Odds of flopping a set
How often does a pocket pair flop a set? 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 a pair, two cards of your rank are left among the 50 unseen. The flop misses only if all three cards come from the other 48:
P(no set) = C(48, 3) / C(50, 3) = 17,296 / 19,600 = 88.24% P(set or better) = 1 − 88.24% = 11.76% = 1 in 8.51 By the turn = 1 − C(48, 4) / C(50, 4) = 15.51% By the river = 1 − C(48, 5) / C(50, 5) = 19.18%
The build dealt all 19,600 flops to 7♣7♦ and counted; every pair gives the same numbers because only the two matching cards matter. The engine then said what each of those flops actually makes:
| Flop | Probability | 1 in | Odds against | Count |
|---|---|---|---|---|
| A set (three of a kind) | 10.78% | 9.28 | 8.28 to 1 | 2,112 / 19,600 |
| A set and the board pairs: full house | 0.73% | 136 | 135 to 1 | 144 / 19,600 |
| Both remaining cards: quads | 0.24% | 408 | 407 to 1 | 48 / 19,600 |
| Set or better, total | 11.76% | 8.51 | 7.51 to 1 | 2,304 / 19,600 |
| Board trips: a full house nobody needs your pair for | 0.24% | 408 | 407 to 1 | 48 / 19,600 |
Set mining: the price
Calling a raise only to flop a set wins on 11.8% of flops and gives up on the rest. To break even on the call alone, the hands where you hit must win 7.51 times the call on average, because you miss 7.51 to 1. Call 3 bb, and you need to win about 22.5 bb more when the set comes. That ignores the times a set loses (to a bigger set, a straight or a flush) and the times you hit and get no action, so the real requirement is higher. Effective stacks decide it: a call that needs 23 bb of profit cannot work with 20 bb behind.
Once you have it, see how often a set fills up, and on the pair's own page (77, say) its push/fold range at every stack depth.
More on the flop
- Flopping a flush or flush draw0.8%
- 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.