How to count hand combinations in Poker

Practice with exercises

Content by Tools of Poker Methodology and calculation assumptions

Start with two specific cards

A combo is one exact two-card hand, including the suits. These two hands are different combos:

As Ks Ah Kh

Both belong to AKs: an ace and a king of the same suit. AKs is the hand class; each specific pair of cards is one of its combos.

Read the hand notation

  • AA is a pair: both cards have the same rank.
  • The s in AKs means both cards have the same suit.
  • The o in AKo means the cards have different suits.
  • AK without a suffix includes both suited and offsuit hands.

The counts below assume that all 52 cards are available.

How to read the combination matrices

Choose one card from the row and one from the column. The cell where they meet represents those two cards together. Count the cells marked with a check.

× The same card twice is impossible. ↩ The reverse order is already counted. — The suits do not match the requested hand type.

AA: 6 different combinations

There are four aces in the deck. AA means choosing two different aces. Build the pairs in order so that none is repeated:

As Ah Ad Ac
  • With As, choose Ah, Ad or Ac: 3 combos.
  • Next use Ah with Ad or Ac: 2 new combos. AhAs was already counted.
  • Finally use Ad with Ac: 1 new combo. All the other pairs are already counted.
3 + 2 + 1 = 6
AA: 6 different combinations
As Ah Ad Ac
As
As Ah
As Ad
As Ac
Ah
Ah Ad
Ah Ac
Ad
Ad Ac
Ac
  • Valid combination
  • The same card cannot be used twice
  • Already counted in the opposite order

AKs: 4 different combinations

There is one combination per suit: spades, hearts, diamonds and clubs.

As must go with Ks, Ah with Kh, Ad with Kd and Ac with Kc. That is one combo for each of the four suits.

4 × 1 = 4
AKs: 4 different combinations
Ks Kh Kd Kc
As
As Ks
Ah
Ah Kh
Ad
Ad Kd
Ac
Ac Kc
  • Valid combination
  • Does not match the requested suits

AKo: 12 different combinations

Each of the four cards of the first rank can be paired with three cards of the other rank in a different suit.

Start with As: it can go with Kh, Kd or Kc. Ks has the same suit, so it is excluded. Repeat for the other three aces: four groups of three combos.

4 × 3 = 12
AKo: 12 different combinations
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
  • Does not match the requested suits

AK: 16 different combinations

Each of the four cards of the first rank can be paired with any of the four cards of the other rank: 4 suited plus 12 offsuit.

Every AKs combo and every AKo combo belongs here. The two groups do not overlap: the cards either share a suit or have different suits.

4 + 12 = 16
AK: 16 different combinations
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

Hand combinations reference table

Counts for one starting hand when all 52 cards are available.
Hand type Example Combos
PairAA6
Suited handsAKs4
Offsuit handsAKo12
Any suits (suited + offsuit)AK16

These counts apply to any ranks: 88 has 6 combos, QJs has 4, QJo has 12 and QJ has 16. The next lesson explains what changes when some cards are already known.

4.2 · Known-card blockers

Questions about hand combinations

No. A spade ace with a heart ace is the same hand as a heart ace with a spade ace. Count this pair only once.

It includes every AK combination: 4 suited and 12 offsuit, for 16 in total.

For AA, each ace can pair with three others, but reversing them repeats the same combo: 6 unique pairs. For AKo, each of the four aces can pair with three kings of a different suit: 12 unique combos.

No. With no known cards removed, every pair has 6 combos, every suited hand has 4 and every offsuit hand has 12. Two different ranks without a suit restriction have 16 combos.