How many starting hands are there? 1,326, counted
Why a pair is 6 combos, a suited hand 4 and an offsuit hand 12, how often each turns up, and why a range’s percentage is always measured in combos.
The first card can be any of 52 and the second any of the 51 left, but A♠K♥ and K♥A♠ are the same hand, so divide by two: 1,326 two-card hands. Players group them into 169 classes by rank and by whether the suits match, and the classes are not the same size. That one fact is why a range quoted as “20% of hands” is measured in combos, never in classes.
all hands 52 × 51 / 2 = 1,326 pairs 13 ranks × C(4, 2) = 13 × 6 = 78 suited C(13, 2) rank pairs × 4 suits = 312 (78 classes × 4) offsuit C(13, 2) × (4 × 4 − 4) = 936 (78 classes × 12) 78 + 312 + 936 = 1,326
| Kind | Example | Combos each | Classes | Combos |
|---|---|---|---|---|
| Pocket pair | AA | C(4, 2) = 6 | 13 | 78 |
| Suited | AKs | 4 suits = 4 | 78 | 312 |
| Offsuit | AKo | 4 × 4 − 4 = 12 | 78 | 936 |
| All hands | C(52, 2) | 169 | 1,326 |
How often you are dealt it
| Dealt | Combos | Chance | Frequency |
|---|---|---|---|
| a pocket pair | 78 | 5.88% | 1 in 17 |
| a suited hand | 312 | 23.53% | 1 in 4.3 |
| an offsuit hand | 936 | 70.59% | 1 in 1.4 |
| one specific pair (say AA) | 6 | 0.45% | 1 in 221 |
| AK, suited or not | 16 | 1.21% | 1 in 82.9 |
| AKs specifically | 4 | 0.30% | 1 in 331.5 |
| AA, KK or AK | 28 | 2.11% | 1 in 47.4 |
The pocket aces page follows this through to how often someone at a full table has a bigger pair.
What share of hands is that range?
The four opponents on this site, measured both ways. Count classes and the Maniac plays 32.0% of the 169; count combos, which is what actually gets dealt, and it is 25.5% of hands, because most of its classes are suited (4 combos) or pairs (6) rather than offsuit (12).
| Range | Classes | Of 169 | Combos | Of 1,326 |
|---|---|---|---|---|
| The Nit | 8 | 4.7% | 50 | 3.8% |
| The Calling Station | 38 | 22.5% | 242 | 18.3% |
| The Maniac | 54 | 32.0% | 338 | 25.5% |
| The Reg | 30 | 17.8% | 172 | 13.0% |
Counted flops: four ranges side by side
- A♠ 7♦ 2♣ dry ace-high, rainbow→
- K♠ 8♦ 3♣ dry king-high, rainbow→
- Q♥ J♥ T♣ broadway, two-tone→
- 9♠ 8♠ 7♦ middling and connected, two-tone→
- 6♣ 5♦ 4♥ low and connected, rainbow→
- J♦ 7♦ 2♦ monotone→
- 8♠ 8♦ 3♣ paired low, rainbow→
- K♠ K♥ 5♠ paired king-high, two-tone→
- A♦ K♣ Q♥ three broadway cards, rainbow→
- T♣ 9♣ 4♥ middling, two-tone→
The counting behind it
- The counts are exact. Every combo in the range is dealt against the deck with the board and your cards removed. Nothing is sampled or rounded until display.
- The ranges are assumptions. The four opponents are stated ranges, printed in full on /opponents so they can be argued with. They are not solver output, and nobody arrives on the flop with exactly these hands. Paste your own range into the counter to count yours.
- Each combo is counted once, in its strongest bucket: top pair with a flush draw counts as top pair. Draws are only listed for hands without a pair.
- Straight draws are counted by ranks: two ranks that complete a straight is open-ended (a double gutter counts), one is a gutshot. Board-only straights and flushes that need none of your cards do not count as draws.
- Combos are not equity. A range with more sets is not automatically ahead: the equity calculator and spot check deal the run-outs.