Let me know if Im doing this math correctly regarding required Fold Equity. This is a real hand...

EP ($1000) opens $15.
Button ($600) calls.
Hero ($1300) calls JsTs SB
BB ($600) calls

Flop ($60) 5s5c4s. Check to EP raiser who bets $35. Button calls.
Hero check raises to $135. BB folds.

EP reraises to $275. Button folds. Lets say I decide to jam it all in here. If he calls.....Ill be putting in $865 at this decision point and the total pot will be $2095 if he calls. I'm putting in 41% of the money.

Lets say he has 9h9d. I have about 50% equity so if he calls I'm obviously OK.

Lets say he has KhKd. I have about 30% equity. Can I subtract the 30% from 41% and say I only need 11% FE for this jam to be neutral EV and if he folds more than 11% of the time its a +EV play?

We can talk about whether I should not have check raised in the first place or whether I should just call the flop reraise, but I want to know if I'm calculating needed FE correctly.

To prove (or disprove) I think it would just be a matter of doing the math on your guess. So 11% of the time you take down the pot compared to 89% of the time you don't and then have to compare the 30% of the time you win vs the 70% of the time you lose. I'm too lazy to math, but if it works out to $0 EV then likely your guess is right?

Gno?G

https://redchippoker.com/fold-equity-calculator/

I didn't get 11% when I plugged in your values assuming a 30% equity against KK, but who knows I could be adding in your values wrong. I got 32% so you need villain to fold 1/3 of the time with QQ-AA to make it profitable.

If we knew villain's range was 77-99 a shove here would be great and wouldn't even require fold equity, but any extra fold equity just makes it all the better.

First you need to split V's range on the turn into a folding range and calling range.

Then you need to calculate what % of villain's range is made up of each.

Then you need to calculate your equity against villain's entire calling range.

Then the play's EV is ( (POT * FOLD %) + ( (POT + BET*2) * EQ vs CALL RANGE - BET) * CALL %

The easiest way to estimate is to start with what % of villain's range will fold. If you bet pot, villain needs to fold only half the time for the play to be immediately profitable. If villain calls 2/3rds of the time, then you would lose 1/3rd of a PSB if you had 0 equity. You would break even if you had 33% equity, but that is a lot and fairly unlikely.

But just because a play is +EV doesn't mean it's the best. It could be that checking or calling is more +EV, and folding is always 0EV even though we don't usually think of it like that (if someone bets into you on the river, and you have the nuts, and I say what about folding, you would say "but that is lighting a ton of money on fire", not "that is 0EV")

in short fold equity is a @#$%^ to calculate because there are a ton of variables and you're not even sure what you are calculating it in comparison to.

No.

And we are playing against a range of hands, not KhKd. As someone else already pointed out, it's generally pretty complicated to calculate. You'd either have to set very specific/simpler assumptions such as assuming you have zero equity when called, e.g. how much of his range has to fold for our 3b shove to be instantly profitable, similar to 3-betting preflop and the required fold equity to immediately breakeven/profit assuming you don't see a flop/have zero equity when called. this one is not hard to calculate, but it's missing a lot of information because you obviously do have equity when you get called, or you in the 3b preflop hand you end up leaking money when you flop a pair or cant get away from TP, etc. or second you end up making a model with too many variables that you assign subjective probabilities/EV and calculate the EV, and compare your hand equity vs that range, which would also not be very accurate.

X/r is getting into grey territory but most likely better than flatting. Folding is probably the best play given flop is 4-way and his cbet range here is going to be tighter on a board that sucks for his range and given there's 4 people in the pot than vs HU. Imo fold >>>> raise > call. He also has a ton of NFDs which aren't folding and you're only getting stacked by those hands, and he should have 55/44 here and some 54s which you draw dead against. Also you dont really rep much on this board and have a lot of perceived bluffs. BTN is also uncapped here and can have NFDs/5x slowplays/FHs and obviously BB can have every 5x/FH here as well/is uncapped, so raising is pretty big spew.

There’s an equation for FE. Yours is not it and it’s certainly not sometihing you’ll be doing in your head at the table.

So what is it?

For the record I did jam it in, but that's not the point. I want to know what the formula is for future reference.

Mike, here's my math on your *specific* up-against-KK case using your numbers and your hypothesis. I did this quickly so you should probably double check for mistakes.

11% of the time we take down $370 = $41.

89% of the time we get called and 30% of those times we win $1215 = $324.

89% of the time we get called and 70% of those times we lose $850 = -$530.

For an overall EV of -$165.

So, if I've mathed right (???), it suggests your hypothesis ain't correct.

And of course it gets even trickier/uglier/hazier when you start factoring in ranges and weighted actions (as suggested above).

