Folding equity

[knightunner]

I hear this term thrown around quite a bit, but I am not sure I know what it means, or how it is used in a game.

Can someone please clarify this for me?
Thanks,

~knight

[Kurn, son of Mogh]

It's usually used with respect to NL games, particularly when you are deciding how much to raise or whether or not to raise all-in preflop. The value of your hand (it's equity) is a combination of it's worth going to showdown, and the value of getting your opposition to fold x% of the time. The percentage of the play's EV that comes from how often you get the opposition to fold is its fold equity.

[fimbulwinter]

an example may better clarify this:

say you and I both have 200 bucks and are playing NL.
on the flop, I have a flush draw with $100 in the pot (we both now have 150 behind) and you have some hand which is ahead, but not great (underpair, TPBK, Ace high etc.) Whether I push all-in on you is a choice I must make depending on how often I feel you will fold to a bet of $150. If i know you will never fold, this is obviously a foolish bet as I am putting my money in with the worst of it.

My flush draw has around 1/3 of the pot equity with two cards to come, that is, if we were both all-in, I will win 1/3 of the time. If i check and call when you push all-in, this is all i get, 1/3 of the pot, where I am contributing (assuming we're playing heads-up) 1/2 of the money. i dont like this /images/graemlins/frown.gif . If you're first to act and you push all-in my decision is purely mathmatical, i will call 150 to win 250, which would be an EV mistake as I will only win 1/3 of the time, yielding me a total loss of $50/3 per time I make this call.

However, If i feel you will fold 75% of the time when I push all-in on you, I will do it every time. 3/4 of the time, you fold and I win $100. 1/4 of the time, you call and I lose 2/3 of the time, making my total = -((50/3)/4) +100(3/4) which nets me ~70 dollars on average.

that edge which turns the flopped flush draw is the folding equity of your bet. when considering a bet in NL, it is important to consider the equity of your bet in terms of implied odds, folding equity and pot equity, as well as the times you will be called when you are ahead. in NL, postflop bets generally have a good degree of folding equity as they are larger relative to the pot than in limit. however, the folding equity of a bet is important as a bluff in limit.

say you flopped that same flush draw and kept betting it into a large pot and on the river a player who had called all the way checks to you. if you know him to be a player wherehe could have been chasing two overcards the whole way and missed and will fodl to your river bet, then your bet will be only a small portion of the pot and will be hugely +EV, even if you only make him fold a fraction of the time. For example, if there is $100 in the pot and your river bet is $10, if he folds even 1/9 times this is a profitable bet for you.

hope i didn't ramble, in summary:
- consider the folding equity of any bet made with a hand that does not figure to be the best (a bluff or semi-bluff).
- In NL the bets are much bigger and so a semi-bluff must work more often to be profitable, but, since the bets are bigger, it often will and often will set you up to get all-in when you hit your hand.
- folding equity in limit is smaller because of the size of the bets in realation to the pot, however, they must not work as often to be profitable and are often +EV and ++++Variance bets.

fim

[CrisBrown]

Hiya knight,

Kurn and fimbul have both answered. I'll give you another statement of it, but I'm just saying the same thing they've said in another way.

Folding equity (or steal equity) is the value of a bet itself, regardless of your cards. If there are 10 units in the pot, and you know your opponent will fold 100% of the time if you bet, then your steal equity is 10 units. In this case, it doesn't matter whether you have the nuts or a dead hand. Your steal equity alone justifies the bet.

Of course, that's an extreme situation. Here's a more reasonable example. Let's say there are 10 units in the pot, and both you and your opponent have 10 units remaining in your stacks. If you both flipped up your cards right now, and there were no more bets, your hand would win -- i.e.: hold up if it's the better hand, or draw out if you're behind -- 35% of the time at showdown.

Now, let's say that if you bet the pot (your remaining 10 units), your opponent will fold 50% of the time. If you check, he will bet his 10 units 50% of the time.

