Pocket Pair to Set on Flop Calculator
Probability of flopping a set, full house, or quads with a pocket pair.
Includes set-mining break-even pot odds for cash and tournament play.
The famous 7.5 to 1. When you hold a pocket pair, you flop a set (or better) about 11.76% of the time. That is roughly 1 in 8.5 — call it 7.5 to 1 against. The exact math:
The setup. Two cards in your hand, 50 unseen, 3 cards on the flop. Two of the remaining 50 cards complete your set. Probability of NOT hitting on any of the three flop cards:
- (48/50) × (47/49) × (46/48) = 88.24%
- So P(at least one set card) = 1 - 0.8824 = 11.76%
Flopping better than a set.
- Set: 10.78%
- Full house: 0.74%
- Quads: 0.24%
- Set or better: 11.76%
The full-house and quads numbers come up because the flop can pair a different rank or you can flop the case card.
Set mining as a strategy. Limp-call or call a small raise with a small pocket pair (22 to 88), aiming to flop a set against a strong made hand. The standard rule is “you need 15:1 implied odds for set mining to be profitable.” Why 15? You hit 1 in 8.5, lose your call about 7.5 times, and need to make those losses back on the one time you hit big. Reverse engineering says you need to win at least the call × 15 from your opponent on the hits.
When set mining fails.
- Effective stacks too small (you cannot win 15x your call).
- Multi-way pot where someone else has a draw beating your set on later streets.
- Tight opponents who fold to your raise after the flop instead of paying off.
Hit a set, what now? Play it fast. Bet half pot to two-thirds pot on the flop. Sets do not retain equity well against draws on bad runouts (flushes, straights). Slow-playing is for the river or a dry board.
Versus the “set on flop given you saw the flop” math. This is exactly the same — 11.76%. The flop is dealt regardless. Some sources quote it as 11.8% or 12% rounded.
Quick mental math. 1 in 8.5 ≈ 12%. If you remember nothing else, remember that.