♦ Fold Equity: What It Is and How to Calculate It on a Shove

You flop a flush draw, your opponent bets, and you are deciding between calling and moving all in. If you call, you win only when the card comes. If you shove, you also win when he folds. That second way of winning has a name: fold equity. Understanding it is what separates a shove that makes sense from one that just burns chips.

What fold equity is

It is the value you get from your opponent folding to your bet. When you bet, there are two ways to take the pot: your opponent folds right there, or he calls and your hand ends up winning. Fold equity measures how much the first one is worth.

It depends on two things: how often the opponent folds and how big the pot is when he does. An opponent who never folds leaves you with zero fold equity, however much you bet. A small pot does not give you much either, even if the opponent folds often.

The simplest case: a pure bluff

Say the pot is 10 big blinds and you shove for 20 with a hand that never wins when called. You risk 20 to win 10. To break even, your opponent has to fold often enough to make up for the times he calls.

The formula is risk divided by risk plus pot: 20 divided by 30. Your opponent has to fold two times out of three, 67 percent, for that bluff to break even. If he folds more, the bluff wins money. If he folds less, it loses.

• Pot: 10 big blinds.
• Your shove: 20 big blinds.
• Required fold frequency: 20 / (20 + 10) = 67%.

A draw changes the math

Now you have a flush draw on the flop. If you get called you are not dead: with two cards to come you win about 35 percent of the time against a made hand like an overpair. That 35 percent means you need far fewer folds.

Same 10 pot and same 20 shove. If you are called, the final pot is 50 (the 10 already there, plus your 20 and his 20). You win 35 percent of 50, which is 17.5, and you put in 20. When called you lose 2.5 big blinds on average. When he folds, you win 10.

To break even, the folds have to cover the 2.5 you lose when called. Solving it, he only needs to fold 20 percent of the time. You went from needing two folds in three to needing one in five.

• When called: 0.35 × 50 − 20 = −2.5 big blinds.
• When he folds: +10 big blinds.
• Break-even: F × 10 = (1 − F) × 2.5, so F = 20%.

This is why aggressive players semi-bluff with draws and not with air. Hand equity and fold equity add up, and together they turn a losing play into a winning one.

What decides how often your opponent folds

The arithmetic is easy. The hard part is estimating the fold frequency, and that comes from reading the opponent and the spot.

• Player type. A recreational player who never lets go of a pair leaves you almost no fold equity. A disciplined regular who can fold leaves you plenty.
• Your image. If they just saw you bluff three times in a row, they will call more.
• Relative bet size. A shove that puts the opponent's whole stack at risk gets more folds than a bet he can call without thinking.
• Board texture and your range. If the board favors hands you can have, your story is believable and they fold more.
• ICM pressure in tournaments. Near the bubble or the pay jumps, many players fold hands they would call in a cash game.

When fold equity disappears

If your opponent has already put so much in the pot that little is left behind, he will call with almost anything. The same happens when your shove is small compared with the pot: the price you offer is so good that folding would be a mistake. In those spots your play is worth only your hand's equity, and you should decide as if you were calling.

There is also no fold equity when your opponent bets first and you can only call. That is why aggression has an edge that calling does not: only the bettor can win without showing a hand.

How to use it at the table

You do not need a calculator every hand. Keep two reference points in mind. A pure bluff the size of the pot needs your opponent to fold half the time. A bluff twice the pot, like the example, needs two folds in three. Any equity your hand has lowers that number.

To practice, go back after a session to the shoves you made with draws. Write down the pot, the shove size and your rough equity, and work out how many folds you needed. After a handful of hands you will see whether you are picking the right opponents and moments to apply pressure.

Play only if you are 18 or older and with money you can afford to lose. Poker has variance and no formula removes it.