[Kurn]

In the most basic sense, during the play of a hand, the cards you hold have a given equity (share of the money) in the pot. That equity has 2 components: Showdown equity (the portion EV of your hand vs your opponent(s) range the percentage of time you to go to showdown), and fold equity (the portion of EV your hand has attributable to the percentage of time you bet and make your opponent fold)

Example. On the turn there is x in the pot and you hold a flush draw. You believe you must make your flush to win and when you make your flush, you will always win.

If that were your only option, your equity in the pot would be 9/46* x.

However, if your opponent checks and you bet y, you suspect your opponent will fold z% of the time. (note 1 > z > 0)

Your fold equity when you bet y is (1-z) * x and here we assume for simplicity that opponent never check-raises.

Of course when your semibluff gets called that creates a new showdown equity value and new EV calc for the river but lets not muddy the waters.

The cleanest real-world example of fold-equity based strategy is ICM in SNGs.

Equal stacks on the bubble, pure equity theory states that 1st in from the SB, it is always +EV to shove any 2 cards and the EV of that shove increases as the blinds increase.

Take a normal 'Stars STT with 4 equal stacks of 3375. Blinds of 100/200/a25. Assume opponent will only call a shove with 15% of hands.When called, assume your random hand will win 30% of the time.

EV

He folds you win = 3650 * .85 = 3102.50
He calls you lost = 0 * .105 = 0.00
He calls, you win = 6800 * 0.45 = 306.00

EV(shove) = 3408.50
EV(fold) = 3250.00

Poker math is often counter-intuitive. In this scenario it is impossible for the BB to reduce your EV to zero by tightening up his range as your fold equity just goes up. Theoretically, if the BB knows you're shoving any 2, the only way he can reduce your EV to 0 (he can never makes it -EV to shove) is to call with any 2.

Late in a SNG, fold equity is god.