Odds of flopping a flush (and a flush draw)
How often do suited cards flop a flush? 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
Holding two hearts, 11 hearts are left among the 50 unseen cards and 39 are not hearts. Count the flops by how many hearts they bring:
Flush 3 hearts: C(11, 3) = 165 Flush draw 2 hearts: C(11, 2) × 39 = 2,145 Backdoor 1 heart: 11 × C(39, 2) = 8,151 Nothing 0 hearts: C(39, 3) = 9,139 Total = 19,600 = C(50, 3)
| Flop | Probability | 1 in | Odds against | Count |
|---|---|---|---|---|
| Flush (three of your suit) | 0.84% | 119 | 118 to 1 | 165 / 19,600 |
| Flush draw (two of your suit) | 10.94% | 9.14 | 8.14 to 1 | 2,145 / 19,600 |
| Backdoor flush draw (one) | 41.59% | 2.40 | 1.40 to 1 | 8,151 / 19,600 |
| None of your suit | 46.63% | 2.14 | 1.14 to 1 | 9,139 / 19,600 |
| A flush by the river, using both cards | 6.40% | 15.6 | 14.6 to 1 | 135,597 / 2,118,760 |
The build dealt all 19,600 flops to 9♥8♥, and the engine agreed: it scored exactly the 165 three-heart flops as a flush or straight flush, no more. The by-the-river line counts all 2,118,760 five-card boards with three or more hearts.
What suited is worth
A flush on the flop is a 1-in-119 event, and the river figure, 6.40%, is the real value of being suited: against a random hand, the suited version of a hand has 1.7 to 3.7 points more equity than the offsuit one (see the starting-hand rankings). The flush draw, at 10.94%, is the more common gift. From there it is 9 outs and 35.0% by the river.
More on the flop
- Flopping a set11.8%
- Flopping a straight or straight draw1.3%
- Flopping a pair or two pair32.4%
- An overcard to your pair41.4%
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.