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StrategyPoker Basics

Ranges & Equity (4): Equity: Final Calls

Before this lesson you should have read:

Your equity is the single most important consideration if you have to decide between calling and folding when closing the action. This is the case in the following situations:

  • You are facing an all-in.
  • Your opponent is betting the river and you don't want to raise.

In these situations, following these three steps will help you to make the correct decision:

Step 1: Calculate the required equity.

Step 2: Put your opponent on a range.

Step 3: Calculate your equity against your opponent's range.

Facing an all-in

$25 NL Hold'em (6 handed)
100BB Stacks

Preflop: Hero is Button with QdQh
3 folds, Hero raises to $0.50, SB raises to $2.00, 1 fold, Hero raises to $5.00, SB raises to $25.00 and is all-in, Hero?

Step 1: Calculate the required equity

Your required equity is how often you will need to win the pot at showdown in order to make a call profitable.

Required equity = price of calling / (pot size + price of calling)

Price of calling: The difference between your last raise and the all-in.

Pot size: All the money you can win. Your raises, your opponent's all-in, the blinds.

Remember that you can only win as much money from others as you can put in the pot yourself. So if your opponent shoves all-in for 200BB and you only have 100BB, you will only be able to win 100BB from him.

In this case, you need 40% equity to make a call profitable. You can find the exact calculation if you click on the spoiler.

Calculation of the needed equity Close spoiler Open spoiler

Pot size = $5 + $25 + $0,25 = $30,25

In this case the pot size is $30,25: Your own $5, the $25 of your opponent and the $0.25 from the BB.

The price of calling is $20: Your opponent went all in for $25. You already invested $5 into the pot, so you have to pay the remaining difference: $25 - $5 = $20.

We end up with the following calculation:

Required equity = price of calling / (pot size + price of calling)

Required equity = $20 / ($30,25 + $20) = $20 / $50,25 ≈ 0,398 ≈ 0,4 = 40%

Your required equity is always below 50%. This is because the price of calling is represented at least twice in the denominator of the formular. If the pot size was 0 before your opponent bets, then the pot size would be equal to the price of calling and we would have:

Required equity = price of calling / (price of calling+ price of calling) = ½ = 50 %. However, since the pot always contains at least the blinds, the required equity will always be below 50%.

Step 2: Put your opponent on a range

The following range is a good starting point, since many opponents will go all-in with these hands in the given situation: JJ+, AK

Step 3: Calculate your equity against your opponent's range

Since you are holding QQ in this spot, you have 47%  equity against your opponent's range (JJ+, AK). That is more than the required equity of 40%, so you should call.

If AK was not in your opponent's range, that is if he would only go all in with JJ+, your equity against that range would be exactly 40%. That would be almost exactly the same amount as the required equity.  A call would break even and thus be unprofitable considering the rake.

If your opponent would only shove all in with QQ+ and AKs, you would only have 29% equity when holding QQ. That is less than the required equity of 40%, so you should fold.

Facing a river bet

$25 NL Hold'em (6 handed)
100BB Stacks

Preflop: Hero is Button with QcJc
2 folds, CO raises to $0.75, Hero calls $0.75, 2 folds

Flop: ($1.90) Qs3s9h (2 players)
CO bets $1.30, Hero calls $1.30

Turn: ($4.50) 4c (2 players)
CO bets $3.00, Hero calls $3.00

River: ($10.50) 3h (2 players)
CO bets $7.00, Hero?

Step 1: Calculate the required equity

Required equity = price of calling/ (pot size + price of calling)

The price of calling is $7 and the pot size is $17.50.

Required equity = 7 / (17.50 + 7) = 7 / 24.50 ≈ 0.29 = 29% equity

 

Step 2: Put your opponent on a range

Your opponent's betting range on the river could consist of:

  • Made hands: AA-QQ, 99, 33, AQ
  • Air (busted flush draws): As2s, As4s, As5s, As6s, As7s, As8s, AsTs, AsJs, AsKs, KsJs, KsTs, JsTs

Step 3: Calculate your equity against your opponent's range

You can use Equilab to calculate your equity. In this example you would have 32% equity. That is more than the required 29%, which means that you can make a profitable call.

How card removal affects equity

Imagine that you are holding a different hand in the last example: Instead of QcJc you are holding AsQc.

Your hand looks better now, your absolute hand strength has increased.

As you already know, you should always make your decision based on your relative hand strength. So you have to calculate the equity of your holding against your opponent's range again.

