Odds of an overcard on the flop
How often does an overcard flop when I hold queens? The short answer is below, and under it the working: the formula with the numbers put in, and the count from dealing every possible card.
The working
Queens have two ranks above them, eight cards. The flop is overcard-free only if all three cards come from the other 42 of the 50 unseen:
P(no overcard) = C(42, 3) / C(50, 3) = 11,480 / 19,600 = 58.57% P(overcard) = 1 − 58.57% = 41.43% General: pair with m overcards → 1 − C(50 − m, 3) / C(50, 3)
| Pair | Overcards left | On the flop | By the turn | By the river |
|---|---|---|---|---|
| KK | 4 | 22.6% | 29.1% | 35.3% |
| 8 | 41.4% | 51.4% | 59.9% | |
| JJ | 12 | 57.0% | 67.9% | 76.3% |
| TT | 16 | 69.5% | 79.9% | 86.9% |
| 99 | 20 | 79.3% | 88.1% | 93.3% |
| 88 | 24 | 86.7% | 93.5% | 96.9% |
| 77 | 28 | 92.1% | 96.8% | 98.8% |
| 66 | 32 | 95.8% | 98.7% | 99.6% |
| 55 | 36 | 98.1% | 99.6% | 99.9% |
| 44 | 40 | 99.4% | 99.9% | 100.0% |
| 33 | 44 | 99.9% | 100.0% | 100.0% |
| 22 | 48 | 100.0% | 100.0% | 100.0% |
Every row was counted over all flops, turns and rivers. From JJ down, an overcard is more likely than not on the flop; jacks see one 57.0% of the time. An overcard is not a loss: it only matters if the opponent holds that card, and the hand pages put the pair against whole ranges (see QQ). For the all-in version, QQ vs AQo shows how often the ace actually arrives against a hand that holds one.
Facing kings with the queens? How often someone has a bigger pair.
More on the flop
- Flopping a set11.8%
- Flopping a flush or flush draw0.8%
- Flopping a straight or straight draw1.3%
- Flopping a pair or two pair32.4%
Other odds
- Counted, not quoted.
tools/build-odds.mjsdeals every possible flop, turn, river or starting hand and counts. Where a closed-form formula exists, the build refuses to publish unless the count matches it exactly. - Made hands come from the engine. Whether cards make a straight, a flush or a full house is decided by the same Rust/WebAssembly evaluator the trainer runs, not by hand-written rules.
- Odds are not equity. Hitting your hand is not winning the pot. For that, the matchup pages deal every board against a specific hand and the spot calculator works against a range.
- Raw data: odds.json.