GcluelessmathnoobG

https://redchippoker.com/fold-equity-calculator/

you need to figure out your equity vs his continuing range and then see what part of his min-raising range he is actually folding, hope this simplifies things

For this exercise I dont care what part of his range hes folding. Im not trying to determine if this is a good play or not. I just want to calculate how often he has to fold if he has X% of equity to make the overall play +EV. If he has a QQ-AA then he has about 70% equity so how often does he have to fold that to make the play +EV.

There's not $370 in the pot when we jam. There's $505.
So if he folds 11% of the time, we win $505 11% of the time. = $56

I think your other numbers are wrong also.

If he calls, the 30% of the time we win, we win the $505 pot plus the additional $725 he has to put in = $1230

Im not sure where you got $1215 from.

X*505=((1-X)*.3*1230)-((1-X)*.7*865)
Fold rate * pot = call rate times equity times pot minus call rate times 1-equity times raise size.

Solve for X to give you the break even fold rate. If he folds more than that you win less than that you lose.

I'm trusting GG's math on pot sizes btw. Edited because GG was wrong haha.

Yes , but his continuing range will determine your equity when called, idk if you clicked on the link but if you fill in the boxes it will tell you how often you need to generate folds to break even

so you want to see if you generate folds more frequently than that percentage for this play to be +EV

you can play around with it and put in worst case scenarios such as QQ+ , so put in 30% for equity when called , and see what the last box says

@ Mike

Early in the morning when I did that one so I definitely wouldn't trust.

But basically, just make sure you plug in the proper numbers (at first glance your $505 looks more correct than my $370, and I haven't bothered to double check the other ones). If it doesn't come out to about $0, then you likely can't think the way you were thinking with regards to what FE you need; if it does, then there's a chance the thinking (against that very specific KK case, yada yada yada) may be ok.

ETA: I think the other slight discrepancy is to do with the fact you say you have $865 left (effective against EP) but I think you actually have $850 (if I've added right, which there is like a 50/60 chance I've done). Just break it down and show your work and I'm sure you'll come up with the right numbers.

GaddingishardG

I looked at the calculator but it doesnt make sense to me.

It wants me to enter pot size before I shove...which is $505
How much I have to call...which is zero since Im not calling anything
How much am I shoving which is $1000.....but do I enter $725 since thats what HE has to call after already putting in $275? Doesnt make sense

I think the correct answer may be about 25% of FE needed if he calls and his hand has 70% equity.

he raised you 140 right ? this is the amount that you would have to call (hypothetically)

there's a video if you scroll down that explains it

in this case you want to put in : [505, 140, 865] ( this is what you are shoving at that point) and yes you are only looking at effective stacks so you would do 140 + what ever else you can shove for effectively which is 725

and then put in the estimated percent that he folds , I'll look over the post again to confirm but im pretty sure this is accurate

this is what you want to use for what you are shoving for total

calculating eff shove: 1000-15-135= 850

and then with 30% equity ( which is pretty worst case)

you'd need greater than 31% folds to be profitable here

According to applications of no limit hold em (page 5), you risk your bet of x to win the pot p. The equation to determine your odds to break even, assuming you lose every time you are called is x/(x+p)

So in this instance, the equation is 850/(850+470)= 64%

You need a fold 64% of the time for this to work, which makes sense since your bet is larger than the pot.

That was the base case with the easy equation you can do at the table, and holds true for bluffing with a hand that has 0% equity. Since you have equity you can calculate the EV of this line, but that requires going into ranges and more math.

I need a fold 64% of the time if I'm drawing dead. That has nothing to do with what this thread is about.

So what are you trying to calculate?

I thought you wanted to know the equation to calculate required fold equity.

Are you trying to calculate required fold equity given your hand on this board?

Assuming that I have 30% equity when called.....how often do I need him to fold for this move to break even considering that Im putting in 41% of the total money.

You've shown that he needs to fold 64% of the time if I'm drawing dead but unless he has 44 or 54 I'm not drawing dead.

I think he has an overpair. If he has an over pair QQ+ then I have 30% equity so if Im right, how often does he need to fold for my 4 bet jam on the flop to be at least breakeven?

Im not worried about his entire hand range. I just want to know if there's an easy to use formula for required FE with a given amount of equity when called.

There is an easy formula.
W = percent you win = 30%
L = percent you lose = 70%

0 = W*(2095-850) - L*850 + x*505

You need to solve for x that is the percent fold equity you need.

2095 is the total pot you win 30% of the time but you need to deduct the 850 because that isn’t profit

850 is what you lose 70% of the time

And 505 is what you make if he folds.

The answer is 43%