The result: your equity drops from 32% to 26%. Your equity is actually worse and you should fold.

The reason is as follows: because of card removal, As can no longer be in your opponent's range. That means that you are blocking a good part of your opponent's bluffing range. His range now consists of:

  • Made hands: AA-QQ, 99, 33, AQ (#20)
  • Air (busted draws): AsKs, AsJs, As8s, As7s, As6s, As5s, As4s, As2s, AsTs, KsJs, KsTs, JsTs, (#12, #3)

If you hold AsQc instead of QcJc, your opponent's bluffing range on the river now consists of three combos instead of 12. Against that range you only have 26% equity, which is considerably less.

So you should fold, despite the fact that your absolute hand strength is actually stronger. The basis of your decision should always be relative hand strength, that is the equity of your hand against the range of your opponent.

Summary

If you are facing an all-in or a river bet, you should follow three steps to decide whether to call or to fold:

  • Step 1: Calculate the required equity.
    Required equity = price of calling / (pot size + price of calling)
  • Step 2: Put your opponent on a range.
  • Step 3: Calculate your equity against your opponent's range.

Next steps

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Discussion
 

Comments (26)

#1 RawadN, 22 Jul 13 04:51

It's a great Lesson, but how can u do all the 3 steps in more or less 15 seconds. is it possible to memorize a huge number of samples hands?

#2 lollo1588, 27 Jul 13 11:52

ok

#3 RawadN, 27 Jul 13 13:02

ok for what?

#4 Benm473, 02 Aug 13 22:32

It's supposed to be done after a session to sharpen your in-game intuition help you to focus on getting your opponent's ranges correct in set situations and work out whether you are making moves that will give you a profit vs your opponents ranges in the long term. Also using the combinatrics you can work out if perhaps you are being to passive or too aggressive with specific holdings vs specific opponents on specific boards.

#5 C1016905, 15 Sep 13 11:16

I don't understand why opponents range has changed just because you have a different hand...

#6 kanpoker, 01 Nov 13 04:47

Good but so complicate for me, I will learn again ^^

#7 UTGDog, 31 Jan 14 11:52

To answer C101,the opponent's range changes when you hold AQ because it states in the example that Villain could be bluffing with a busted A-high flush draw. However, since you are holding the A needed to complete his flush draw, it then eliminates all of Villain's bluffs with any A-high flush draw he may have been holding.<br /> <br /> Not so complicated once you get around the math behind it. It's essentially just calculating your pot odds and then comparing the strength of your hand vs Villain's range of hands to figure out if you are ahead, behind, or can outdraw him profitably over the long term.

#8 turnfolder, 05 Mar 14 19:51

very good explaining i seen, i tried understand the equity and notation from different source, but here its like lightning in clear sky.<br /> Only bad thing about site so far it wont let me do this test...hopefully temporary problem.

#9 ixpiyacol, 22 May 14 03:24

The subjects of outs, odds, card removal and equity are very interesting, but when should I apply them? In the early or late stages of tournaments? On the cash tables only? FL, PL, or NL? Everywhere?

#10 rebelbhoy67, 10 Jul 14 20:19

kool

#11 tashaleigh3, 09 Oct 14 10:00

okay

#12 catblank, 14 Oct 14 09:01

ok

#13 Denboy78, 03 Nov 14 22:47

I get the concept, but I don't get how your supposed to accurately know your opponents range all the time? How can def say his range is jj+, or qq+

#14 azhardelisya, 11 Dec 14 22:16

Ok

#15 gohomeman2690, 31 Oct 15 15:25

ok

#16 bubamarasr, 20 Jan 16 19:51

Read it. Thank you.

#17 setyaida, 25 Jan 16 11:07

Great

#18 ptpokermyth, 26 Feb 16 16:33

range is very important

#19 sedinbsng, 01 Apr 16 20:30

ok

#20 pharaonsgold, 07 Apr 16 00:36

great

#21 CroZoZo, 26 Apr 16 13:20

doctor

#22 TetonSouix, 16 May 16 02:38

intricate,,,

#23 Tezza459, 25 May 16 15:25

I enjoy being on this site because I have been learning so much about Poker and is making me a wiser gambler

#24 Freelemon, 30 May 16 18:27

ok

#25 armorrrat, 08 Jun 16 19:10

Nice stuff, but to put all that in practice... And these are just basics.

#26 reaper7, 16 Jun 16 05:53

Why the villain can't have As9s?