Fold Equity Formula - Needs Explaining

[madtom1337]

I've read in 'Let There Be Range' that you can calculate fold equity by plugging numbers into a fold equity formula. It doesn't bother demonstrating how to and why to use it, it doesn't give any examples. I really pity anyone who paid the full price for such a lack of attention to detail, but regardless, here's the formula:

0 = XP + (1 - X)(-LV + WH)

Where...

X = Breakeven Folding Frequency
P = Current Size of the Pot
L = Maximum Loss
V = Villain's Equity
W = Maximum Gain
H = Hero's Equity

So... My questions...

1) Is this of any use whatsoever in practice? If not, I presume there may be some use to understanding the theory of this formula.

2) What is 'Breakeven Folding Frequency?'

3) Fold equity isn't a variable in the equation, so how do you get to it?

4) To get villain's equity, would you just take your own equity estimation and subtract that from 100?

5) If, for example, your equity (Hero's Equity, H) is 30%, do you translate this into a decimal and put 0.3 into the equation?

I think that's about it for now.

Thanks.

 

[Pascal-lf]

You planning on working all that out on the go?

 

[madtom1337]

Erm, I dunno... Is it just for HA then? Lol

 

[Dwilius]

1) as an estimation from experience when you're playing, sure. To study more exactly afterwards so have the background to estimate in the future, absolutely.

2) The equation is set to equal zero (when the play is breakeven; money you win from folds = money you lose when called), that's why X is referred to as breakeven folding frequency instead of just folding frequency.

3) I need to check the exact definiton of fold equity.

4) yes, villains equity will be 1 - yours (that is from the comparison of how your hand fares to the range of hands he calls with)

5) yes.

 

[slycbnew]

3 - "fold equity" isn't a variable because it isn't precise. If you calculate the breakeven folding frequency (i.e., as long as Villain folds this often given the play I'm making/money I'm putting in the pot given the equity I have in the pot, I will breakeven over the long run), you think of this as "I need Villain to fold at least this often just to break even". If you feel it likely he will fold more frequently than the break even point, the play is profitable, if you feel he's not likely to fold as frequently as the break even point, it's not a profitable play.

 

[smurray139]

That would be ridiculous to work out in one go.

 

[Effexor]

1) Is this of any use whatsoever in practice? If not, I presume there may be some use to understanding the theory of this formula.

The theory itself is far more important than the formula, which you will never use in practice.

2) What is 'Breakeven Folding Frequency?'

It's an estimation on your part:

Lets say there is a $100 pot after all the cards are out, and you know for sure you don't have the best hand. By your estimate, the villian will fold 1/3 of the time to a $50 bet, and the other 2/3 of the times he will call and you will lose. That is the Breakeven Folding Frequency.

1/3 of the time you will win $100 and the other 2/3 of the times you will lose $100

3) Fold equity isn't a variable in the equation, so how do you get to it?

Once again, it's an estimation on your part. Your goal is to find the amount that has the highest average return based on your opponent. I don't want to go into the math here, because I suck at that. But it should be clear that the more or less you bet will affect how often the opponent will fold. This is obviously based on a multitude of factors such as board textures, the range you put your opponent on, your perceived range, the frequency the opponent actually is willing to fold etc etc.


.

hope that was clear

 

[F Paulsson]

The most common definition of fold equity is the direct value of getting a fold. That is, the likelihood of a fold times the size of the pot. It's not a great definition because it misses a lot of finer points, but it can be expanded:

Fold equity is the "value" of getting a fold, and then we're ignoring all the hands that are drawing dead versus us (obviously common on the river), and instead look at the average equity of the hands that fold and how often they fold. So if he folds 50% of the time with an average equity of 30%, then our fold equity is 0.5*0.3*pot size.

Slight derail: I've been toying in the past with the idea of what's essentially the bastard child of reverse implied odds and fold equity. Two examples to show what I mean:

If a turn bet will make people fold a gutshot draw, our fold equity would be something like 10% of the pot size (his chance of hitting) for that range. Except that's not a good estimate for his equity when we have a strong hand. His EV is in fact better than that since HIS implied odds are better than just the money in the pot on the turn; we will likely pay a big price on the river when he gets there. This, I argue, should be included in estimating the value of getting a fold. It's not just the equity we fold out of the current pot, but the money we save by not paying him off on the river.

Or perhaps even more clearly: Flopping bottom set. Folding out a higher pocket pair is worth quite a bit more than just his two outs times the pot size, because if he spikes on the turn, we're often going to lose our stack.