Quote:
Originally Posted by Olaff
I like Sherman's way much better than mine, it's more comprehensive.
EV = p(call) * equity when called * (pot when called - shove amount) + p(fold) * pot
Now let's make this even more bad ass.
p1= probability of a fold
p2 = probability of a call = (1-p1)
p3 = probability of winning if called
p4 = probability of losing if called = (1-p3)
X= initial pot size
AX = shove amount, where A > 1
EV of calling = P3 * (X+AX) - (1-P3)*AX = P3X+ P3AX - AX + P3AX = P3X + 2*P3*AX - AX = X (P3 + 2*P3*A - A)
EV of folding = P1 * X
Neutral EV = 0 = P1*X + P2*X (P3 + 2*P3*A - A)
P1 * X = P2* X (P3 + 2*P3*A - A )
P1 = (1-P1) (P3+ 2*P3*A - A)
P1 = P3 + 2*P3*A - A - P1*P3 - 2*P3*A + P1 * A
P1 = P3 -A - P1*P3 + P1*A
We'll assign 0.33 to P3.
P1 = 0.33 - A - 0.33*P1 + P1*A
1.33*P1= 0.33 + A (P1-1)
A = (1.33*P1 - 0.33) / (P1-1)
Err nevermind, my algebra sucks. But I know I'm on the right track.
You didn't copy my formula correctly. You added a parenthesis where there is none. It should be this:
EV = p(call) * equity when called * pot when called - shove amount + p(fold) * pot
What you call p1 is my p(fold). What you call p2 is my p(call). What you call p3 is close to, but not the same as my "equity when called." Equity when called includes 50% of ties, whereas your p3 does not.
Now what is it that you are going for when trying to make it "more badass." That is, I am not sure what you mean by that and what you are trying to find out.
The biggest issue that can come up with these calculations is that changing one number (e.g., p(call) ) a little bit should change the other numbers (e.g., equity when called). That is, change in one number is not independent from change in the others. The dependence between p(call) and p(fold) is obvious. Less obvious is the fact that if an opponent calls with a wider / tighter range, your equity when called changes (in a direction that is unknown without knowing the specific hand ranges).