Out Play Your Opponents by Using PokerStove

Part 4: Determine fold equity using PokerStove.

On the previous page I talked about how often a Villain is folding, but I didn't really explain how I arrived at that conclusion. Now I will explain how you can use PokerStove to determine your fold equity, using two separate examples.

The first example is an SNG, blind vs blind and we have 8 BB after posting the SB. There are no antes. We want to calculate if shoving 85s is +EV against the BB, and we have a pretty good idea of his calling range:

We can see that he's calling with 17% of hands. Since his range is 100% of hands, he is folding 83/100 = 83% of the time. When he calls we have about 34.8% equity.

Shove/fold = .83 * 1.5 = 1.245

Shove/call/win = .17 * 9 * .348 = 0.532

Shove/call/lose = .17 * -8 * .652 = -0.887

Result: Shoving 85s in this spot on average results in a 0.89 BB gain.

(If you want more information on equity calculations, see CodeRed036 and CodeRed038)

In the second example, we are facing a short stacker (40 BB) who is raising UTG at 6max with 55+/ATs+/KQs/AQo+. We have decided to flat with 8: 8 and the flop comes 9 7 6. He bets 8BB into a 9BB pot (28 BB back) and we believe it is with his entire range. Is it profitable for us to shove 36BB in order to win the 17BB pot?

Let's assume he calls with 66+ and flush draws. First we give him his initial range, which turns out to be 7.8% of hands. His calling range (66+, AcKc, AcQc, AcJc, AcTc, KcQc) is 4.4% of hands.

FOLD EQUITY CALCULATION

Of all his hands (7.8%), he is calling with 4.4% of hands, meaning that he is folding 7.8 - 4.4 = 3.4% of all hands. Since he has 7.8% of hands in his range, he is folding about 3.4/7.8 = 43.5% of the time.

Against his calling range, we have 35.6% equity:

Shove/fold: .435 * 17 = 5.95

Shove/call/win: .565 * 45 * .356 = 9.05

Shove/call/lose: .565 * -36 * .644 = -13.10

Result: Shoving 88 in this spot has an expected value of +1.9 BB

In review, to determine fold equity, we first narrow Villain's range given the action so far and see what percentage we get. We then determine Villain's calling range, and subtracting that number from the range gives us the percentage of total hands that are folding. Dividing the percentage of hands that fold by the percentage of hands in Villain's range gives us fold equity.