Fold Equity

05-06-2008, 08:24 PM

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hockeyplayer12

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Fold Equity

Just a quick question: Can anyone explain the principe behind Fold Equity or what its benefit is? I know it sounds like a newbie question...and it is lol. I hear alot of people throwing it around but I dont quite understand the concept, any help would be awesome THANKS!

05-06-2008, 10:18 PM

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k06mars

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Fold equity is essentially the value you have in your opponents folding, multiplied by the chance you put them on folding. Let's say there's 1000 in the pot, and you figure with your bet of 500 they will fold 40% of the time. in this case, your fold equity is 400.

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05-06-2008, 10:41 PM

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gimmemymoneyback

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Have absolutely no clue what you just said mars. I will take a pass on fold equity.

I guess your final number of 400 is the amount you must bet to get your opponent to fold is this correct?

Last edited by gimmemymoneyback; 05-06-2008 at 10:55 PM.

05-07-2008, 02:47 AM

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k06mars

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Quote:

Originally Posted by gimmemymoneyback

Have absolutely no clue what you just said mars. I will take a pass on fold equity.

I guess your final number of 400 is the amount you must bet to get your opponent to fold is this correct?

No - fold equity is the amount you would expect to gain from the hand, if you only consider the possibility of your opponents folding (i.e., you're on a total bluff).

Let me try this again:
You're heads up in a pot with any given villain. There is 1000 in the pot on the river, and you have nothing more than middle pair. You figure your opponent to have top pair, mid kicker. He's playing a little scared, and so you figure you can bluff him off the pot. However often you think he'd fold to your bet of size X, multiply that by 1000 to get your fold equity for your bet.

So, you bet 800, and villain folds 65% of the time. This means on average, you will win 650 chips. One thing I forgot to add in my initial explanation is you also have to figure in the times you'd be called down. So, continuing with our example, 35% of -800 is 280. Subtract your losing number from your winning number - 650 - 280 is 370, which is what your equity would be for the hand.

One thing you have to consider, though, is there will be a number of times when you WON'T know if your hand is best, and at that point the numbers get a little complicated.

Let's take our above scenario - 1000 in the pot, you bet 800 with middle pair. 65% of the time villain will fold, the other 35% of the time he will call you down. Let's also say you think there's a 40% chance that you actually have the best hand. Let's add up all of our equities, then:

Villain folds: +650
Villain Calls and wins: (-800 - this is the amount you lose) * (35% * 60% - this is the likelihood of you getting called and beat) = -168
Villain Calls and loses: (1800 - this is the amount in the pot + villain's call) * (35% * 40% - this is the likelihood of you getting called and winning) = +252

Add everything up, and your equity for this situation is 734 - you would expect to take down (on average) 734 of those 1000 chips. This would make your bet a winning play; however, if you played around with the numbers I'm sure you could get a more profitable play by risking a little less. This would increase the probability of you getting called, however - so you have to find the highest spot on the equity curve.

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05-07-2008, 04:36 AM

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CardLovinCat

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I got a headache trying to follow this.

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05-07-2008, 06:04 PM

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hockeyplayer12

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Thanks for the detailed info!!!!!!!! was a little confused on the frist post, but your 2nd was much clearer, THANKS MAN!Ill have to practice those principles a few more times before i use them in a real siuation but with time should help understand certain situations. Thanks again!

05-07-2008, 06:12 PM

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k06mars

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Okay, I have a little bit of time to spare (currently waiting to take a final), so I'll expand upon my last point, which is that playing around with numbers will yield different results.

Once again, you have 1000 in the pot. Let's say, though, that you decide to make a bet of only 600, and this would result in villain folding 50% of the time. Win % numbers are the same; i.e., you will lose the hand at showdown 40% of the time.

So, your equity would be:
Fold: 1000 * 50% = 500
Call and lose: -600 * 50% * 60% = -180
Call and win: 1600 * 50% * 40% = 320

Add them all up and your equity is 640 - so not quite as high as when you decide to bet 800, you should stick with an 800 bet.

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05-08-2008, 02:20 AM

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JayC170

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Very informative post Mars, definetly developed my understanding of it, Thanks!

05-08-2008, 03:09 AM

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CalifNaughti

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I think my fold equity was spot on for this. To be honest I dont even think about things like that ..especially if I dont understand them. What I do understand is this..in a hand just like this...was a no brainer to me.

