Ranges & Equity (4): Equity: Final Calls

Before this lesson you should have read:

• Ranges & Equity (1): Introduction to Ranges
• Ranges & Equity (2): Combos & Card Removal
• Ranges & Equity (3): Equity Introduction

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
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.

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
2 folds, CO raises to $0.75, Hero calls $0.75, 2 folds

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

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

River: ($10.50) (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 you are holding .

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, 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 instead of , 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.