Fold Equity (Request for Definition and Examples)

[BiiiiigChips]

I see the term Fold Equity (FE) thrown around alot on the boards. I've read a few poker books but I don't think I've ever seen the topic addressed in any of them, at least not at length. So for the posters of 2+2 what is the meaning of the term Fold Equity and what are some examples of some situations where your Fold Equity is high, low, or not a factor?

[WhiteKnight]

Fold equity occurs when you expect to profit from the other players folding to your bet/raise. I suppose it could be mathematically expressed as [Pot Size] * [Probability of Villain(s) Folding].

Tournaments: We have high fold equity in bubble situations when we are shoving any two cards first in.

Cash Games: We have low fold equity when we are bluffing 72o on a TJQ monotone board into a field of 6 players.

Am I more or less on here?

[_TKO_]

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Fold equity occurs when you expect to profit from the other players folding to your bet/raise. I suppose it could be mathematically expressed as [Pot Size] * [Probability of Villain(s) Folding].

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When you combine it with the pot, then it becomes the EV gained from the chance that your opponent(s) will fold. I've been thinking an unhealthy amount about FE in the past couple of weeks, so maybe I can offer some insight.

Consider it's relation to the term "pot equity", which represents the frequency with which you will win a showdown. PE is a constant value regardless of the outcome of the hand, but it ultimately only comes into being when a showdown actually occurs. That is, it is independent of the size of your bets or the size of the pot. Fold equity on the other hand, represents the frequency with which you will win with no showdown. Since this varies according to the size of the pot and the size of your bet, we would say it's dependent on these variables.

Visually, if you were to make a graph of PE vs bet size, it would be a straight, horizontal line. If you were to graph FE vs bet size, it might look something like a sigmoid (ignore the labels on the axes, I just scraped it off a math website):



A small bet has less FE than a large bet. When people say things like "maximize FE", they are referring to the fact that you want to launch the bet that gives your opponent the greatest chance to fold. It took me a while to grasp the concept that PE and FE have no relation on each other, but each of them does affect EV. Your EV for a bet would be something like:

EV(total) = EV(opponent calls) + EV(opponent folds)

Let f = fold equity, p = pot size, e = pot equity, and b = bet size. I think the full EV equation would look something like this:

EV(total) = (reward of call) * (chance of a call) + (reward of fold) * (chance of fold)
= (reward of call) * (1-f) + (reward of fold) * (f)

Since the reward of him folding is the pot, we get
= (reward of call) * (1-f) + p*f

The reward of a call falls back on the more common EV calculation related to PE (ignoring implied odds):
reward of call = e*(p+b) - (1-e)*b

So, the whole thing is:
EV(total) = (e(p+b) - (1-e)b)(1-f) + pf

Does this make sense?

[Kurn, son of Mogh]

Here's an extreme example of Fold Equity.

Standard 'Stars single-table SNG. 4 left, so its the bubble. Equal stacks - everyone has 3375. Blinds are 200/400/a25.

Folded to you in the SB. You shove any 2 cards. Why?

Opponent will likely only call with the top 10% of hands.

Thus 90% of the time, he folds and your resulting stack is 3875.

10% of the time he calls, and on the average you are maybe a 3:1 dog vs his range. So we get

3875 * 0.9 (he folds) + 0 * 0.075 (he calls you bust) + 6800 *0.025 he calls you win) = 3657.5

Thus the EV of shoving 3657.5 > the EV of folding 3150. Therefore shoving any 2 is correct from a CEV perspective.

The vast majority of this equity comes not from the value of your cards at showdown, but from the simple fact that your opponent folds 90% of the time.

[deucethree]

Semi-bluffs might be the easiest example to see the fold equity concept. Say you've got the nut flush draw plus a gut-shot straight after the flop. With a big combo draw like this you're prolly a small favorite to make the winning hand by the river. A lot of people decide to push a strong drawing hand like this because if they are called they're prolly not in a bad situation but by pushing the betting instead of waiting for the hand to develop they pick up a lot of fold equity when their opponent has a hand that has a good amount of equity in the pot (let's say middle pair against that strong combo draw where both players have about 50% equity in the pot) but decides to fold. That's the easiest way to start understanding the concept anyway, imo. FE is a big part of the reason why they say "it's better to be a bettor than a caller".

[BiiiiigChips]

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Semi-bluffs might be the easiest example to see the fold equity concept. Say you've got the nut flush draw plus a gut-shot straight after the flop. With a big combo draw like this you're prolly a small favorite to make the winning hand by the river. A lot of people decide to push a strong drawing hand like this because if they are called they're prolly not in a bad situation but by pushing the betting instead of waiting for the hand to develop they pick up a lot of fold equity when their opponent has a hand that has a good amount of equity in the pot (let's say middle pair against that strong combo draw where both players have about 50% equity in the pot) but decides to fold. That's the easiest way to start understanding the concept anyway, imo. FE is a big part of the reason why they say "it's better to be a bettor than a caller".

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Alright this example and the one about shoving ATC in certain situations probably makes things the most clear because it's something I already do and understand. I didn't really know there was a term for it but yeah the whole concept makes sense. It just seems like whenever I see someone talking about FE on the board it's not always consistent or maybe some people just explain or apply it differently. Thanks for the help guys.

[JocK]

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[..] what is the meaning of the term Fold Equity and what are some examples of some situations where your Fold Equity is high, low, or not a factor?

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For a definition, see:

http://www.google.com/base/a/1121639...16285364122504