Four of a kind #3 of 10
All four cards of one rank, plus a fifth card. Also called quads. It beats a full house and everything below it, and loses to a straight flush and everything above.
How often, card by card
| Cards dealt | Probability | 1 in | Odds against | Count |
|---|---|---|---|---|
| 5 cards: the flop, or five-card draw | 0.02% | 4,165 | 4,164 to 1 | 624 / 2,598,960 |
| 6 cards: the turn | 0.07% | 1,388 | 1,387 to 1 | 14,664 / 20,358,520 |
| 7 cards: the river in hold'em, or seven-card stud | 0.17% | 595 | 594 to 1 | 224,848 / 133,784,560 |
“Best hand” means exactly this hand and nothing better: a full house also contains a pair, but it counts once, as a full house. These are the odds for any two hole cards; your own starting hand moves them, which is the grid further down.
The working
Four of a kind, five cards: quads rank × any of the other 48 cards 13 × 48 = 624 enumerated by the engine: 624 of 2,598,960 probability: 624 / 2,598,960 = 0.024%
There are 156 different four of a kind hands once suits are ignored: 13 × 12 = 156: the quads rank, then the kicker rank. Every one of them can still be your best hand with seven cards.
When two players both have four of a kind
Higher quads win. Same quads (on the board): the fifth card decides.
Four of a kind on the board: the fifth card decides
| A♦2♣ | 8♣8♦8♥8♠A♦ | Four of a kind, eights, ace kicker | Wins |
| Q♣Q♦ | 8♣8♦8♥8♠K♠ | Four of a kind, eights, king kicker | Loses |
Check your own showdown in the hand checker →
Four of a kind by starting hand
The chance each of the 169 starting hands ends the river with four of a kind as its best hand, from every one of its 2,118,760 boards. 13 hands tie for most often (0.84%): AA, KK, QQ and 10 more; 156 hands tie for least often (0.13%): AKs, AQs, AJs and 153 more. Averaged over their combinations: pocket pairs 0.84%, suited hands 0.13%, offsuit hands 0.13%.
| Starting hand | Four of a kind by the river | 1 in |
|---|---|---|
| AA | 0.84% | 119 |
| KK | 0.84% | 119 |
| 0.84% | 119 | |
| JJ | 0.84% | 119 |
| TT | 0.84% | 119 |
| 99 | 0.84% | 119 |
| 88 | 0.84% | 119 |
| 77 | 0.84% | 119 |
| 66 | 0.84% | 119 |
| 55 | 0.84% | 119 |
| … | ||
| 32o | 0.13% | 794 |
| 42o | 0.13% | 794 |
| 43o | 0.13% | 794 |
Four of a kind beats
- Full house 2.60% by the river
- Flush 3.03% by the river
- Straight 4.62% by the river
- Three of a kind 4.83% by the river
- Two pair 23.5% by the river
- One pair 43.8% by the river
- High card 17.4% by the river
Four of a kind loses to
- Royal flush 0.0032% by the river
- Straight flush 0.028% by the river
Making four of a kind: the odds pages
- Every five-, six- and seven-card hand was dealt and classified by the site's engine (
tools/build-rankings.mjs). The five-card count must equal the formula above or the build fails; the six- and seven-card counts must equal the standard published tables. - The starting-hand figures deal each hand every possible board. Suits are interchangeable, so one deal of each hand gives the exact figure for all its combinations.
- The showdowns above were scored by the same engine; the build fails if any of them comes out differently from what its title says.
- Back to all ten hands. Raw data: rankings.json.