Fold Equity

I misunderstood the term Fold equity. So hear is the definition as it is in Wikipedia:

Fold equity is a concept in poker strategy that is especially important when a player becomes short-stacked in a no limit (or possibly pot limit) tournament. It is the equity a player can consider him or herself likely to gain if he or she bets. It equates to:

Gain in equity if opponent(s) fold x likelihood that opponents fold
The first half of the equation is known because it is whatever share of equity the folding opponent has. The second cannot be known but must be estimated based on reads or previous actions.

It becomes an important concept for short stacks for the following reason. Opponents can be considered likely to call all-ins with a certain range of hands. When they will have to use a large percentage of their stack to make the call, this range can be expected to be quite narrow (it will include all the hands the caller expects to win an all-in against the bettor). As the percentage of stack needed to call becomes lower, the range of cards the caller will need becomes wider, and he or she becomes less likely to fold. Consequently, fold equity diminishes.

There will be a point at which a caller will need a sufficiently small percentage of their stack to call the all-in that they will do so with any two cards. At that point, the all-in bettor will have no fold equity.

Here is an example:

A holds A6. She is heads up with B, who holds 22. The flop is 973 rainbow (no cards of the same suit).

A has pot equity of 31.5% B has pot equity of 68.5%

(In other words, if there was no further betting, and the players simply turned up their hands and were dealt the turn and river, A is 31.5% likely to win.)

If B is 70% likely to fold, A's fold equity is 47.95% (68.5 x .7). Consequently, A can consider that her hand equity if she bets will equal 31.5 + 47.95%, more than 80%.

I'm not sure that I completely understand this. If someone has a better explanation I would love to hear it.

Before I try to explain fold equity: Do you understand what 'equity' means in poker terms?

Sure. I understood equity before, but, I have also read your article on it.

We should have the same understanding.

Okay, good.

So "fold equity" is, roughly put, the increase in expectation that comes from your opponent folding because you bet. For instance:

If your opponent has a 0% chance of winning this pot, you can never have any fold equity. You stand nothing to gain from him folding if he's drawing dead. Right?

If your opponent has a 100% chance of winning this pot (you're bluffing with a hopeless hand on the river) but will fold every time you bet, your fold equity is the entire pot. Right?

But there are degrees in between. For instance, if your opponent has you beat all the time, but will only fold 50% of the time, your fold equity is half the pot. Now, we're getting into the trickier areas.

If there are cards still to come, both you and your opponent will have some chance of winning (unless one of you are drawing dead, which doesn't happen often). So let's say that you have a 20% chance of winning, and he has an 80% chance of winning.

You bet. He will fold half the time, which you for some reason just know. What's your fold equity expressed as a percentage?

40%

Right.

Now, obvious as it may be, you of course have fold equity even when you're ahead of your opponent. Anyone with a live draw - including stuff like backdoor straights - has some equity in the hand. If you make them fold, you gain whatever equity they had to give up. The line between when you want them to call instead of folding is the line where you're break-even; when the fold equity that you would have gained from betting equals the expected value you get when they call.

If that makes sense.

OK. I think I got it. Now only if my reads are as good as I would like them to be.

So if my thinking is correct we should use this along with pot odds to determine exactly what we should raise/call in order to get the most out of each playable hand.

Yeah, I suppose you could say that. The fold equity is what makes a semi-bluff profitable, for instance. The chance of hitting our draw doesn't make raising good in itself; only coupled with the chance that our opponent will (incorrectly) fold does it become playable.

In some cases, most notably in limit hold 'em, you want your opponent to make a "bad" fold with the worst hand. Like this:

I have 7-7 and raise it up from middle position. One cold-caller on the button and the big blind calls as well. The flop comes K-8-8.

As it turns out, the cold-caller has A-5, so I have him crushed, but the blind has QJ. When the blind checks to me, I bet, button calls (with his three outs, I'm making money off of this) and then the blind folds!

That's great for me. The big blind had six outs to beat me, but must have gauged that he had much fewer live outs than that, so he folded. When that happens - managing to fold out a six-outer in an 8-bet-pot - it's very good news. Sure, we were favorites to beat his hand, but poker isn't a game about favorites. The equity he gave up cost him more than it would have to call a bet on the flop, but he didn't know that - for all he knew, I could have been holding AK or AA or some other hand that effectively gave him only runner-runner outs - so he folded.

Inducing incorrect folds is as much a part of a good limit hold 'em player's arsenal as inducing incorrect calls.