Fold Equity and Expected Value +EV

Fold Equity and Expected Value +EV 0001

Raising is not something you always only do for value. You can also do it because you have fold equity. But what exactly is that? Continue reading and you'll find out.

What exactly is fold equity? Simply put: you bet or raise because you think it's +EV (expected value), not because you probably have the best hand, but because your opponent will fold often enough to make this move profitable.

Example: You have {j-Clubs}{j-Diamonds} UTG at a tight full ring table with Blinds of $1/$2. You raise to $8 and a tight player in middle position re-raises to $30. This player doesn't 3-bet too often and you've seen him call a raise with {a-Hearts}{k-Hearts} before. He's not a great player, otherwise he would know that he should be re-raising with AK. What range are we putting him on? Well, usually a tight player at a full ring table will only 3-bet with hands like AKo/AQs+/JJ+. We have already seen him calling a raise with AK, so we cant really include that in his range. In this specific situation, against this specific player, his range becomes JJ+. We take a look at his effective stack which is 100BB, so we decide to call for setvalue. The flop comes {a-Diamonds}{7-Hearts}{4-Spades}. We missed the flop and its our turn to act. What are we going to do? Usually we would check/fold the hand, but isn't there a better option?

Well, we have Jc-Jd, and according to PokerStove our 20% pot equity puts us clearly behind our opponents JJ+ range. Here is a list of his possible hands:

AA: 3 combinations ({a-Spades}{a-Clubs}, {a-Spades}{a-Hearts}, {a-Hearts}{a-Clubs})

KK: 6 combinations ({k-Diamonds}{k-Spades}, {k-Diamonds}{k-Hearts}, {k-Diamonds}{k-Clubs}, {k-Clubs}{k-Spades}, {k-Hearts}{k-Spades}, {k-Hearts}{k-Clubs})

QQ: 6 combinations ({q-Diamonds}{q-Spades}, {q-Diamonds}{q-Hearts}, {q-Diamonds}{q-Clubs}, {q-Spades}{q-Clubs}, {q-Hearts}{q-Spades}, {q-Hearts}{q-Clubs})

JJ: 1 combination ({j-Hearts}{j-Spades})

So in total there 3 + 6 + 6 + 1 = 16 combinations.

Against these hands we have the following chances of winning:

{j-Clubs}{j-Diamonds} vs AA: 19% vs 81%

{j-Clubs}{j-Diamonds} vs KK: 19% vs 81%

{j-Clubs}{j-Diamonds} vs QQ: 19% vs 81%

{j-Clubs}{j-Diamonds} vs JJ: 50% vs 50%

Therefore, our average chance of winning is:: (0.19)(3/16) + (0.19)(6/16) + (0.19)(6/16) + (0.50)(1/16) = 21% (also see PokerStove). With chances like these, check/folding definitely is the best option.

Many players will already have realized that the above calculations aren't completely accurate, as they do not take Fold Equity (FE) into consideration. Most of the hands in his range should have him worrying about that Ace. If you fire out a good bet at this point you have tons of FE because your opponent will fold so many hands out of his range. Currently there's $33 in the pot. What will out opponent do if we bet $28? He is going to muck hands like JJ-KK, because he can't go up against our strength. We are, of course, relying on the assumption that our opponent isn't a genius who sees right through this move. So what does he do? He folds JJ, QQ, KK and will raise with AA.

What happens to our chances of winning if we take FE into consideration, together with a bet of $28?

{j-Clubs}{j-Diamonds} vs AA: 19% vs 81%

{j-Clubs}{j-Diamonds} vs KK: 100% vs 0%

{j-Clubs}{j-Diamonds} vs QQ: 100% vs 0%

{j-Clubs}{j-Diamonds} vs JJ: 100% vs 0%

Our new average chance of winning is now: (0.19)(3/16) + (1)(6/16) + (1)(6/16) + (1)(1/16) = 85%.

This is definitely a big improvement compared to the 21% we had earlier. So as we can see, betting out in this situation will improve our chances to win the hand as our opponent will fold his JJ-KK, thereby giving us 100% success rate against those hands. This greatly improves our general chances of beating his range and we can easily bet out. He is only going to raise with 3 out of his 16 possible hands (AA, this is 18.75% of his range) and fold the rest (JJ-KK, this is 81.25% of his range). Our EV of betting out is therefore: EV = (0.8125)(33$) + (0.1875)(-28$) = 21.56$. This is a standard example of FE.

When to consider FE?

