Four of a Kind in Poker: Quads and What Beats Them
Four of a kind, or quads, is four cards of the same rank plus a side card: 9‑9‑9‑9‑K. It beats a full house and every weaker hand, and loses only to higher quads and to straight flushes. A pocket pair makes quads by the river only 0.82% of the time; a set on the flop gets there 4.3% of the time.
Compute four of a kind
9♥9♠ on 9♦ 9♣ K♠: flopped quads
9♥9♠ makes all four nines on the flop, two in hand and two on the board. Equity with the turn and river to come:
| Opponent | What it holds | 9♥9♠'s equity |
|---|---|---|
| A♠A♦ | two pair, aces and nines | 99.9% |
| Q♠J♠ | no pair of its own, runner-runner royal flush draw | 99.9% |
| K♥K♦ | kings full of nines | 95.6% |
Even quads are not certain. A♠A♦ wins only when both remaining aces come, Q♠J♠ only with A♠ and T♠ for a royal flush. K♥K♦ needs a single card, the last king, for higher four of a kind.
How often quads come
| Start | Four of a kind by the river |
|---|---|
| pocket pair, before the flop | 0.82% |
| set on the flop | 4.3% |
With a pocket pair, the five board cards must include both remaining cards of its rank. With a set on the flop, one card is left: it has two chances, the turn and the river. That is why quads are rare enough that they are not worth planning a hand around: see set mining and implied odds.
When quads are on the board
If all four cards of a rank are on the board, every player has the same four of a kind, and the fifth card decides. The highest card left, in a hand or on the board, wins; when it is on the board, the pot is split: see split pots and the kicker in poker.
Keep going
- Which hands beat which: poker hand rankings.
- One step below: the full house in poker.
Sources
- Equities enumerated exactly over every turn and river; quad odds counted over every board.