Can someone define Fold Equity, Pot Equity and Hand Equity

[Borno]

The discussion on equity formula is far too confusing for me. Please define this and expalin how they apply to SSNL HE.


Thanks!!

[PokerFink]

Pot equity is the percentage of the pot that is "yours" based on how often you will win the pot. For example, lets say you are all-in preflop with AA vs KK, and the pot is $100. You are roughly a 80%-20% favorite. Therefore, your pot equity is 80% of the $100, or $80. The KK's equity is just $20.

Fold equity is not so simple, but it is implied equity based on how often you feel your opponent will fold. For example, lets say you are on the river heads up, and you have a hand that will never win a showdown. The pot is $100. You feel that if you bluff by betting $50, your opponent will fold 50% of the time. Therefore, your fold equity would be $75 (50% of the pot, which is now $150 with your bet in it), and this bet is positive EV, because your fold equity of $75 is greater than the bet of $50.

[elmitchbo]

i still don't think this defintion of pot equity is correct. i have been in this argument before in other threads with opinions on both sides. somebody please give me a solid answer.

i say your pot equity is the amount you represent in the pot regardless of your cards. so with your example.... if your heads up your have 50% pot equity, but considering you have an 80% chance to win with your AA you have a 30% pot equity advantage. if it was a 4 way pot then you would have 25% pot equity, regardless of what cards were held by any of the players. this is why drawing hands are profitable against multiple opponents, and top card hands are better against few opponenets. i'd like for someone to really clear this one up for me.

fold equity is tricky. if i can't figure out the first question i won't really take a stab at the second question.


edit: i think what pokerfink described is hand equity.

[PokerFink]

I'm not 100% sure what you're trying to describe, but it isn't pot equity.

In the AA example, the AA's equity is 80%. You could call this hand equity, although I had never heard that term. Once you relate that to the pot size, you get pot equity ($80).

The reason that drawing hands are good multi-way has to do with the pot size, since multi-way pots are usually bigger. You only have to put in one bet to win a big pot (instead of a small heads-up pot), giving you better pot equity for one bet.

[elmitchbo]

i still think your wrong, but it's partly because of semantics. the reason drawing hands are better multi-way is because they offer big pots, which is basically the same as pot equity. if you have a flush draw in a 4 way pot you have 25% pot equity, but a 35% chance of making you hand by the river. that gives you a 10% pot equity advantage(read: hand equity). if you have the same flush draw in a heads up pot you have 50% pot equity but the same 35% chance to make the hand, putting you at a 15% pot equity disadvantage. your hand equity or drawing odds didn't change, put your pot equity did. that's why drawing hand are better multi-way.

anybody else want to weigh in?

[Yosemite Mark]

The generally accepted definition of pot equity is (and I think this is from SSHE): "The percentage of time you expect to win a pot, times the amount of money currently in the pot." Note this definition does not include the amount of money you have put in. What you describe is an interesting concept, but it is not what people are generally talking about when they use the term "pot equity"

[M.B.E.]

Here's a post by MLG explaining "fold equity":

http://archiveserver.twoplustwo.com/showthreaded.php?Number=889067

If you read the rest of that thread, you'll see that there isn't widespread agreement on the precise definition of "fold equity", but what's really important is the concept, which MLG explains. There is widespread agreement on what the concept means.

Here's an example. Playing NLHE, someone with a big stack raises your big blind by $50. If you have $300 remaining in front of you, then your fold equity of reraising all-in is much greater than if you only had $60 remaining.

As for pot equity, PokerFink is exactly right.

[M.B.E.]

[ QUOTE ]
i still don't think this defintion of pot equity is correct. i have been in this argument before in other threads with opinions on both sides. somebody please give me a solid answer.

[/ QUOTE ]
Solid answer: elmitchbo is wrong; PokerFink is correct.

[M.B.E.]

When discussing pot equity, it's always with reference to a particular moment and a particular state of information.

For example, suppose you're playing 15/30 LHE (no rake). You have black AA and open-raise; only the big blind calls. (Pot size: $70.) The flop comes Q/images/graemlins/heart.gif9/images/graemlins/heart.gif8/images/graemlins/diamond.gif. At the end of the hand, you find out that your opponent flopped a straight with JT.

Both of the following statements are correct:

"When the flop came down, based on the information you had at the time, your pot equity was around $55 to $60."

"When the flop came down, based on what your opponent actually held, your pot equity was $2.31."

[PokerFink]

Just a quick clarification in case anyone is confused. If you don't know what your opponent holds, pot equity is hard to figure out exactly. You can calculate pot equity based on what you think your opponent holds, or just against a random hand. In MBE's AA example, the $30 pot equity is against two random cards, since the AA doesn't know what his opponent holds.

[M.B.E.]

[ QUOTE ]
In MBE's AA example, the $30 pot equity is against two random cards, since the AA doesn't know what his opponent holds.

[/ QUOTE ]
I edited my post changing the reference from "$30" to "$55 to $60". Notionally, this is an estimate of your pot equity against your opponent's distribution of hands based on the information you have at that time. That is not the same as "two random cards", because you do have some information about your opponent's hand: namely he called your raise from the big blind rather than folding or reraising.

[M.B.E.]

The term "hand equity" is rarely used and has no accepted definition as far as I know. I propose defining it as how much your hand is currently worth, on average, taking into account the money currently in the pot as well as bets you will gain from your opponents on future streets and bets you will lose on future streets.

To put it another way, suppose your hand were accidentally mucked. How much EV have you thereby lost, based on the information available to you at the time? Let's call that hand equity.

Depending on the circumstances, hand equity might be greater than or less than pot equity. If you have a weak made hand, then generally your hand equity would be less than your pot equity (since you are unlikely to get calls from worse hands on future streets, but might be forced to pay off bets from better hands). If you have a strong made hand, your hand equity would often be greater than pot equity.

[Goodnews]

If your definition of Pot equity is correct, how would one apply it?

For example, you have a nut flush draw, involving 9 other people, that wont make anyone a boat. A clean 35% chance to win a pot of 100 dollars. From your definition, my pot equity is 35 dollars.

So how would you use this information?

While in the 'incorrect' definition, with a similar case, the reason I would bet out in this situation (assuming everyone calls) is because my hand equity of 35% is greater than my 10% pot equity and therefore gives me a 25% edge. But isn't this example just a more proactive version of implied odds?

[PokerFink]

[ QUOTE ]
While in the 'incorrect' definition, with a similar case, the reason I would bet out in this situation (assuming everyone calls) is because my hand equity of 35% is greater than my 10% pot equity and therefore gives me a 25% edge. But isn't this example just a more proactive version of implied odds?

[/ QUOTE ]

The reason why this is an incorrect way to calculate pot equity is because it ignores the size of the pot.

For example, lets say that you have a 5% make a winning hand on the river and there are ten players in the hand. Should you call a bet? Using this incorrect definition, you should fold, because your "hand equity" is 5% but your "pot equity" is 10%. But the truth is that if the pot is larger than 20x the size of the bet, then of course you should call. Since this definition ignores the size of the pot, it is an incorrect calculation.

Implied odds are totally different. Implied odds are bets that you will win on future streets if you make your hand.

[elmitchbo]

i think you're on the right track. i stand corrected as to my 'incorrect definition' of pot equity, but the basis of my statement on equity advantage is still true. the equity advantage is what really matters.

like goodnews said, the 'right' definition doesn't seem to have many useful applications. i also thinks he's right to compare what i was trying to say to implied odds. basically, if you have a pot equity edge(using the correct def.) then you want to see money go into the pot because you have a profitable claim to all bets for there on out.