Paradise 1/2 -- Should I play this slower?

[SixForty]

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It still isn't 1-1, so cap it. Lets face it, when you have the second nuts and run up against the nuts, you're gonna (and you should) lose some bets.

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But do you really need to lose the last 2?

Let's face it - Hero 3bet the flop and was capped. Hero 3bet the turn and was capped. Hero leads out the river and Villain is STILL raising. Hero's hand is well defined. And Villain still keep's going.

This is simply a matter of EV. So let's look at the EV. Folding the river is ridiculous. Everyone knows that. Hero is getting 28.5-1 to call. Since we know that Hero will win this hand well more than the 3.5% or so that he needs to for calling to be correct, calling is therefore +EV.

For raising to be +EV, it's a much different situation. We need to make sure that:

(the percentage of times Villain has 88 or worse and calls * 1)
plus
(the percentage of times Villain has 88 or worse and caps * 2)
minus
(the percentage of times Villain has 99 * 2)

is greater than zero.

If you look at these equations and numbers closely, I think that those advocating a river 3bet are putting too much belief into 2 things:

- the likelyhood of Villain having any of the four hands 9[img]/images/graemlins/spade.gif[/img]9[img]/images/graemlins/club.gif[/img], 8[img]/images/graemlins/spade.gif[/img]8[img]/images/graemlins/club.gif[/img], 8[img]/images/graemlins/spade.gif[/img]8[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/club.gif[/img]8[img]/images/graemlins/diamond.gif[/img], is equal given the action so far
- Villain will still cap the river with a worse hand a somewhat significant portion of the time

So let's say we grant both of these assumptions. Let's say that each of the 4 hands listed is equally likely and Villain will always cap the river with 88. This is best case scenario for Hero. Then the EV of a 3 bet is:

(0.75*2) - (0.25*2) = 1

So absolute best case scenario if we grant those assumptions is that Hero's EV is +1.

But look what happens when we change those assumptions and make them a bit more rational. If we switch things up so that Villain is smart enough to cap with 99 but only call down with 88:

(0.75*1) - (0.25*2) = 0.25

Hero's EV drops to only 1/4 of a bet.

If we change things to weight 99 a little bit higher than the 88's, let's say 99 is 40% likely and each of the three 88 hands is 20% likely. And let's say that Villain will only cap with 88 half the time, and the other half he'll just call:

(0.30*2) + (0.30*) - (0.40*2) = 0.1

A razor thin +EV edge.

If Villain starts capping anywhere less than half the time with 88, then we start getting into a -EV situation. And that's if we keep 99 weighted at only 40%.

I honestly believe that we should be weighting the single 99 at least 50% here given all the action Villain has given us so far. And I honestly think that we can assume Villain will not cap with his 88 anywhere close to 50% of the time given all of the action that Hero has given so far.

So I stand by the fact that I think 3betting here is anywhere from a slightly negative -EV situation to a relatively large -EV situation.