How do I calculate my expected value of shoving, including Fold Equity, in heads up play?
I know several factors are involved
- Pot Size
- My Stack
- His Stack
- My chance of winning if he calls
- His chance of folding when I bet
This will be pretty messy if I don't define some variables, so here goes:
When he calls and you win, you earn:
When he calls and you lose, you lose:
So, if he always called, your EV would be:
But he doesn't always call. When he doesn't call, you win:
So we can add that into the above:
I used this formula for the basis of a Expected Value Calculator web-app at Grinderschool, which calculates EV, Required Fold %, and Required Win % given any/all of the variables represented in this equation.
The EV is (% he folds to All in * Current pot size) + (% of times opponent calls * % you will win * Total size of pot) - (% of times opponent calls * % you will lose * Amount that you bet/shove).
On the left of the "+" sign are the times without a showdown. On the right are the times with a showdown. The times you win or lose can be calculated either against his explicit hand, or against what you assume his range is.
EV = (F% * P$) + (1 - F%) * ((W% * (P$ + S$)) - ((1 - W%) * S$))
this formulae is correct only when P$+S$ = W$, where W$ is the amount earned at showdown. So this formulae as it is only applies at situations where villain open raises and we shove. As this is not always the case(not always W$ = P$+S$), a more general form of this formulae would be by substituting P$+S$ with W$.