1. Who coined "Fold Equity" and....

[ptmusic]

2. What EXACTLY does it mean? and....

3. How does one determine its value? and....

4. What do you do with that value?

e.g. Someone posts "you only had 15% fold equity." What does that mean - villain will fold 15% of the time? Is there some kind of mathematical formula that produces that percentage? Perhaps it is based on hero's stack size, villain's stack size, the pot size, and the tightness/looseness of villain? And now that you know hero's FE is 15% (it is hero's, not villain's, right?), what do you do with that 15%?

Or are most people just talking out of their ass when they state a percentage?

Thanks,

-ptmusic

[McMelchior]

[ QUOTE ]
are most people just talking out of their ass

[/ QUOTE ]
How charming. I get the sense from you post that you're not all that interested in discussing FE ... there are more positive ways of raising issues here.

That said, a way of evaluating your hand in a specific situation is to calculate/estimate it's equity. In the past insightful contributor have made some excellent posts on the subject (highly searchable), but let me just outline the idea here:

Pot equity is an expression of the average amount of chips you will win over an infinitisemal number of trials. If you have 30% chance of hitting your draw and will win if you do, your pot equity is 30% of the amount of chips in the pot. Notice that your chance of hitting your draw is an absolut value, but the assumption that you will win if you do is based on an estimate of your opponents holding(s).

In the excellent book "The Theory of Poker" Sklansky and Malmuth describes the concept "semi-bluff", as a way of adding value to a drawing hand. A semi-bluff is a bet (in a two-way pot) with a drawing hand, giving the bettor two ways of winning: he can hit his draw, or his bet can entice the opponent to fold a better hand.

How much value - the folding equity - that is added can be estimated based on knowledge of the opponent, generalised knowledge of what makes sense in the situation and what doesn't, and over/under type logic:

It's unlikely that the opponent will fold each and every time you bet the turn. A tight opponent will more frequently fold second pair/weak kicker. A "bubble" type tournament situation will increase the likelyhood that small stacks fold to a bet. Etc.

Quantifications - and especially succesful quantifications - of non-absolute values are essential for success in poker.

I guess techinically it would be correct to add a foot note with a disclaimer everytime we quantify estimated values. It just doesn't make one hell of a lot of sense.

Best,

McMelchior (Johan)

[Double Eagle]

1. Don't know

2. Fold Equity is the number of chips you figure to win by betting/raising in situations where you are trying to figure out whether betting/raising/calling/folding is the best action.

3. You calculate this by simply estimating the percentage of time that betting/raising will cause your opponent to fold and multiplying that percentage times the chips in the pot.

4. When trying to figure out if betting/raising (when closing the action) is better than calling/folding, add your Fold Equity (the times when you win the pot without a Showdown) to your Showdown Equity (the times when your bet/raise gets called). Showdown Equity is the amount of times your hand will be the best hand vs your opponent's range of hands after the river is dealt multiplied by the percentage of time your opponent will call your bet/raise.

As an example, let's say you have 2000 in chips with blinds at 75/150. You raise from the CO to 500 holding KQ and you are called by the button who has you slightly covered. You think the button is a little loose and you suspect that 50% of the time he's holding a weakish drawing hand and the other half of the time he has a mid pair 66-99.

The Blinds fold and the flop comes 235 rainbow. Should you check, knowing that he will likely move in regardless of his holdings and you will need to relinquish the pot, or should you move in and risk your remaing chips with King high?

To figure out if pushing is profitable in the long run you do the following:

First figure out your Fold Equity in this spot. If you move in the pot will contain 1225 from the action preflop and your 1500 chips and you would expect to win this 2725 half the time (for simplicity's sake we will say the flop will miss his non-pair hands 100% of the time and he will always fold those hands.) So our Fold Equity in this Pot is 2725*.5=1362.50.

