All You Need to Know About Fold Equity

"If you're planning to call a bet, you're better off betting it yourself." Behind this poker mantra is the reality that by betting, you give yourself two ways to win.
You can win the pot with the best hand at showdown, or you can win it immediately by having your opponent fold. Fold equity refers to your chances of causing your opponent to fold.
Technically speaking, if you think your opponent will fold 20% of the time in a $200 pot, you have $40 in fold equity.
However, in broader terms, fold equity can be used to signify that you're putting thought into the fact that you can make your opponent fold.
Making Moves With No Hand

If you take a look at a nosebleed hand from PL.com's MarketPulse biggest pots section, you can see how fold equity shapes entire games. These high-stakes players are so well-versed in marked cards reading their opponent's range that they can make moves with no hand at all.
They sometimes rely entirely on fold equity. And fold equity can win you pots that you have no business even being in in the first place.
A note of caution, though: I would never suggest for you to rely entirely on fold equity in a hand. To be successful at that you would need to have incredible hand-reading skills.

You are not Phil Hellmuth. And let's all be thankful for that.

Unlike lolphillhellmuthlol we are mere mortals and cannot read people's souls. So leave the stone-cold bluffs for the pros.
What you can and should do is start incorporating more semi-bluffs into your play. Let's take a look at an example where we flop a flush draw and use fold equity in our decision whether to smooth-call, fold or raise.
You are playing in a $1/$2 game at your local casino. Effective stacks are $200. You are dealt A♠ T♠ in the cutoff. A player limps from early position and it is folded to you. You make it $10 and only the early-position limper calls.
The flop comes 7♠ J♣ Q♦. Your opponent donk bets $15. From what you know about your opponent, he would likely do this with any pair of jacks or queens as well as with some weak draws.
What Should You Do?
Well, you do not have the best hand currently, and with one overcard and a gut-shot, you are not getting the correct odds to call. That eliminates calling from your options.
You're left with raising or folding. Folding, although safe, is not the best play. Plus, you want to be the one wielding fold equity to your advantage - don't let your opponent be the one to profit.
So let's take a look at raising.
There are a few reasons for choosing to raise. His range is wide and consists of many hands that cannot stand much action.

Full Tilt pro Phil Ivey: Always using fold equity to his advantage.

Also, your perceived range (how he sees your hand) is strong. You raised pre-flop and are now choosing to raise his flop bet. This represents a made hand, one that wants action.
Of course in reality you only have a weak draw. However, because the range you're representing is so strong and his is primarily weak, you'll often pick this pot up with a raise on the flop.
Even if your villain doesn't fold, all is not lost. You still have seven outs that can improve your hand on the turn. It is a semi-bluff, not a complete bluff.
Fold equity calculations do not work if your opponent doesn't ever fold. Fold equity is the chance that he will fold, so if he doesn't fold, factoring the chance that he will into your considerations is a pointless endeavor.
Getting Mathematical
If you wish to get mathematical, you can assign percentages to the likely outcomes. Using the hand above infrared contactlenses, I punched in our opponent's range into PokerStove to come up with some data.

PokerStars pro Bill Chen: Gets mathematical.

The information you have about your opponent's hand is that he limped from early position, then called a small raise, and when the flop came out he led into you for two-thirds the pot on a 7♠ J♣ Q♦ board.
You can assign him a range of something like TT-77, KQs, Q9s+, J9s+, T8s+, ATo, KQo, QTo+, JTo, T9o - which is a pretty wide range. Against it you're a 40% dog.
However, because the bulk of that range is weak, he will fold to a raise a high percentage of the time. What the exact percent is is impossible to determine, although it's safe to say that he will be folding enough times to make raising a more profitable play on your part than folding.
In Tournaments
In no form of poker do you rely on fold equity more than in tournament poker.
As the blinds increase and your M value decreases, you're going to need to start stealing blinds to keep afloat. If you do not steal blinds, you won't last long. The blinds will swallow you up and your tournament will be finished.
Most tournaments see rapid blind increases. There just isn't time to sit back and wait for aces. You have to make do, and you make do by "stealing" with worse-than-average hands.

Full Tilt pro Allen Cunningham: Big fan of stealing blinds.

Let's say you have seven BBs in the late stages of an online multi-table sit-and-go. The average stack is likely around 15 BBs, and the chip leader may only have 30 BBs. It's time to get moving and accumulate some chips.
In this stage of the tournament you have two options, shove or fold. (This article fills in the background as to why these are your two choices.) As we established earlier, good hands are not going to come along fast enough to save you, so you must start shoving worse-than-average hands.
Shoving a hand like T♥ 9♥ isn't a play made for value. Your goal is to have your opponents fold so you can take down the blinds and antes without a fight.
You rely mostly on fold equity. That's not to say that you should push any two cards and rely completely on your opponents folding, because that just isn't going to happen all the time.
Let's look at a common tournament situation:
You are playing a 45-person tournament online. There are 16 people left and top seven get paid. You have $4,000 and the blinds are $300/$600. It's folded to you on the button, and you have 7♣ 9♣. You shove all-in.

Full Tilt pro Patrik Antonius: Wins without showdown frequently, although much of that can be attributed to handsome panic.

Do you do it for value? No. This is a steal-raise, meaning that you hope your opponents will fold. If every time you went all-in you were called, this would not be a profitable move because you're going to be a dog each time.
The fold equity that your shove has makes the move profitable. Most of the time you're going to win this pot without showdown. Those times you are called you will likely be a 60-40 dog.
The fold equity overcomes this gap in hand value and turns an unprofitable shove into a profitable push. That's all there is to it.
Fold equity is a simple concept. Understanding it won't all of a sudden let you turn water into wine, but once you start factoring in the likelihood of your play getting your opponent to fold, you will be able to turn a marginal situation into a profitable one.