Full House in Poker: Three of a Kind Plus a Pair
A full house is three of a kind plus a pair, like K‑K‑K‑9‑9: kings full of nines. It beats a flush, a straight and every weaker hand, and loses only to four of a kind and straight flushes. Between two full houses, the three of a kind decides first, then the pair. A set on an unpaired flop becomes a full house or better 33.4% of the time by the river.
Compute a full house
K♥K♦ on K♠ 9♦ 9♣: kings full
K♥K♦ makes kings full of nines on the flop. Equity with the turn and river to come:
| Opponent | What it holds | K♥K♦'s equity |
|---|---|---|
| 9♥8♥ | three nines | 95.7% |
| K♣9♠ | nines full of kings | 95.6% |
| A♠A♦ | two pair, aces and nines | 91.3% |
Each opponent needs specific cards. The last nine gives four of a kind to the hand that holds a nine; one of the two remaining aces gives A♠A♦ aces full of nines, which beats kings full, and the last two nines together put four of a kind on the board, where A♠A♦'s ace kicker wins. Nines full of kings is a full house too, but its three of a kind is lower, so it loses.
How often a set fills up
| Start | Outs | Full house or better by the river |
|---|---|---|
| set on the flop | seven on the turn, ten on the river | 33.4% |
| set on the turn (unpaired board) | ten | 21.7% |
On an unpaired flop, the set fills up when the board pairs (six cards) or the last card of its rank comes (one card). If the turn misses, the turn card adds three more outs on the river. See poker outs and set or trips.
When the full house is not safe
- On a paired board, watch for the bigger full house. On K♠ 9♦ 9♣, K♥K♦ is ahead of nines full, but an ace on the turn gives A♠A♦ aces full of nines. A full house built on the board's pair is weaker than it looks, because a higher full house beats it: see paired boards.
- A full house has no kicker. It uses all five cards; when the board itself makes a full house nobody can beat, the pot is split: see split pots.
- Four of a kind and straight flushes are rare. Folding a full house is rare, even on a paired board; the question is how much to bet, not whether to play.
Keep going
- Which hands beat which: poker hand rankings.
- The best possible hand on a board: the nuts in poker.
- Four cards of one rank, and how rare they are: four of a kind in poker.
- Five cards of one suit, and which flush wins: the flush in poker.
Sources
- Equities enumerated exactly over every turn and river; fill-up odds counted card by card.