You won't be needing FE if you're the favorite to win the hand. If you hit an open ended straight draw and a flush draw on the flop (15 outs), then you're the favorite to win the hand, even if you don't have a made hand yet. With those types of monster draws, you bet for value, and if you end up not hitting one of your outs, you basically got unlucky. So if you're the favorite to win the hand, you principally don't bet out for FE but for value, although there could be some FE in there if you don't like your hand too much and you'd rather pick up the pot now than risk your whole stack.

What you need to do is put your opponent on a range and look at the chances your hand has of beating this range. If you're behind, then you don't need to bet for value, but you should think about how much FE you have and then decide if it would be better to fold or bet/raise the hand. If you're behind against his range, but you know he will fold a lot of hands in his range against a bet/raise, then a bet/raise is the right option here. This is because your chances of winning increase to 100% against the hands in his range you know he will fold, which will increase your average chance of winning the hand and the EV of betting or raising.

Many beginners will make the mistake to raise with a flush draw with a hand like {6-Diamonds}{8-Diamonds} on a {j-Diamonds}{a-Spades}{k-Diamonds} flop against a tight IR who raised before the flop. They then think "I have a flush draw, and I'm going to raise it!" But they don't understand the reasoning behind it. You're raising with the worst hand, so you need enough FE to make this raise +EV. If a player with a pre-flop raise percentage of 5% raises, you can put him 99+, AJs+, KQs, KQo, AQo+. If we then see a flop like the one above, raising with a flush draw is not the best thing to do because our opponent has a lot of hands in his range that he will not fold against a raise. JJs+ and AQos+ wont fold. From 99+, only pocket 9's will get folded, TT and up will not be mucked. KQs and KQo might fold given the circumstances, but this definitely wont happen 100% of the time. Therefore you don't have enough FE in this situation to make a raise. So when do you raise for FE? Well, you do it when you know that your opponent will fold many of the hands in his range.

I found a good example here to demonstrate when raising is correct because you have FE. We're in position against a TAG raiser. His statistics look pretty much perfect (22/18/3) and we can assume that he's a good player. In this hand he raises behind a limper in UTG +1. His range here is 22+, A6s+, ATo+, KTs+, KQo, QTs+, JTs, T9s, 98s. Calling with a suited connector in position here is fine. The flop gives us an open ended straight draw and is pretty dry without any high cards. I'm assuming that our TAG player hasn't hit and will fire out a potsized C-Bet. And that's what he does. We now of the option of folding, calling or raising.

I'm behind in this hand, and calling a pot bet is something you only do with enough implied pot odds. I definitely don't have those here as my opponents range is so large that I will never get paid off enough if I hit to make a call profitable. Leaves us with folding or raising. If we have completely no FE, then folding would be the better option. But we have quite a bit of FE here! Which hands are going to call/re-raise us if we raise? These are 22, 88+, A9s, JTs, T9s and 89s+. All his other hands will be folded. So he'll fold 33-77, A6s-A8s, ATs+, ATo+, KTs+, KQo+ and QTs+, a great deal of his range. That's why a raise in situation would make sense because you have a lot of FE, and even if you're behind at the moment, you still have 8 outs. We don't need to worry much about gizalmaster since he checked the flop and probably hasn't hit anything either.

Starting a new hand (#837143379)

Texas Holdem NL$0.10/$0.20 - 2008-02-09 22:17:02 Server - Table Cobar

Seat 1: gizalmaster ( $21.47 )

Seat 3: robdehaai ( $19.70 )

Seat 5: RiverdalePN ( $19.98 )

Seat 8: sobeuc ( $33.40 )

Seat 10: anBealBocht ( $29.55 )

sobeuc posts Small Blind $0.10

anBealBocht posts Big Blind $0.20

Dealing cards {6-Spades}{7-Spades}

RiverdalePN is dealt

gizalmaster calls $0.20

robdehaai raises $1.20 (plays 22/18/3, standard TAG player)

RiverdalePN calls $1.20

sobeuc folds

anBealBocht folds

gizalmaster calls $1

Dealing Flop {2-Spades}{8-Clubs}{9-Hearts}

gizalmaster checks

robdehaai bets $2.40

RiverdalePN raises $7

gizalmaster folds

robdehaai folds

Winner is RiverdalePN $12.87

So before you decide to raise with the worst hand next time, think about whether or not you have enough FE. If you don't have FE, may it be because your opponent only plays premium hands or wont fold a lot of hands in his range, muck your hand and wait for a better one. Don't try to win every pot, but try to win as much money as possible! Put your opponent on a range and decide whether or not he will fold a lot of his hands to a certain raise. If he does, then you have enough FE to bet/raise with +EV. If he doesn't, then you should probably give up the hand and wait for a better spot.

Questions, comments, suggestions, criticism and ideas for new strategy articles are always welcome in the forum.

Kurt Verstegen (Riverdale27)

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