I am really bad at math, so please be easy on me.
Lets say we are short stacked, I want to shove pre-flop my 300 stack into a pot of 450.
My opponent will fold 40% of the time.
How do I work out what minimal equity I need for this shove to be profitable?
Hey!
you win 450 40% of the time when he folds
you win 300+450 with a probability of 0.6*x, where x is your equity against his calling range.
you loose 300 with a prob of 0.6(1-x).
That assumes he made no bet before you shove (when he calls he calls the full 300 you push)
Your EV = 0.4*450 + 750*0.6*x - 300*0.6*(1-x)
put EV = 0 and rearrange:
1050*0.6*2*x = 300*0.6 - 0.4*450
Example is not very good, as we get x=0, meaning you don't need any equity. That is, your push is profitable with just foldequity alone, even if you loose the flip 100% of the time.
In simpler terms (lets assume you lose every time he calls),
Your opponent calls 6/10 times -> You lose 300 * 6 = 1800 chips
Your opponent folds 4/10 times -> You win 450 * 4 = 1800 chips
I.e. As Insanity stated, you don't need equity since you would still be break-even even if you are drawing dead every time he calls.
Exactly.
I just showed a general way of calculating this minimal equity you need if he doen't quite fold enough.
