Flush #5 of 10
Five cards of the same suit, not in sequence. It beats a straight and everything below it, and loses to a full house and everything above.
How often, card by card
| Cards dealt | Probability | 1 in | Odds against | Count |
|---|---|---|---|---|
| 5 cards: the flop, or five-card draw | 0.20% | 509 | 508 to 1 | 5,108 / 2,598,960 |
| 6 cards: the turn | 1.01% | 98.9 | 97.9 to 1 | 205,792 / 20,358,520 |
| 7 cards: the river in hold'em, or seven-card stud | 3.03% | 33.1 | 32.1 to 1 | 4,047,644 / 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
Flush, five cards: four suits × any five ranks of it, minus the straight flushes 4 × C(13,5) − 40 = 5,148 − 40 = 5,108 enumerated by the engine: 5,108 of 2,598,960 probability: 5,108 / 2,598,960 = 0.20%
There are 1,277 different flush hands once suits are ignored: C(13,5) − 10 = 1,277: any five ranks of one suit except the ten in sequence. Every one of them can still be your best hand with seven cards.
When two players both have a flush
Compare the highest card, then the next, through all five. Suits never rank.
A flush beats a straight
| A♥3♥ | A♥K♥9♥3♥2♥ | Flush, ace high (A-K-9-3-2) | Wins |
| T♠6♠ | T♠9♥8♦7♣6♠ | Straight, ten high | Loses |
Two flushes: compare card by card
| K♥3♦ | A♥K♥9♥6♥4♥ | Flush, ace high (A-K-9-6-4) | Wins |
| Q♥J♥ | A♥Q♥J♥9♥6♥ | Flush, ace high (A-Q-J-9-6) | Loses |
Check your own showdown in the hand checker →
Flush by starting hand
The chance each of the 169 starting hands ends the river with a flush as its best hand, from every one of its 2,118,760 boards. K2s makes it most often (6.57%); 3 hands tie for least often (1.95%): TT, 55, T5o. Averaged over their combinations: pocket pairs 1.95%, suited hands 6.51%, offsuit hands 1.95%. Suited hands differ only through straight flushes, which count in the class above, so the gaps between them are tiny.
| Starting hand | Flush by the river | 1 in |
|---|---|---|
| K2s | 6.57% | 15 |
| K3s | 6.57% | 15 |
| Q2s | 6.57% | 15 |
| A9s | 6.57% | 15 |
| A6s | 6.57% | 15 |
| K8s | 6.57% | 15 |
| 72s | 6.57% | 15 |
| K4s | 6.57% | 15 |
| Q3s | 6.57% | 15 |
| J2s | 6.57% | 15 |
| … | ||
| T5o | 1.95% | 51 |
| 55 | 1.95% | 51 |
| TT | 1.95% | 51 |
Flush beats
- 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
Flush loses to
- Royal flush 0.0032% by the river
- Straight flush 0.028% by the river
- Four of a kind 0.17% by the river
- Full house 2.60% by the river
Making a flush: 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.