You'll often hear a poker player say things like "I put him on ace-king". It's certainly good to guess what cards your opponent holds, but putting someone on an exact hand is almost impossible.

To make good poker decisions, you must take into account all the hands that your opponent might hold. Let's see how the pros do this.

Perfect certainty is very rare

If the way your opponent has played the hand indicates that she has AK, how can you KNOW she doesn't have AA or KK or maybe AQ? Most of the time you cannot be sure of this, and you need to keep all these hands in the picture.

You put the opponent on a range of hands that are possible and see how well your hand holds up against that range.

Your hand might lose against some of the hands in that range, split the pot against a few of them, and win against the rest. To sum up all these possibilities, you need to do some counting.

Simple hand range example

Let's look at a simplified example. Say that you have JJ and the board shows A-J-9-6-2 with no flush possibilities. The way the hand has been played makes you certain that the opponent has either AA or AK, any oter hand seems impossible. (In reality, you can rarely be this accurate.). Should you call the opponent's all in move?

Your trips of jacks lose to three aces but beat top pair. With one ace on the board, there are three aces left in the deck (according to the basic hand frequencies), which gives three possible combinations of AA for your opponent. In the same way, there are 12 combinations of AK.

This little calculation shows you that you win against 80% of the hands in the opponent's range (12 out of 15) and lose against 20%. You're a big favorite and the call is easy.

Realistic hand range example

Now to a more realistic example. It's pre flop in a no limit holdem cash game. A player raises from early position. From what you know about the player, and about poker players in general, you put him on the following range: AA-TT, AK, AQ.

You have KK and choose to just call. The flop comes A-8-7. How do you feel about those kings now? Maybe you put the opponent on AK and fold?
Before you fold, let's run through the entire hand range of the opponent and see how the kings hold up when you see the whole picture. 

Opponent's hand

Combinations

Your chances (%)

AA

3

1

KK

1

50

QQ

6

90

JJ

6

90

TT

6

90

AK

6

5

AQ

12

8

 

Total: 40

Average: 45%

(Note how the combinatorics take into account the board cards and your own hand.)

In this case you find that the kings are a slight underdog against the hand range that you put your opponent on.

But as you know, pot odds can compensate for bad cards. If the opponent was to move all in here with a pot sized bet, the pot would lay you 2-to-1 odds for your call. You need 33% winning chances to motivate a call, and your 45% is more than enough. You have an easy call.

In this case, if instead you had put your opponent on exactly AK, you wouldd have to fold - a mistake according to the analysis above. Against AK you're only 5% to win, which is far below the necessary 33% you need to motivate the call.

More complications

A further complication that is present in the real world is the tendency of skilled players to not always play a certain hand in an identical manner. They'll be mixing up their game, and you need to bring this fact into your calculation.

In our example, let's say you think that your opponent would limp-call with the pairs approximately half of the time. Then you have the following table for the different hands in the hand range: 

Opponent's hand

Combinations

Your chances (%)

AA

1.5

1

KK

0.5

50

QQ

3

90

JJ

3

90

TT

3

90

AK

6

5

AQ

12

8

 

Total: 29

Average: 33%

Your chances have gone down. The call is still correct, but marginal.

On the other hand, if you accomodate for a certain bluff percentage on behalf of your opponent, your chances go up again. Say ten percent:

Opponent's hand

Combinations

Your chances (%)

AA

1.5

1

KK

0.5

50

QQ

3

90

JJ

3

90

TT

3

90

AK

6

5

AQ

12

8

Bluff

3

100

 

Total: 32

Average: 39%

 

Then, again, we haven't even started to digest the information the opponent gives away by moving all in. With that short stack, maybe this move doesn't tell us much, he could very well do it with all the hands in the range. On the other hand, with that short stack maybe we should put him on another range pre-flop.

But hey, we're just trying to explain a conceot, okay? =)

Putting it into practice

Of course, at the poker table, when the clock is ticking and the heart is racing, most players simply don't have the brains to perform this kind of computations.

Don't dispair, though! With some training, quick estimations of these things can be done, and that's already helpful. Try to figure out what hands are most likely for your opponent and how your hand performs against those. You can neglect those that are very unlikely due to the basic hand frequencies. See how many combinations that beat you, how many that don't. Try to feel the average, or the primary tendency.

Even though this practice is approximative, it's a better way to make good poker decisions than just making a wild guess and putting opponents on one particular hand.

/Charlie River

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