PokerStars Game #17275849979: Tournament #82217926, $10+$1 Hold'em No Limit - Level V (75/150) - 2008/05/07 - 22:06:16 (ET)
Table '82217926 1' 9-max Seat #2 is the button
Seat 1: GWCGWC (5455 in chips)
Seat 2: Cantonese (2360 in chips)
Seat 3: CalifNaughti (5490 in chips)
Seat 4: hoodini (2340 in chips)
Seat 5: montrealphil (3332 in chips)
Seat 6: 'olnumber7 (2165 in chips)
Seat 7: Hub Dub 04 (4733 in chips)
Seat 8: armen13 (4430 in chips)
Seat 9: rdog7811 (1035 in chips)
CalifNaughti: posts small blind 75
hoodini: posts big blind 150
*** HOLE CARDS ***
Dealt to CalifNaughti [Ah Th]
montrealphil: folds
'olnumber7: folds
Hub Dub 04: folds
armen13: folds
rdog7811: raises 885 to 1035 and is all-in
GWCGWC: raises 885 to 1920
Cantonese: folds
CalifNaughti: folds
hoodini: folds
*** FLOP *** [8c 5c 3h]
*** TURN *** [8c 5c 3h] [Qd]
*** RIVER *** [8c 5c 3h Qd] [Ts]
*** SHOW DOWN ***
rdog7811: shows [Qc Jc] (a pair of Queens)
GWCGWC: shows [Ac 9c] (high card Ace)
GWCGWC said, "nh"
rdog7811 collected 2295 from pot
*** SUMMARY ***
Total pot 2295 | Rake 0
Board [8c 5c 3h Qd Ts]
Seat 1: GWCGWC showed [Ac 9c] and lost with high card Ace
Seat 2: Cantonese (button) folded before Flop (didn't bet)
Seat 3: CalifNaughti (small blind) folded before Flop
Seat 4: hoodini (big blind) folded before Flop
Seat 5: montrealphil folded before Flop (didn't bet)
Seat 6: 'olnumber7 folded before Flop (didn't bet)
Seat 7: Hub Dub 04 folded before Flop (didn't bet)
Seat 8: armen13 folded before Flop (didn't bet)
Seat 9: rdog7811 showed [Qc Jc] and won (2295) with a pair of Queens

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05-08-2008, 04:13 AM

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k06mars

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OK, let's take Cali's above hand and examine it - it brings up how fold equity comes into play when someone is all in.

When it gets to Cali in the small blind, the pot is at 3180. However, fold equity does not apply to all of this, as rdog7811 is all in (and therefore can NOT fold). With that said, there is a (albeit relatively small) side pot of 885 which exists. To obtain the fold equity of this sidepot, we compare the raise she is considering with the probability of GWCGWC folding.

Her raise will have to be at least 885 on top of villain's raise, which would make her total bet AT LEAST in the range of 3000, over half her stack. Because of this, we should probably just consider the all-in option. Now, villain is already fairly committed to the pot, I think we have to place his probability of folding at a mere 5%. Now, let's change the scenario up a little bit (as if Cali knew villain had A9, she would have pushed) - let's say villain has Cali dominated, and holds AJ - for the sake of making the math easy, we'll say he's a 75% favorite. Then the fold equity looks as follows:

Villain folds = 885 * 5% = 44.25
Villain calls, Cali loses = -5455 * 95% * 75% = -3886.6875
Villain calls, Cali wins = (5455-1035) * 95% * 25% = 1049.75

Add them all up, and Cali's all-in bet would lose her 2792.6875 chips on average each push. In other words, if someone goes all in, don't bluff for a small side pot!!

Now, let's make things a bit more complicated - we'll include the all-in player in the calculations (as there IS a main pot involved here, too!). For this, we'll go with a 5% fold chance for GWCGWC, and assume both villains have the same hands as they did in Cali's HH (i.e., Cali is the favorite):

Villain folds	(885 * .05) + (chance of Cali winning main pot) * 2295
	(885.05) + (.57142295)
	44.25+1311.363
	1355.613
Villain calls, Cali wins side pot, and main pot	(8635.95.3985)
	3268.995125
Villain calls, Cali wins side pot, not main pot*	(5455-1035).95.6435*.5714
	4420.95.6435*.5714
	1543.9550841
Villain calls, Cali loses side pot and main pot*	(-5455).95.2604
	-1349.4579

*I evaluated ATs vs A9s and QJs individually, not as they faired with 2 cards in the deck dead. Because of this, ATs has a slightly higher chance of winning in both situations than actually stated.

Anyways, add it all up together and Cali's equity for pushing in her spot would be: 4819.1053091. In other words, it would generally be a very profitable play to push in her spot. With that said, you also have to consider the fact that this is a tournament - and so equity isn't quite what it seems. While she may be winning chips on average in this situation, those chips hardly guarantee her a win (or even a good cash) in a tournament. Meanwhile, if she loses, she is EXTREMELY crippled, and has very little chance of even cashing.

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