Hello, would be great if someone could have a look at this!
Assuming villain bets 50$ into 100$ and he has 100$ left in his stack (we cover). Now I want to calculate the EV for (1)Shove and (2) Call.
(1) We shove all-in:
We split Villains total range into 2 parts, of which one is his "Nut-Range" that he always calls and that makes 40% of his total range and against which we have 10% equity, and the remaining 60% that we call his "Semi-Calling-Range", that he calls 80% of the time and against which we have 85% Equity:
EV(Shove vs Nut-Range) = (100+100+50)*0.4*0.1 - 150*0.4*0.9 = - 44
EV(Shove vs Semi-Calling-Range) = (100+50)*0.6*0.2 + (100+100+50)*0.6*0.8*0.85 - (100+50)*0.6*0.8*0.15 = 109.2
EV = -44 + 109.2 = 65.2
(2)We call the turn (what happens on the river doesnt matter):
EV(Call vs Nut-Range)= (100+50)*0.4*0.1 - 50*0.4*0.9 = 6 - 18 = -12
EV(Call vs Semi-Calling-Range) = (100+50)*0.6*0.85 - 50*0.6*0.15 = 76.5 - 4.5 = 72
EV = 72 - 12 = 60
It would be great if someone could confirm that the formula I'm using is correct so I'm not using wrong numbers in the future