How often does a pocket pair flop a set?
A pocket pair flops a set (or better) 11.76% of the time — about 1 in 9 flops, about 7.5 to 1 against.
Two of the 50 unseen cards match your pair. The flop is three cards, so the question is: how often do three cards drawn from 50 include at least one of those two? It is easier to count the flops that miss — C(48, 3) of the C(50, 3) — and subtract.
The number includes the rare flops that make quads (both remaining cards arrive, 0.245%). Missing the set is by far the normal outcome: about seven flops in eight.
- Cards that make a set2
- Unseen cards5052 − 2
- Flops that miss17,296C(48, 3)
- All flops19,600C(50, 3)
- Probability11.76%1 − 17296 / 19600
Quick check
About how often does a pocket pair flop a set?
Show answer
About 12% — roughly 1 in 8.5.
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