HU Pot (SB vs BB).
$50 stacks.
We are SB.
SB Open $1.50
BB calls

Pot on Flop: $3
SB cbet $3.00
BB raises to $9
Total Pot so far: $15
**SB shoves all in remaining stack. (50-9-1.50 = 39.5)

BB calls 50% of time, folds 50% of time.
We have 40% equity vs his calling range.

50% * win $15 (when he folds).
50% * ([win pot] $100 * 40%) - ([lose shove] $39.5 * 60%)

(.50 * 15) - ((.40 * 100) - (.60 * 39.5)
= 7.5 - 16.3
= -8.8 EV

Is this correct?


** = is this is correct way to find out how much more we need to shove?
Subtract the blind from our effective stack size, plus the bet we have to call?

if this calculation is correct, how do we find out at what point it becomes 0EV to shove?

SB 3xs pre, c-bets pot, gets raised, and presumably wants to compare EV(jam) to EV(fold).

If SB folds, he ends up with 50-1.5-3 = $45.5.

If SB jams, then working with your assumptions, he ends up with

(0.5)*(60.5)+(0.5)*(0.4)*(100) = $50.25.

So jamming is better than folding by 50.25-45.5 = $4.75.

Thanks for the reply.

I want to assume SB shoves 100% of the time for learning purposes on how the EV calcs work, and wanted to see if shoving with 40% EQ vs a 50% calling range was +EV or not, and at what equity point it becomes neutral EV.

In your example you have:
(0.5)*(60.5)+(0.5)*(0.4)*(100) = $50.25.

Does this mean we win 50% * $60.5 when he folds, and not the $15 in the pot before our shove?

That equation is meant to say how much money total we end up with if we jam. So, yea, if we jam, then the 50% of the time he folds, we end up with $60.5. The other half the time, he calls, and we end up with 40% of the $100 pot.