Calculating the EV of shoving

This formula we've been working off of for the past bit, it's not 100% correct.
I didn't notice that we've failed to notice that Hero's shove amount is not the same as Villain's call amount, since Hero is facing a bet.
So in the example

Size of pot before hero shove is $1.30 (0.25 BU raise, 0.05 SB, 1.00 BB 3bet)
Villain has to call $9 if I shove.

You have to shove $9.75 to put Villain all-in.

So this
F*P + (1-F)[E*(P+S) - (1-E)*S]

should be this

F*P + (1-F)[E*(P+S) - (1-E)*(S+B)]

B is the size of the bet that Hero faces.


The total amount Hero loses if he shoves, Villain calls, and Hero loses the hand is the $9.75.
Hero has to "call and raise" when he shoves, so the total amount Hero could lose is ESS + whatever bet Hero is facing.
or (S+B)

Each term has the form: (probability of occurrence)*(value of occurrence)
So (1-E) is the probability that Hero loses when the shove is called
and (S+B) is the amount of the loss.

Originally Posted by MadMojoMonkey

This formula we've been working off of for the past bit, it's not 100% correct.
I didn't notice that we've failed to notice that Hero's shove amount is not the same as Villain's call amount, since Hero is facing a bet.
So in the example

You have to shove $9.75 to put Villain all-in.

So this
F*P + (1-F)[E*(P+S) - (1-E)*S]

should be this

F*P + (1-F)[E*(P+S) - (1-E)*(S+B)]

B is the size of the bet that Hero faces.


The total amount Hero loses if he shoves, Villain calls, and Hero loses the hand is the $9.75.
Hero has to "call and raise" when he shoves, so the total amount Hero could lose is ESS + whatever bet Hero is facing.
or (S+B)

Each term has the form: (probability of occurrence)*(value of occurrence)
So (1-E) is the probability that Hero loses when the shove is called
and (S+B) is the amount of the loss.

OK, thanks MMM. I think I got that.