Out of 100 such hands, if you bet you will win 10 units 50 times (when he folds), win 20(*) units 17.5 times (when he calls and you win at showdown), and lose 10 units(**) 32.5 times (when he calls and you lose at showdown). That works out to 500 units (you bet, he folds) + 350 units (you bet, he calls, you win) - 325 units (you bet, he calls, you lose) for a net +525 units over 100 bets, or 5.25 units per bet.

(*) You win 20 units when he calls and you win at showdown, the 10 units already in the pot, and the 10 units he adds to the pot by calling.

(**) You lose only 10 units when you lose because that's how much more money you're putting in the pot. The money already in the pot isn't yours.

If you check, he will bet 50% of the time. If he checks behind (we'll assume this goes to the river), you win 10 units. If he bets, you have to fold, as you are taking the worst of it to call. So, out of 100 such pots, you win 10 units 17.5 times (you check, he checks, you win), lose 0 additional units 32.5 tines (you check, he checks, you lose), and lose 0 additional units 50 times (you check, he bets, you fold). That's 175 units over 100 checks, or 1.75 units per check.

So if you bet, your EV is 5.25 units. If you check, your EV is 1.75 units. The difference -- the 3.5 units you gain on average by betting over checking -- is your folding or steal equity. Because you have the same cards in both cases, that difference is the value of the bet itself, regardless of your cards.

I hope this helps. /images/graemlins/smile.gif

Cris

[knightunner]

These posts are great, thanks everyone. I know Sklansky talks about this concept in TOP, but I haven't been able to put the pieces together...

One more question just to further clarify things for me. (sorry!) This process roughly involves determining the outs of my hand and converting it to a percentage. Then I calculate pot odds normally. After I have finished this process, then I need to determine whether the other person is bluffing? or do I determine equity solely on pot odds?

thanks again,
~knight

[CrisBrown]

Hi knight,

Okay, now you're talking about the difference between made equity (the value of your hand if you're ahead) and draw equity (the value of your draw if you're behind).

Let's say you have JT on a board of 9-8-T (disregarding suits). You have a pair of 10s, and an open-end straight draw. It's heads-up. Your opponent raised pre-flop, and you called on the button. There were 10 units in the pot pre-flop, and you both have 50 units behind. Your opponent bets out 10 units (the pot) on the flop. It's now to you.

* If he's on AK, AQ, AJ, A7 or less, KQ, KJ, or a pair 77 or less, you're ahead right now with a pair of 10s, and you'd consider the likelihood that your hand will hold up (made equity).

If you're behind, you consider how likely you are to outdraw him (draw equity):

* If he's on AA or KK, you have 13 outs (4 7s, 4 Qs, 3 Js, 2 10s).

* If he's on QQ, you have 8 outs (4 7s, 2 Qs, 2 10s).

* If he's on JJ, you have two outs (2 10s) to win, and eight outs (4 7s, 4 Qs) to split.

* If he's on TT, 99, or 88, you have 8 outs (7s and Qs).

* If he's on QJ, you have the equivalent of 2 outs to win (you need a running full house or quads), and 3 outs to split (the 3 remaining Qs).

In a hypothetical game, where you could calculate all of this on a spreadsheet or some such, and where you had a finite list of hands that your opponent would play this way, you could use Bayes Theorem to assign probabilities to each of his possible holdings (6xAA + 6xKK + 16xAK, etc...)

From that, you could determine the probability that you are ahead and by how much on average (your made equity), and the probability that you are behind and how many outs you have on average (your draw equity). Then you'd consider the probability that he will fold if you raise (steal equity). Finally, you'd consider the probability that you will call his flop bet and be forced to fold at the turn, plus the probability that you will draw to a second-best hand (negative equity). (E.g.: Your opponent is on KJ and a Q falls. You've made a Q-high straight, but he has a K-high straight. It would take an incredible read for you to get off this hand without losing a lot of money.)

You'd factor all of those equities in together, and reach a conclusion about how to play the hand.

In the real world, of course, you can't make exact calculations for such things; you simply don't have that much time to make a decision. So you make some quick estimates, based on your read of this opponent and your knowledge of how the odds generally work out in similar situations, and make your decision on an analysis which, while incomplete, is at least as complete as you can make in the time available.

Cris