Help me with some simple EV math

[Halv]

400NL, 400$ effective stacks. I open raise to 14$, villain 3-bets to 50$, I shove with a hand that has 30% equity vs his calling range. How often does he have to fold for me to break even on the shove?

[Halv]

An anonymous source tells me that he has to fold 63% of the time. Someone confirm/deny and/or show me the math?

[euphoricism]

400 - 14 = 386 in your stack
50+14 = 64 in the pot.

I'm too dumb for the math, but here's the chart.




Looks like 63% is more or less correct, meaning he calls 37% of the time.

[Pelion]

*Maths*

(Using euphs numbers) If you each have $400 then there is going to be $800 in the pot. You have 30% of the equity of that $800 so you expect to get back 0.30*800 = $240 from each shove. At the moment you have $386 in your stack so that would be a net loss of $146. Each time he folds you win $64.

The total probability of his actions must add up to 1 so if the probability of him calling is x, then the probability of him folding is 1-x.

The EV is then:

-146x (when he calls) + 64(1-x) (when he folds).

which is

-146x -64x + 64

-210x + 64

You break even when the EV is 0 so when

-210x + 64 = 0

or when 210x = 64


which means x = 64/210 = 0.30

You need him to call less than 30% of the time.



Hope this makes sense.

[Pelion]

Euph. Looking at your chart the sign of the EV obviously changes between 30-35% so how did you get 37% ?

[Halv]

So does this mean the chart is wrong then? It says that the shove has an EV of 4.6$ when he calls 30% of the time, right?

lynch euph?

[kmind]

Pelion is right. I use a different formula and get .695

[euphoricism]

Euph. Looking at your chart the sign of the EV obviously changes between 30-35% so how did you get 37% ?

I'm a donkey and screwed up in a few places, but I think the chart is fine, halv. I think it depends on the rounding. Youre at 400nl, so 30% win and 30% call of $4 would be 1BB?

[euphoricism]

Not saying the chart IS right, I didn't make it. I'm way too dumb to make it.

EDIT: Halv, send me an AIM when you see this. I added the capability to do Pelion's exact math to the chart. I played around a bit and did indeed find disparity between the maths and the chart. I'll ask the maker about it when he's online but it could be a while.

[euphoricism]

Yuppo chart was off. Updated version: