Fold Equity

I would like to hear a good explanation of "Fold Equity." If I have had it explained to me then I guess I haven't really understood it so I would appreciate hearing it again please?

Determining the expected value of a bet is as follows.

We win the pot whenever villain folds.

We win the pot and villains call whenever villain calls, and we end up winning.

We lose our bet whenever villain calls and villain wins.

Expressed mathematically, p is the pot size, x is our equity, b is the bet, and f is how often villain folds we get

EV = PF + (1-F)*((P+B)x - b(1-x))

So, one way to think of expected value is of being a function of how often villain folds.

For different x,b, and p, it is possible that our EV can be negative, zero, or positive and in varying degrees.

Ok...now to answer the question :P

Fold equity is simply shorthand for defining what is needed to increase our EV. So if villain folding improves our equity then we want some fold equity when we make a bet. If villain folding makes our equity go from negative to otherwise...then we NEED fold equity.

Example time

We have 33% equity for some reason...lets say its a flush draw. We shove all in for 2x the pot, and the pot is currently $1. Whats our EV?

EV = PF + (1-F)*((P+B)x - b(1-x)) as before. Subbing in our equity, bet size, and pot size we get

EV = $1*F + (1-F)*(($1+$2)*.33 - $2*(1-.33))....ok stay with me here

Simplifying
EV = $1*F + (1-F)*($1 - $1.33) = $1*F + (1-F)*(-$.33)

EV= $1F +$.33F -$.33.

So thats our Expected Value without knowing how often villain folds.

So...do we need fold equity?

Well if villain never folds then F=0. So EV = $1(0) +$.33(0) -$.33 = -$.33

So if villain never folded we'd on average expect to lose 33 cents each time we shoved $2 to win $1 with 33% equity here. So we do in fact need some fold equity for this play to be breakeven...and a lot of it to make this play +EV.

As it so happens...EV is a linear function with respect to how often villain folds. So if villain folding at all improves our EV...then we want villain to fold as much as possible. So we would expect that villain folding 100% of the time would greatly increase our EV

Sure enough...if villain always folded then F=100%=1
EV= $1*(1) +$.33(1) -$.33. = $1, a positive expectation as opposed to our previous negative one.

And for a break even point...

EV = $1F +$.33F -$.33 = 0 for a breakeven expectation
F($1+$.33) = $.33, getting all the F's to one side and factoring it out
F=$.33 / ($1.33) = 25%

So we'd need villain to fold at least 25% of the time for our play to be breakeven. In this case, ppl will often call that 25% needed to be the required fold equity.

I guess I should have prefaced this with " I only completed basic math in high school 30 fucking years ago!"

LMAO at my dumbass

I will read through this and try and figure it out. If anybody else want to jump in and take on the challenge of helping the old guy give it a shot.

All is appreciated!!!

You will definitely be able to figure out. Just work through it slowly.

In simple terms, Fold Equity = likelihood an opponent folds * gain in equity if opponent folds.

Poker Strategy Tips - All You Need to Know About Fold Equity - PokerListings.com

A simpler way without all the mathy justification

We bet something like 1 into a pot of 1. If villain always calls...then we're risking 1 to actually win 2 right?

So we need to have at least 33% equity in the hand in order to profit (1:2 pot odds, 1:2 hand odds). If we dont have that much equity...then we need villain to fold at least some percent of the time, and our expectation increases the more he folds.

If we have more than 33%, then we dont need fold equity..but might still want it to increase our expectation.

maybe that is a simpler answer

I like how the concept of hand combinations wasn't mentioned in this thread yet.

I just got back from a jog and will probably explain that and its connection to fold equity later. For now, I gots to eat and shower.

Hopefully somebody else will comment on hand combinations and fold equity before I get the chance to do so.

i'll give a brief, fishy insight.

we can determine how many possible combinations of certain hands a villain can have based on how many of each card there is left in the deck. look up spoons "how to: calculate hand combinations" post (title is something like that, search it and you will be rewarded) to learn how to determine the possible combos. basically once we know how many combinations of hands are in villains range, we can make an estimate as to how he plays each hand. for simplicity, if villain bets into me on the river with a range of 120 combos, and he folds 60 of them to a raise, he's obviously folding 50% of that range to a raise. which will be the number we use for villain's fold % in our EV equation. this probably isnt clear enough without an actual hand example. i certainly struggled understanding this without seeing it done in relation to the actual play of a hand. i made a thread once called "EV calcs thread", HarleyGuy. Kiwi and Stacks, amongst others, helped me out in doing this kind of stuff in there, so that might also be worth you checking out (there are hand examples there)

ask in irc is probably the best bet

Thanks guys your explainations and patients are very much appreciated!

Originally Posted by HarleyGuy13

I guess I should have prefaced this with " I only completed basic math in high school 30 fucking years ago!"

LMAO at my dumbass

I will read through this and try and figure it out. If anybody else want to jump in and take on the challenge of helping the old guy give it a shot.

All is appreciated!!!

OK, y'all leave the non-mathematical explanation to me, why don't ya?

Fold equity is the times Villain folds because of the way the hand plays out when it's not justified based on our hand. If we're running a semi-bluff, we usually need a chunk of fold equity, or it fails. For a cbet to work, we need some fold equity.

You can think of fold equity like showing up with the bottom of your range. You don't have much, but folks'll believe you've got something good.

Example 1: You hold 55, a TAGG image and bet your normal opening raise from the HJ. The BB calls and everyone else folds. The flop is AQ8, he checks and you cbet. You have tons of fold equity here. You don't have much real equity, since you're behind even junk like 86o all of a sudden, but there's a reasonable chance he'll fold hands like 77 ad 66 a lot.

Example 2: You hold TT in the HJ, open with your standard raise and get called from the BB. The 976 two-suited flop is checked to you, and you bet your overpair + GSSD. Here, you just have regular equity.

Example 3: You hold 98s and 3b from the blinds against a BTN steal, and the flop is AQJ, and you bet right out half the pot on the flop, counting on some fold equity. A lot of ppl's 3b range has mostly Ax, so if he doesn't hold an Ace he's likely folding. Of course, a lot of the stealing ranges have Ax in them tons, too, so this one's read dependent. And I'm not saying you should 3b 98s, by the way, just giving a clear example of fold equity.

Fold equity is about spots where we've got a better chance of villain folding than we deserve to, just based on our cards.

To relate it to the mathematics above, we NEED fold equity when we don't have quite enough card strength to make a certain bet. If our range "looks" strong enough, we can still bet (semi-bluff) profitably. In the same situations, if we don't have any fold equity, we're better off not continuing.

I think about it as a risk/reward ratio. If you risk too much for the money already in the pot; then your opponet only has to have you beat fewer times. They can fold more often and still make money. Fold equity.

may i suggest you read JKDS' first two posts in this thread? as best i know, fold equity is about the value we gain by getting a hand to fold which is technically correct in calling based on pot odds/equity etc.
ie if we bet the pot on the turn with As 4s on Ks Js 4h 8c, and villain folds Jh Qh then we gained from fold equity. villain was getting 2:1 (33%) pot odds on the turn with a hand that was


Board: Ks Js 4h 8c
Dead:
equity win tie pots won pots tied
Hand 0: 68.182% 68.18% 00.00% 30 0.00 { QhJh }
Hand 1: 31.818% 31.82% 00.00% 14 0.00 { As4s }

68% favourite to win the hand. so if villain knew what we had, he would have known it was mathematically correct to make the call. but he folded. if we agree to check it through after the turn, we win 32% of the time with our pair+FD, however betting and making villain fold increases our share of the pot from 32% because a certain % of the time villain folds.