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Probably TLDR for a lot of people, I left the main points in bold.
So if we have 0 equity when called villain has to fold bet/(bet+pot); we would be shoving 9 into 4.7 so 9/(9+4.7)=0.6569, thus villain has to fold roughly 66% of the time for us to break even.
Lets say villain cold 4bets QQ+ AK and calls off everything. We have 40.21% equity.
(0.4021)(11.35)+(0.5979)(-9)=-0.82
Lets say villain cold 4bets QQ+ AK but folds AK to a jam. AK is 55% of his 4betting range, QQ+ is 45%. We have 20.7% equity when called.
(0.55)(4.7)+(0.45)(0.207)(11.35)+(0.45)(0.793)(-9)=0.43
I think it's interesting that even though he's never calling worse in this scenario we still have a +eV bet. Am I missing something here?
Lets say villain cold 4bets premiums and a mix of semibluff ish hands, like QQ+ AK, A2s-A8s. In this case he has 29 combos of value and 28 combos of bluff. Lets say he folds his bluffs here but calls his premiums, meaning he's folding 49% of the time and we have 40.21% equity when called.
(0.49)(4.7)+(0.51)(0.4021)(11.35)+(0.51)(0.5979)(-9)=1.89
So when he's got a lot of bluffs but is only calling off his premiums jamming is even higher +eV than in the second scenario. It's also interesting that he calls with very few "worse" hands (AK) and yet we still have a +eV bet.
It might be interesting to work out what our eV is going to look like for calling his cold 4bet when he has a range of QQ+ AK, A2s-A8s and compare it to jamming. I may be ill equipped to work out an eV calculation of this scope and I'm going to have to make a lot of assumptions for this scenario so bear with me.
Assumptions:
- We'll see an A/K high flop 40% of the time
- With SPR's so low villain will always bet all in if he chooses to bet
- Villain will bet A/K high flops with everything but QQ and we will fold when this happens
- Villain will bet all flopped flush draws (1/9 of the time)
- Villain will bet KK+ 100% of the time
- We will always call the bet if the flop is not A/K high
Flop is A/K high, villain bets, we fold
(0.4)(-2.35) = -0.94
Flop is Q- high, but two tone, villain bets his flush draws and QQ+ (26% of his range) and we call
(0.6)(0.26)(0.11)(0.6923)(-9)+(0.6)(0.26)(0.11)(0.3077)(11.7) = -0.045
Flop is Q- high, rainbow, villain bets his QQ+ (12% of his range) and we call like donks.
(0.6)(0.12)(0.89)(0.8841)(-9)+(0.6)(0.12)(0.89)(0.1159)(11.7) = -0.42
Add all that together and we get -1.40 eV for calling the bet, within the restrictions of our assumptions and under the assumption that my calculations were correct which is by far the most reaching assumption here (lol).
I suspect that our eV increases dramatically as we add bluffs to his flop betting range in this scenario so I'll work that out tomorrow, I'm dead tired right now.
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