on this type of board?
Also, do people call 3bets and 3barrels vs unknown with 4th pair here? If they do then we'd have over 50% to value bet. Maybe I'm wrong assuming they don't.
I understand what improve and others are saying, I just don't see the benefits outweighing the negative EV of an outright bet. And while I have no doubt lots of people that posted here are better HU players, this is mostly a math question. So please, post the range you think this guy is likely to call a 3bet & triple barrel with on this board.
The math is uber trivial.. The problem is that it is based on way too many assumptions. I would not be surprised to see villain flip over A6o when we jam the river. Not jamming the river is beyond terrible.
It is close to impossible to have a good enough measure of villain's range in spots like this.. Play your own range. We have some busted FDs and straight draws that we certainly want to ship on this river... Why you may ask.. because we have no clue how villain will play his range and there is only one way to find out..