Now half the time we will be called by the pair hands so we need to figure out what our Showdown Equity is in those situations. When our opponent calls the pot will be 4225 with the additional chips from his call. Using Pokerstove we can find out very easily how often we will win this hand by the river:

Board: 2c 3d 5h
equity (%) win (%) / tie (%)

Hand 1: 24.4444 % [ 00.23 00.01 ] { KQo }
Hand 2: 75.5556 % [ 00.74 00.01 ] { 99-66 }

So our Showdown Equity is now calculated by multiplying the pot size by the percentage of time we will win the showdown and by the percentage of time we will be called. In this case that is 4225*.24444*.5 = 516.3

Our final step is taking the Fold Equity (1352.5) plus our Showdown Equity (516.3) to calculate the Expected Value (1868.8) from pushing in this spot. So in this case risking our remaining 1500 chips by pushing would net us 368.8 chips on average and would qualify pushing as a very profitable move in this case.

Now by playing around with your assumptions regarding your opponents holdings and the frequency with which he will fold you can start to get a feel for how to deal with different types of players in the same circumstances. IE a profitable play vs a player who folds a lot might not be so profitable vs a looser caller.

Whew, I hope this helps.....

[Blindcurve]

[ QUOTE ]
Pot equity is an expression of the average amount of chips you will win over an infinite number of trials.

[/ QUOTE ]

FYP. Infinitesmal is very, very small.

[SoBeDude]

Very nicely done.

-Scott

[ptmusic]

Yes, I agree, very well done. It's still fairly complicated to me though, so I'll need to reread this multiple times to really get my head around it.

-ptmusic

[ptmusic]

Thanks. I did try a search for "fold equity" and didn't find anything as useful as the posts already in this thread.

But maybe my search missed something good.

Does anyone know any other good discussions on fold equity?

-ptmusic

[ptmusic]

A few follow up questions....

- Does fold equity apply at every round of betting? (I'm pretty sure the answer is yes)

- What if you are not heads up?

- Doesn't FE become nearly $0 when villain has very few chips or a whole ton of chips relative to the potsize? How do you incorporate relative stack sizes into the equation? What should your action normally be in such cases?

Thanks,

ptmusic

[Double Eagle]

[ QUOTE ]
A few follow up questions....

- Does fold equity apply at every round of betting? (I'm pretty sure the answer is yes)

[/ QUOTE ]


Fold Equity of course applies every time you bet or raise.

[ QUOTE ]

- What if you are not heads up?


[/ QUOTE ]

Still Applicable though harder to estimate when you start adding opponents.

[ QUOTE ]

- Doesn't FE become nearly $0 when villain has very few chips or a whole ton of chips relative to the potsize? How do you incorporate relative stack sizes into the equation? What should your action normally be in such cases?


[/ QUOTE ]

Yes there are times when your FE is so close to zero that it is irrelevant to the analysis. In those cases Showdown Equity is the only component in the equation.

[ptmusic]

I feel I'm close to "getting" it, but I'm stuck on some math stuff. Any help by anyone would be most appreciated.

Why wouldn't one do the math as follows (using your assumptions about villains range and folding likelihood):

50% of the time, villain folds, hero wins the current 1225, for and EV of .5(1225)=+612.5

12% (or 24% of 50%) of the time, villain calls, hero wins the 1225 plus villain's call of 1500, for an EV of .12(1725)=+207

38% (or 76% of 50%) of the time, villain calls, hero loses the 1500 he just pushed, for an EV of .38(-1500)=-570

Thus, hero's EV for pushing right now = 612.5 + 207 - 570 = +249.5


I guess I don't understand why our hero's upcoming push bet should be included in the calculations of what he wins. He either wins the pot plus anymore money villain puts in, OR he loses the money he is about to bet.

In this article I just found here (http://teamfu.freeshell.org/tournament/theorem_blind_stealing.html), and this post I found here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1978062&page=&view=&s b=5&o=&vc=1), they seem to do the calculations without incorporating the hero's upcoming bet.

In your calculation, you subtract the push bet at the end in order to come up with a final EV. Your way makes sense to me, but so does mine. But our EV's are different by a significant amount.

Am I wrong? I'm not sure....

