How do I do this EV calculation?

[DonkBluffer]

$3/$6NL game, I've called villain PF. Effective stacks $857.

There is $105 in the pot after our villain cbets on the flop.

I raise to $160. Villain will fold 69% of the time to the raise and we win the pot. 31% of the time he will 3bet all-in and we call, having 42% equity vs his range. (If we get all-in, the total pot will be $1720 minus rake. His all-in is $670 more to call.)

What's the EV of this whole line?

[jay_shark]

I have a formula that works well in situations like this but it assumes that villain makes a psb and that you have a 40% equity when called . (good enough for your purposes )

So suppose there was 52.5 in the pot and villain makes a psb so that there is 105 in the pot . You take your effective stack otf which I will say is 830.75 and the current pot size before you shove is 105 .

x>=(spr-2)/(spr+8)

where x is the percentage of time villain needs to fold and
spr = stack to pot ratio .

spr = 830.75/105 ~ 7.9

x>= (7.9-2)/(7.9+8)
x>= 37.1%

[DonkBluffer]

I already know the percentages that he will call and fold, and my equity when we get all-in.

I raise his cbet. He will fold 69% of the time and then we just win the $105 pot. The remaining 31% of the time he goes all-in, I call and will have 42% equity vs his push range.

So 69% of the time I win the $105, and 31% of the time I have 42% equity in the all-in pot. How do you write this out in a formula? And the thing I want to know is the money I will win on average taking this line. Expected $$$.

[jay_shark]

Here is the formula .

Lets restrict this to a two player game where the sb raises to 3bb and you call .Villain has hero covered and hero's effective stack before the hands begins is S.

On the flop , villain makes a pot bet which we will call P .Let X be the percentage of time you think villain would fold to a shove . Let Y denote your equity when villain calls your shove .

Hero's EV is (6+p)*x + (1-x)*2*S*Y-(S-3) .

[Ricks]

I think I know what you are looking for but I must warn you that I am a novice at this. This calculates the EV of your flop raise assuming you will be all in if he doesn't fold.

69% of the time you will win $105. 31% of the time you will be all-in for your $160 plus the rest of your stack, which I believe would total $807.50, (1720-105)/2 = 807.5, plus the $105. You will win the all-in 42% of the time and lose the all-in 58% of the time.


.69*105 + .31*.42*(105 + 807.5) + .31*.58*-807.50 = + $46