How often does a flopped set make a full house or quads by the river?
A set on an unpaired flop improves to a full house or quads 33.40% of the time by the river.
Probability
33.40%
about 1 time in 3
Exact. All 1,081 turn-and-river combinations were evaluated.
On the flop a set has seven outs to fill: three of each other board rank and the case card. If the turn misses it usually adds a new rank, so the river has ten outs. 7/47 plus (40/47 × 10/46) works out to about one time in three.
This is why a set is such a strong hand on draw-heavy boards: even when a flush or straight gets there, the set has a third of the deck to overtake it.
- Run-outs that make a full house or better361
- All turn-and-river combinations1,081C(47, 2)
- Probability33.40%361 / 1081
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Change any card; the numbers recompute from the same engine that produced the answer above.
Your hand
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Opponent
Opponent
Every possible turn card
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Computing every runout…