One pair #9 of 10
Two cards of the same rank and three unrelated cards. It beats high card and everything below it, and loses to two pair and everything above.
How often, card by card
| Cards dealt | Probability | 1 in | Odds against | Count |
|---|---|---|---|---|
| 5 cards: the flop, or five-card draw | 42.26% | 2.37 | 1.37 to 1 | 1,098,240 / 2,598,960 |
| 6 cards: the turn | 47.80% | 2.09 | 1.09 to 1 | 9,730,740 / 20,358,520 |
| 7 cards: the river in hold'em, or seven-card stud | 43.82% | 2.28 | 1.28 to 1 | 58,627,800 / 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
One pair, five cards: pair rank × its two suits × three other ranks × their suits 13 × C(4,2) × C(12,3) × 4³ = 13 × 6 × 220 × 64 = 1,098,240 enumerated by the engine: 1,098,240 of 2,598,960 probability: 1,098,240 / 2,598,960 = 42.3%
There are 2,860 different one pair hands once suits are ignored: 13 × C(12,3) = 2,860: the pair rank, then any three kicker ranks. With seven cards only 1,470 of them can be anyone's best hand. The weakest five-card one pair is 2♣2♦5♣4♣3♣, but in hold'em the weakest you can finish the river with is 2♣2♦8♦7♦5♣: any weaker seven cards contain something better.
When two players both have one pair
Higher pair wins. Same pair: compare the three kickers from the top down.
Same pair: the kicker decides
| K♥Q♣ | K♥K♠Q♣9♦5♣ | Pair of kings, Q-9-5 kickers | Wins |
| K♦J♥ | K♦K♠J♥9♦5♣ | Pair of kings, J-9-5 kickers | Loses |
Check your own showdown in the hand checker →
One pair by starting hand
The chance each of the 169 starting hands ends the river with one pair as its best hand, from every one of its 2,118,760 boards. K2o makes it most often (46.3%); 2 hands tie for least often (35.1%): TT, 55. Averaged over their combinations: pocket pairs 35.5%, suited hands 42.6%, offsuit hands 44.9%.
| Starting hand | One pair by the river | 1 in |
|---|---|---|
| K2o | 46.3% | 2 |
| K3o | 46.1% | 2 |
| Q2o | 46.1% | 2 |
| A9o | 46.0% | 2 |
| A6o | 46.0% | 2 |
| K8o | 46.0% | 2 |
| K4o | 46.0% | 2 |
| Q3o | 46.0% | 2 |
| J2o | 46.0% | 2 |
| 72o | 46.0% | 2 |
| … | ||
| 55 | 35.1% | 3 |
| TT | 35.1% | 3 |
| 66 | 35.2% | 3 |
One pair beats
- High card 17.4% by the river
One pair 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
- 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
Making one pair: 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.