How often does two pair fill up?
Two pair on the flop (using both hole cards) improves to a full house 16.47% of the time by the river — four outs.
Probability
16.47%
about 1 time in 6.1
on the next card
8.51%
Exact. Hypergeometric probability over the 47 unseen cards.
Two of each of your paired ranks remain: four outs, the same as a gutshot. 8.51% on the turn and 16.47% by the river.
Note the difference from a set, which has seven outs and picks up more on the turn. Two pair is a strong made hand but a weak drawing hand.
- Outs to a full house4
- Unseen cards on the flop4752 − 2 − 3
- Ways to miss twice903C(43, 2) = 903
- Total two-card run-outs1,081C(47, 2) = 1081
- Probability of hitting by the river16.47%1 − 903 / 1081
- Rule of 4 estimate16.00%4 × 4%
- On the turn alone8.51%4 / 47
- Rule of 2 (turn)8.00%4 × 2%
Try it
Change any card; the numbers recompute from the same engine that produced the answer above.
Your hand
Board
Hand now
Two Pair, Queens and Sevens
Outs
4
of 47 unseen
By the turn
8.5%
4 / 47
By the river
16.5%
two cards to come
The 4 highlighted cards are your outs.
What you’re drawing to
- Two pair to full house4 outs
Shortcut vs. exact
| Cards to come | Rule of 2/4 | Exact | Gap |
|---|---|---|---|
| Turn only | 8% | 8.51% | −0.51 pts |
| Turn and river | 16% | 16.47% | −0.47 pts |