[A_PLUS]

Gotcha, I just misunderstood how you were presenting your thinking.

Here are some numbers I worked out for the hand.

3450 in the pot, we have 2 options.

1.)Call to try to induce a river bluff or get a hand like TT to let us off cheap by checking behind the river.

2.)CR to shut out hands that are drawing live, possibly getting 99-TT to fold

We can make it easier by ignoring hands are going to the felt regardless JX, QQ+, 22, 33. They are getting all of the chips in no matter what, and we are resigned to call. Our line is irrelevant. Same goes for any hand we beat that villan is married to, 66,77, etc.

Inducing the Bluff
Worst case scenario is that he has 2OC hearts. But they are infrequent enough that I am willing to ignore them.

The most likely worst case scenario is Villan has 5-6 outs. I could see situations where 2 OCs or pair+OC would get here.

The most likely best case scenario is Villan has an underpair, drawing to 2 outs.


6 outs
12% of the time, he will hit on the river and we pay him off
-Hero has 790 after the hand

88% of the time, he will miss, and either chose to bluff or check behind.
-Hero has 7400 when Villan checks behind
-Hero has 9560 assuming Villan bluffs off his entire stack.

So, when villan is not a bluffer with 6 outs
.12(790) + .88(7400) = 6606

When villan is a bluffer
.12(790) + .88(9560) = 8507

We need him to be the bluffing type 41% of the time here for a call to be correct. Of course, if he wont bluff off his entire stack that changes. For instance, if he only will bluff 1000 chips, we would need him to do it 90% of the time.

Here is some examples of how often we need him to bluff given his outs and bluff size,

O(outs)=5, B(bluff size)=2160 = 34%
O(5), B(1000) = 73%
O(2), B(2160) = 13%
O(2), B(1000) = 28%

The Call, also has the added benefit of possibly causing him to check behind the river with 99, TT, when he would have called a CR push on the turn.

Take the pot
The check-raise is easy to value. Since there arent any likely draws, we assume that the value of the play is 7400 + the EV from causing 99-TT to fold.

Hands like 99-TT are only a small portion of villans range, and since both plays give the villan a chance to make a mistake on our behalf, I think we can ignore them too, when deciding between lines.

So, as usual, we go through the math, and it comes down to specific read. How many outs do we think he has (I would 2-5 most likely), and how often to we think he will bluff off his stack here.