Four of a kind odds in Texas Hold'em
Four of a kind, or quads, means all four cards of one rank, such as four aces. Its probability depends on the question: five random cards, seven available cards, or completing a particular pocket pair are different events.
| Situation | Probability | About one in |
|---|---|---|
| Five random cards contain quads | 0.0240% | 4,165 |
| Seven random cards contain quads | 0.1681% | 595 |
| Pocket pair makes quads of its rank on the flop | 0.2449% | 408 |
| Pocket pair makes quads of its rank by the river | 0.8163% | 123 |
"One in" is the reciprocal of the probability, not odds against. The pocket-pair rows assume you already hold that pair and see the specified community cards. They exclude making quads of another rank on the board.
Five-card four of a kind probability
Choose the rank of the quads in 13 ways. All four suits of that rank must appear. The fifth card can be any of the other 48 cards, giving 13 × 48 = 624 qualifying hands.
There are C(52, 5) = 2,598,960 unordered five-card hands. So the probability is 624 / 2,598,960 = approximately 0.0240%. C(n, k) means the number of ways to choose k objects from n without counting their order.
Seven cards in Texas Hold'em
At the river you have seven cards available: two private cards and five community cards. For a random seven-card set, choose the quads rank, then choose three other cards from the remaining 48:
13 × C(48, 3) / C(52, 7) = 224,848 / 133,784,560 = approximately 0.1681%.
You cannot have two different sets of quads within seven cards, so this count does not duplicate hands. These are the unconditional odds before you know your cards, not the chance that a particular starting hand will make quads.
Starting with a pocket pair
With two kings in your hand, two kings remain among 50 unseen cards. To flop four kings, the flop must contain both remaining kings and one of the other 48 cards:
C(48, 1) / C(50, 3) = 48 / 19,600 = approximately 0.2449%.
To make four kings by the river, both remaining kings must appear among the five community cards. The other three board cards can be chosen from the remaining 48:
C(48, 3) / C(50, 5) = 17,296 / 2,118,760 = approximately 0.8163%.
This assumes you see all five community cards. It is not the chance per hand you actually play if you sometimes fold before the river. Known cards change the calculation.
Does four of a kind always win?
No. A straight flush beats quads. If all four matching cards are on the board, players share those quads and the best fifth card decides the result; they may tie. See the hand rankings and kicker rules for how five-card hands are compared.
A rare outcome is not a reason to ignore the price of a call. Use the coach to practise equity and pot odds, and use Reveal to explore repeated outcomes. A simulation estimate is different from the exact card-counting probabilities above.