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Lolpwnt - I value all the work you have already put into these forums. So first of keep it up. Second, I have just begun doing more and more ev calculations, and decided to give a go at this hand on whether a shove on the flop is +ev. Only reason I'm posting is because according to my math (which is very likely to be wrong), I believe we need around 22% fold equity to have a BE shove. So here's the math.
Figuring the villain is tight, I'm using the same range you used to determine our equity when called (QQ+, 99, 77, AQo, AQs). Given our hand if we shove and are called we have ~37% equity against villains range. So using this formula:
EV = [Ev(fold)] * x + [Ev(call)] * (1 - x), with x = % villain folds.
We first find the EV of us shoving and villain folding. This is rather easy because we just need to add up the pot, as that is how much we will win. In this case that is $5.10 (.90 + .70 + 3.50).
Next we need to find the Ev for when we shove and villain calls. We have already determined we will have 37% equity. So:
Ev (call) = (our equity)(total pot) - our bet
=(.37)(20.1) - 8.9
= -$1.46
So now we have the Ev(fold) and the Ev(call) so we can plug this into the first formula and find how often villain needs to fold for this to be a BE shove.
Ev (fold) = 5.10
Ev (call) = -1.46
Ev (shove) = [Ev(fold)] * x + [Ev(call)] * (1 - x), with x = % villain folds.
= [5.10]*x + [-1.46]*(1-x)
= 5.10x - 1.46 + 1.46x
1.46 = 6.56x
x = .222 or 22.2%
This means, according to my math, we need villain to be folding 22% of the time to be breakeven on our shove. If he folds more often we are +ev, and if he folds less often we are -ev.
I have yet to do a range assessment on this hand to determine just how often villain is folding (and am in a hurry to go right now), so someone else can do that.
*I hope I didn't fuck up the math too much. Keep in mind I'm relatively new to incorporating this much math into my game and this is one of the few ev calcs I have done in a while.
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