Poker odds, answered
Odds of flopping a set with a pocket pair
A pocket pair flops a set (or better) 11.8% of the time, about 1 flop in 8.5. By the river it makes at least a set 19.2% of the time.
Exact counts, not simulations.
How it is counted
Two cards of your rank are left among the 50 you cannot see. The flop misses both when all three of its cards come from the other 48: C(48,3) of the C(50,3) possible flops. Everything else gives you a set or quads.
Flop: 1 − C(48,3) ÷ C(50,3) = 1 − 17,296 ÷ 19,600 By the river: 1 − C(48,5) ÷ C(50,5)
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