How known cards block combos

Practice with exercises

Content by Tools of Poker Methodology and calculation assumptions

Which combos can the opponent still hold?

A known card cannot also be in the opponent’s hand. Cross out every combo that contains it. The combos you have not crossed out are still available.

Use the same three counts throughout: original combos before seeing cards, blocked combos that contain a known card, and available combos left over.

Review basic hand combinations

A first example: AA with one known ace

Imagine that As, the ace of spades, is the only known card. We want to count the opponent’s AA combos.

As

1. Count the original combos

AA starts with 6 combos, just as in lesson 4.1.

2. Remove combos containing known cards

As can pair with each of the other three aces. These three combos disappear because the opponent cannot use As:

As Ah As Ad As Ac

3. Count the available combos

Ah, Ad and Ac are still available. They can form these three pairs:

Ah Ad Ah Ac Ad Ac
6 − 3 = 3

One known card has blocked three combos. Count removed combinations, not just the number of known cards.

Now include your cards and the board

Each example below starts again with the cards shown. Your cards and every board card are known. In the matrix, a crossed-out card blocks every combo containing it; a check marks a combo that remains possible.

Remaining combos for AA: 1

Your cards

As Qc

board

Ah 7d 2c

Your As and the Ah on the board leave only Ad and Ac. The opponent has just one possible AA combo: AdAc. Of the original six combos, five are blocked.

Original combos
6
Blocked combos
5
Remaining combos
1
6 − 5 = 1
Remaining combos for AA: 1
As Ah Ad Ac
As
As Ah
As Ad
As Ac
Ah
Ah Ad
Ah Ac
Ad
Ad Ac
Ac
  • Valid combination
  • Blocked by a known card
  • The same card cannot be used twice
  • Already counted in the opposite order

Remaining combos for AKs: 2

Your cards

As Qc

board

Kh 7d 2c

As blocks AsKs and Kh blocks AhKh. The two other suits remain: AdKd and AcKc. Two of the four AKs combos are still available.

Original combos
4
Blocked combos
2
Remaining combos
2
4 − 2 = 2
Remaining combos for AKs: 2
Ks Kh Kd Kc
As
As Ks
Ah
Ah Kh
Ad
Ad Kd
Ac
Ac Kc
  • Valid combination
  • Blocked by a known card
  • Does not match the requested suits

Remaining combos for AKs: 3

Your cards

As Ks

board

Qh 7d 2c

As and Ks both belong to AsKs. Cross out that combo once. AhKh, AdKd and AcKc remain, so two known cards have blocked only one combo.

Original combos
4
Blocked combos
1
Remaining combos
3
4 − 1 = 3
Remaining combos for AKs: 3
Ks Kh Kd Kc
As
As Ks
Ah
Ah Kh
Ad
Ad Kd
Ac
Ac Kc
  • Valid combination
  • Blocked by a known card
  • Does not match the requested suits

Remaining combos for AKo: 7

Your cards

As Qc

board

Kh 7d 2c

As blocks three offsuit combos and Kh blocks three, but AsKh is in both groups. Remove it only once: five combos are blocked and seven remain.

Original combos
12
Blocked combos
5
Remaining combos
7
12 − 5 = 7
Remaining combos for AKo: 7
Ks Kh Kd Kc
As
As Kh
As Kd
As Kc
Ah
Ah Ks
Ah Kd
Ah Kc
Ad
Ad Ks
Ad Kh
Ad Kc
Ac
Ac Ks
Ac Kh
Ac Kd
  • Valid combination
  • Blocked by a known card
  • Does not match the requested suits

Remaining combos for AK: 9

Your cards

As Qc

board

Kh 7d 2c

Without a suit restriction, three aces and three kings remain. Each ace can pair with each king, giving nine combos. Seven of the original sixteen combos are blocked.

Original combos
16
Blocked combos
7
Remaining combos
9
16 − 7 = 9
Remaining combos for AK: 9
Ks Kh Kd Kc
As
As Ks
As Kh
As Kd
As Kc
Ah
Ah Ks
Ah Kh
Ah Kd
Ah Kc
Ad
Ad Ks
Ad Kh
Ad Kd
Ad Kc
Ac
Ac Ks
Ac Kh
Ac Kd
Ac Kc
  • Valid combination
  • Blocked by a known card

Blockers reference table

In these examples, As is the only known card. As

Start with all the combos. Cross out every combo containing the known card. Count those that remain.
Hand typeSee which combos disappear
PairAA

Pair As with each of the other three aces: those 3 combos are blocked.

As Ah As Ad As Ac
Original combos
6
Blocked combos
3
Remaining combos
3
Suited handsAKs

Only AsKs contains As: that one suited combo is blocked.

As Ks
Original combos
4
Blocked combos
1
Remaining combos
3
Offsuit handsAKo

As can pair with three kings of a different suit: those 3 combos are blocked.

As Kh As Kd As Kc
Original combos
12
Blocked combos
3
Remaining combos
9
Any suitsAK

As can pair with any of the four kings: those 4 combos are blocked.

As Ks As Kh As Kd As Kc
Original combos
16
Blocked combos
4
Remaining combos
12

Remove each blocked combo only once. Knowing both As and Ks still removes just one AKs combo.

The next lesson applies this same subtraction to every hand class in an opponent range, then adds the results.

4.3 · Range combinations

Questions about blockers

Yes. If the known cards remove every possible combo, the opponent cannot hold that hand. For example, three known aces leave only one ace, so AA has zero combos.

No. A queen does not remove any AK combo. Only known cards of the ranks in the target hand affect its combinations.

As and Ks both belong to the same AKs combo. Knowing both cards removes that combo once, leaving the other three suits available.

No. With As known, AA goes from 6 original combos to 3 available combos. Only the 3 combos containing As are blocked; the other aces can still form AA.

Yes. Any identified card is unavailable to the opponent. What matters is which specific card it is, not whether it is in your hand or on the board.