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Fold Equity

Posted by matthew dougal on

Fold Equity

When you make a bet or raise in poker, you give yourself two ways to win the hand.  You can win at showdown if you have the best hand, and you can also win the pot right away when your opponent folds. Fold equity is the equity gained when your opponent folds and it allows you to open up the aggression in some interesting spots.

Fold equity in practice

Let’s look at this spot where you hold some sort of draw and are considering raising as a semi bluff rather than calling.

You are playing a 9 handed cash game with $1/$2 blinds and after losing a few small pots earlier you have $90 in front of you. One player Limps and you make it $10 to go on the button with AhQh. The big blind and the limper both call making the pot $31. The flop comes 9h 4s 2h.  The big blind has you covered and bets $15, the limper folds. What do you do?

From your previous experience playing with the big blind you know he most likely has some sort of weakfish 1 pair hand like 54 or 77 but occasionally he will show up with a set or a draw. You figure he is unlikely to have 2 pair as that would mean he called a raise out of position with 94, 92 or 42 which is unlikely.

Using PokerStove you calculate that your hand will win 50% of the time versus your opponents range. If you make the call for $15 and no more money goes in, you will make $46 half the time ($31 pot plus the $15 bet) and lose $15 half the time. So your expected profit when you call is:

(0.5) ($46) + (0.5) (-$15) = $16.50

A call has a positive expected value, easy call right? Wrong! It is true that calling will make you $16.50 on average, but raising all in for $80 allows you to utilise fold equity which will make you more money on average. Let’s take a look at how.

Your opponents range is not very strong here and we can easily have strong hands in our range so it is reasonable to estimate that your opponent will fold at least some of the time. Based on your previous play with this opponent you estimate that, if you shove, he will call 50% of the time and fold the other 50% of the time.

When he calls you will win $121 half the time and lose $80 half the time.

So the EV when he calls = (0.5) ($121) + (0.5) (-$80) = $20.50

When he folds you win $46

 

So to calculate the overall EV of the all in we take

(Probability of call) (Value when called) + (Probability of fold) (Value of fold)

= (0.5) ($20.50) + (0.5) ($46)

= $33.25

As you can see raising all in and utilising your fold equity makes you double the amount that calling does.

Aggression and your image

Plays like the one in the example above have another added advantage. They will make you a more aggressive player and therefore a more difficult player to play against. Even if your opponent calls and you end up losing, it can still have a positive affect. From your point of view you made a play with a positive expectation which is great, do that all day and you will crush your opponents. From your opponents’ point of view you just went all in with just a draw which may make him more inclined to call you next time you have a monster.

Fold Equity in poker tournaments

So far we have just looked at cash game situations but fold equity is an extremely important concept in poker tournaments. Many players will use it without even realising it.

The added effect of fold equity in tournaments comes from the fact that a players tournament life is on the line if he calls an all in. In a tournament it is often correct to fold a hand that has a slight equity edge over your opponents range. This leads people to tighten up their calling range thereby increasing the chances of them folding and increasing fold equity.

This allows for some super aggressive play which can look downright maniacal to someone who doesn’t understand the concepts behind the play. This is discussed further in our article on The Independent Chip Model.

Fold Equity and your opponents’ tendencies

The amount of fold equity you have in a given situation will depend greatly on the opponents that you are facing.

You are unlikely to have a lot of fold equity against a calling station that will call down with bottom pair, so eliminate bluffs from your raising range and just take him to value town.

Conversely some opponents will play so fit or fold after the flop that your fold equity will shoot through the roof. Bluff and semi bluff these guys to death to take advantage of it. They won’t know what hit them.

Being observant of your opponents and their tendencies will allow you to calculate your equities much more accurately. The art of estimating these figures will come with practice. It can also be helped greatly by studying away from the table with the aid of programs such as PokerStove.


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