Help with an EV calc?

100bb stacks, we're in the SB pushing over the BB. He will call with his top 5.4% of his hands because our image sucks (99+, AJs+, AQo+). Whats the correct range, to push every time?

94.6% we open push, he folds, and we win 1.5bb.
5.4% of the time we're called and we're x% against his range to win 101bb. And our effective stack is 99bb.

Whats a +EV range?

Here's what I'm getting... but i suck at math and i think im screwing it up.

If we lose every time he calls we're..
(.946*1.5)-(.54*99) =
1.419-53.46 = -52.04bb EV

If we win 33% of the time he calls..
(.946*1.5)-[(.54*99)/3] =
1.419 - 17.82 = -16.401 bb

Am I doing that right?

Now for what I really want = find what % of the time we need to win to break even and this can be simplified toooooo (i think)
1.419 - (53.46*x) = 0

and uh.. Its wrong. I get .02 which is 2% and... no.. I'm pretty sure we need to win more than 2% of the time?

.054 * 99, not .54.

Isn't this situation more interesting if we flip it? Ie, calculate what a correct calling range is against someone who open shoves SB every time.

This kinda sounds like a tournament problem btw .

binnnggoooo wow that changes lots..

If we lose every time he calls we're..
(.946*1.5)-(.054*99) =
1.419 - 5.346 = ~-3.9bb

So to find out the break even range its simply..
1.419 - 5.346x = .265 or

26.5% of the time

So if we're a 30% dog against his range, this is immediately profitable. Wow.

So now the test is if villain is going in with 5.4% of his hands, what can we shove that is a 30% dog against that range.

Pokerstove says that 22+,A7s+,K9s+,QTs+,JTs,ATo+,KTo+,QJo is 60/40 -- thats a pretty huge range and a really profitable spot.

This is kind of intriguing.

Yeah I guess it is pretty applicable to late stage tourny play. If you had 20bb, what would be the correct range would be interesting to see.

Edit: I just did it with 20bb, and its profitable even if we lose every time we're called. Villain needs to call with 7.5% of his hands (and have us never suck out) in order for us to break even. I'd bet the tourny people already know this, tho :P

Edit: nvm, I'm dumb.

It's still wrong. The equation has to be like this:

(.946 * 1.5) + (.054*100.5*x) - [.054*99.5*(1-x)] = 0

I get x = 0.366

I think it's +EV to push with a widish range from the SB, but not maximally +EV. Unless villian is way better than you post flop (and he does have position).

Also, after the third time you do this (profiting <5BBs) he widens his range....

Originally Posted by 2_Thumbs_Up

It's still wrong. The equation has to be like this:

(.946 * 1.5) + (.054*100.5*x) - [.054*99.5*(1-x)] = 0

I get x = 0.366

Yeah I dont follow... but it looks righter...

( EV if he folds) + (EV if he calls and you win) - (EV if he calls and you lose)

oh. Duh.