Poker combinatorics sounds like advanced math, but it really comes down to counting. Knowing how many combos each hand has lets you understand what percentage a range plays, why AKo weighs more than AKs and how your cards and the board change what your opponent can hold. Here’s everything you need, with examples.
What is a combo in poker?
A combo (combination) is one specific way of holding a hand with specific suits. “AK” is a hand type; A♠K♥ is one combo of AK. Range charts show hand types (169 squares), but at the table you’re always dealt one specific combo.
The three basic numbers: 6, 4 and 12
Each rank comes in four suits (♠ ♥ ♦ ♣). From that you get three numbers worth memorizing:
| Hand type | Combos | Why |
|---|---|---|
| Pair (AA, 77…) | 6 | There are 4 aces and you pick 2: 4×3/2 = 6 |
| Suited (AKs, 76s…) | 4 | One per suit |
| Offsuit (AKo, 76o…) | 12 | 4×4 = 16 combinations minus the 4 suited ones |
So an unpaired hand like AK has 16 combos in total: 4 suited and 12 offsuit. That’s why, even though AKs and AKo take up one square each on the chart, AKo shows up three times as often.
Why there are 1,326 starting hands
If you add up every square in the 13×13 matrix:
- 13 pairs × 6 = 78 combos
- 78 suited hands × 4 = 312 combos
- 78 offsuit hands × 12 = 936 combos
That’s 1,326 combos in total. It’s the same number you get by choosing 2 cards from a 52-card deck: 52×51/2 = 1,326. Look at the split: over 70% of the hands you’re dealt are offsuit, and only 6% are pairs.
Handy fact
You’re dealt a pocket pair roughly 1 in every 17 hands (78/1,326), and a specific pair, like AA, 1 in every 221 (6/1,326).
Combos and range percentages
When a chart says a range plays “20%”, it means combos: add up the combos of every hand in it and divide by 1,326. For example:
| Range | Combos | % of hands |
|---|---|---|
| QQ+, AK | 18 + 16 = 34 | 2.6% |
| All pairs (22+) | 78 | 5.9% |
| All suited aces (A2s+) | 48 | 3.6% |
| All offsuit aces (A2o+) | 144 | 10.9% |
This calculation explains two things you’ll see on charts all the time:
- Offsuit hands inflate the range: adding A2o+ adds almost 11 points; adding A2s+, less than 4.
- Suited hands are cheap: you can include lots of playable suited hands without the range growing much.
Example · range by hand type · 17.9%
Pairs: 22+ (78 combos). Suited: A2s+, K9s+, QTs+, JTs (76 combos). Offsuit: A9o+, KJo+ (84 combos). Total: 238 combos, 17.9%.
Notice that the offsuit hands take up only 7 squares versus 19 for the suited ones, and still contribute more combos (84 versus 76). To review how the matrix is laid out, see how to read a poker range chart.
Known cards and blockers
Combos change when you see cards: yours and the board’s. Every card you know about can no longer be in your opponent’s hand. This is called the blocker effect or card removal.
Pairs with known cards
A pair has 6 combos. If you see one of its four cards, 3 cards are left and only 3 combos. If you see two, 1 combo is left.
Unpaired hands with known cards
Multiply the remaining cards of each rank. AK with no cards seen: 4×4 = 16. With an ace on the board: 3×4 = 12. With an ace and a king: 3×3 = 9.
| Opponent’s hand | No cards seen | One ace visible | Two aces visible |
|---|---|---|---|
| AA | 6 | 3 | 1 |
| AK | 16 | 12 | 8 |
| KK | 6 | 6 | 6 |
Why it matters preflop
Holding an ace reduces the AA and AK combos your opponent can have. That’s why hands like A5s make good 3-bet bluffs: they block the hands your opponent would continue with. We explain it in when to 3-bet.
In the Burn EV editor you paint your ranges by hand, and practice mode quizzes you on each hand with random suits, just like at the table.
A worked example in a hand
You hold Q♠Q♦ and the flop is A♥7♣2♠. Your opponent makes a big bet and you think they’d only do it with AK, AA or 77. How many combos of each can they have?
- AA: there’s an ace on the board, 3 left → 3 combos.
- 77: there’s a seven on the board, 3 left → 3 combos.
- AK: 3 aces left × 4 kings → 12 combos.
Of their 18 possible combos, 12 are AK. Your queens lose to all of them, but now you know the most likely hand by far is AK, not a set. This kind of reasoning is the foundation of reading ranges postflop.
Frequently asked questions
How many starting hand combinations are there in poker?
1,326: 78 pair combos, 312 suited combos and 936 offsuit combos.
How many combos does a pocket pair have?
Six. If you see one of its cards, three are left, and if you see two, one is left.
Why is AKo more common than AKs?
Because AKo has 12 combos and AKs only 4. You’ll be dealt AK offsuit three times as often as suited.
What is a blocker in poker?
A card you hold (or that’s on the board) that reduces the combos of certain hands in your opponent’s range. For example, holding an ace reduces their AA and AK combos.
Read next: what EV is in poker and how to calculate it.