Sets, two pair and trips: how many combos on the flop
The counting behind “they could have a set”: 3 combos per board rank, 9 per pair of ranks, and what a paired board does to both.
On an unpaired flop each board card leaves three of its rank. A set needs two of those three, so there are C(3, 2) = 3 set combos per rank and 9 in all. Two pair using both hole cards takes one of the three left of one board rank and one of the three of another: 3 × 3 = 9 combos per pair of ranks, and three pairs of ranks make 27. That is why, in any range, two pair outnumbers sets three to one, before the range decides which of them it contains.
A paired flop changes the counting. The paired rank has two cards left: one combo of quads, and each of those two cards with any of the 47 other live cards makes trips or a full house, 94 combos. The unpaired card’s set is still 3 combos, and on a paired board it is a full house.
unpaired flop, e.g. A♠ 7♦ 2♣ sets AA, 77, 22: 3 × C(3, 2) = 9 two pair A7, A2, 72: 3 × (3 × 3) = 27 any hand: C(49, 2) = 1,176 paired flop, e.g. 8♠ 8♦ 3♣ quads 88: C(2, 2) = 1 trips+ one 8 × 47 other live cards = 94 33 C(3, 2), a full house = 3
Any two cards, flop by flop
All 1,176 hands that can be held on each counted flop, in their strongest bucket. A set that is also a straight or flush counts as the straight or flush, so some columns sit below the raw counts above.
| Flop | Straight flush | Full house+ | Flush | Straight | Set | Trips | Two pair |
|---|---|---|---|---|---|---|---|
| A♠ 7♦ 2♣ | – | – | – | – | 9 | – | 27 |
| K♠ 8♦ 3♣ | – | – | – | – | 9 | – | 27 |
| Q♥ J♥ T♣ | – | – | – | 48 | 9 | – | 27 |
| 9♠ 8♠ 7♦ | – | – | – | 48 | 9 | – | 27 |
| 6♣ 5♦ 4♥ | – | – | – | 48 | 9 | – | 27 |
| J♦ 7♦ 2♦ | – | – | 45 | – | 9 | – | 27 |
| 8♠ 8♦ 3♣ | – | 10 | – | – | – | 88 | – |
| K♠ K♥ 5♠ | – | 10 | – | – | – | 88 | – |
| A♦ K♣ Q♥ | – | – | – | 16 | 9 | – | 27 |
| T♣ 9♣ 4♥ | – | – | – | – | 9 | – | 27 |
For your own pocket pair, the chance of flopping the set is on the flopping a set page.
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.