Thanks to all the commenters on my last post. I think it's super close between folding and shoving. Calling and then folding at some point seems pretty spewy, as does calling and then calling a 4b shove from MP...4-betting and then folding is even worse. I think 4-bet/calling is essentially the same as shoving, so I'm not going to differentiate between the two in my analysis.
The first step is making a guess at the shorty's range. Given that MP opens pretty loose and CO is a donk with 40 bbs, it's an awesome spot for him to squeeze. I'd make his range something like 66+, AT+, although I wouldn't be surprised if he showed up with lower pp's, lower aces, and the occasional KQ/KJ. Against that range I have 54.8% equity. If I shove and get heads up with the shorty and win, then I win (22.2 + 7 + 1.5)*.9 = 27.63 (the .9 is there to account for the rake). If I lose, then I lose 22.2. So my EV given that I get HU with the shorty is:
.548*27.63 - .452*22.2 = 5.1.
So that would be clearly good, to get HU with the shorty. The issue is how often that happens, and how much equity I have when MP calls my shove. I'd estimate his range for calling my shove to be pretty much exactly JJ+ and AK, with some possibility of him folding JJ. But say he sticks around with JJ. Then in a 3-way pot, my TT has 26.3% equity. That is, 26.3% of the time, I win the whole thing. In this case I win 102.6 + 3.5 + 22.2 + 1.5 - 3 (the rake) = 126.8. Then sometimes I win the side but not the main (when I beat MP but the shorty beats me). The shorty wins 26% of the time, so maybe 10% of the time I win the side but not the main (I don't know how to get PS to do this, so it's a well-informed guess). In this case I win 80.4 - 22.2 = 58.2. If I lose both, I lose 102.2. So given that MP calls, my expected profit is:
.263*126.8 + .1*58.2 - .637*102.6 = -26.2
So that's obviously bad. But it doesn't happen all the time! AK and JJ+ represent about 3.2% of all hands. They're maybe a LITTLE bit less likely given that the shorty has shoved (more likely to have some high cards), and also that the CO called (more likely to be QJo than 56o, for instance). But then I have TT, and not T's are in his calling range. On net, I don't think I can make too many conclusions based on card removal. But he's calling about 3% of his range. How often does he have to fold for me to show a profit? In other words, what's the solution to this equation:
5.1*f - (1-f)*26.2 > 0
Answer: f > .837. So if he's calling 3%, he has to be opening .03/(1-.837) = 18.4% for me to show a profit. And I'm pretty sure that's the case. Folded to him in the hijack, he's 19/15 overall...I'd guess he's raising something like 20-25% from there. But it's razor thin. If the shortstack were a bit tighter, for instance, I'd need more folds from MP and the play wouldn't be profitable anymore. I've also just assumed that CO will fold every time, which is probably a fair assumption, but if he slowplays AA or KK a significant % of the time that might swing the play to -EV. In any case, I did shove and MP used almost his entire time bank before calling with JJ. The shorty had AK and the board bricked off. So, in summary, it's quite close and I couldn't fault a fold, but shoving probably slightly better.
-BRUECHIPS
2 comments:
You put MP on approx. the same range I did. I figured JJ+, A-Q, A-K. I also imagined you would have to fade every overcard to the river in order to win since you might have 2 opponents. That was also the case except for the Q.
Although I agree you did have +EV, a fold is still quite reasonable.
As I commented elsewhere, it was really close and JJ is clearly borderline so yeah, I guess your shove was good. I think that's where my problem is... when it's that close, I tend to fold - good players tend to shove.
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