-ptmusic

[PrayingMantis]

Here you go:

FE discussion (http://archiveserver.twoplustwo.com/showthreaded.php?Cat=&Number=888770&page=&view=&sb =5&o=)

There were also a few discussions at the mid-high NL forum about who coined it, but obviously it doesn't really matter, because good players always understood this concept intuitively, even without giving it a name.

[ptmusic]

Thanks buddy!

Anyone with some help on the math in my last post in this thread?

-ptmusic

[Double Eagle]

[ QUOTE ]
I feel I'm close to "getting" it, but I'm stuck on some math stuff. Any help by anyone would be most appreciated.

Why wouldn't one do the math as follows (using your assumptions about villains range and folding likelihood):

50% of the time, villain folds, hero wins the current 1225, for and EV of .5(1225)=+612.5

12% (or 24% of 50%) of the time, villain calls, hero wins the 1225 plus villain's call of 1500, for an EV of .12(1725 this amount is incorrect, should be 2725 )=+207 should be 2725*.12 = 327

38% (or 76% of 50%) of the time, villain calls, hero loses the 1500 he just pushed, for an EV of .38(-1500)=-570

Thus, hero's EV for pushing right now = 612.5 + 207 - 570 = +249.5


I guess I don't understand why our hero's upcoming push bet should be included in the calculations of what he wins. He either wins the pot plus anymore money villain puts in, OR he loses the money he is about to bet.

In this article I just found here (http://teamfu.freeshell.org/tournament/theorem_blind_stealing.html), and this post I found here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1978062&page=&view=&s b=5&o=&vc=1), they seem to do the calculations without incorporating the hero's upcoming bet.

In your calculation, you subtract the push bet at the end in order to come up with a final EV. Your way makes sense to me, but so does mine. But our EV's are different by a significant amount.

Am I wrong? I'm not sure....

-ptmusic

[/ QUOTE ]

Actually either method works to come up with the answer. The reason you came up with a different answer has to do with the pot size you used in the cases where your push gets called and you win. I've bolded the correction above.

[ptmusic]

[ QUOTE ]
[ QUOTE ]
I feel I'm close to "getting" it, but I'm stuck on some math stuff. Any help by anyone would be most appreciated.

Why wouldn't one do the math as follows (using your assumptions about villains range and folding likelihood):

50% of the time, villain folds, hero wins the current 1225, for and EV of .5(1225)=+612.5

12% (or 24% of 50%) of the time, villain calls, hero wins the 1225 plus villain's call of 1500, for an EV of .12(1725 this amount is incorrect, should be 2725 )=+207 should be 2725*.12 = 327

38% (or 76% of 50%) of the time, villain calls, hero loses the 1500 he just pushed, for an EV of .38(-1500)=-570

Thus, hero's EV for pushing right now = 612.5 + 207 - 570 = +249.5


I guess I don't understand why our hero's upcoming push bet should be included in the calculations of what he wins. He either wins the pot plus anymore money villain puts in, OR he loses the money he is about to bet.

In this article I just found here (http://teamfu.freeshell.org/tournament/theorem_blind_stealing.html), and this post I found here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1978062&page=&view=&s b=5&o=&vc=1), they seem to do the calculations without incorporating the hero's upcoming bet.

In your calculation, you subtract the push bet at the end in order to come up with a final EV. Your way makes sense to me, but so does mine. But our EV's are different by a significant amount.

Am I wrong? I'm not sure....

-ptmusic

[/ QUOTE ]

Actually either method works to come up with the answer. The reason you came up with a different answer has to do with the pot size you used in the cases where your push gets called and you win. I've bolded the correction above.

[/ QUOTE ]

That's the kind of mistake that screws up your SAT or GMAT score! Thanks. I really get it now!

Okay, if you (or any of the 400+ folks lurking) are still with me, here is the BIG QUESTION:

How do you determine the Fold Equity Percentage?

In your example, to teach the math more easily, you chose a very simple FE percentage of 50%. Good choice!

But in the real world, how do you guesstimate the percentage of time your opponent will fold?

-ptmusic

[Double Eagle]

You can never correctly calculate the percentage, all you can do is estimate it based upon your opponents range of holdings, tendencies, etc.