High card the weakest hand in poker
Five cards with no pair, not all one suit and not in sequence. It beats nothing: any made hand is better.
How often, card by card
| Cards dealt | Probability | 1 in | Odds against | Count |
|---|---|---|---|---|
| 5 cards: the flop, or five-card draw | 50.12% | 2.00 | 1.00 to 1 | 1,302,540 / 2,598,960 |
| 6 cards: the turn | 32.48% | 3.08 | 2.08 to 1 | 6,612,900 / 20,358,520 |
| 7 cards: the river in hold'em, or seven-card stud | 17.41% | 5.74 | 4.74 to 1 | 23,294,460 / 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
High card, five cards: rank sets that are not a straight × suit patterns that are not a flush (C(13,5) − 10) × (4⁵ − 4) = (1,287 − 10) × 1,020 = 1,302,540 enumerated by the engine: 1,302,540 of 2,598,960 probability: 1,302,540 / 2,598,960 = 50.1%
There are 1,277 different high card hands once suits are ignored: C(13,5) − 10 = 1,277: every set of five different ranks, minus the ten straights. With seven cards only 407 of them can be anyone's best hand. The weakest five-card high card is 7♦5♣4♣3♣2♣, but in hold'em the weakest you can finish the river with is 9♦8♦7♦5♣4♣: any weaker seven cards contain something better.
When two players both have high card
Compare the highest card; if equal, the next highest, and so on through all five.
Check your own showdown in the hand checker →
High card by starting hand
The chance each of the 169 starting hands ends the river with high card as its best hand, from every one of its 2,118,760 boards. K2o makes it most often (20.2%); 13 hands never can. Averaged over their combinations: pocket pairs 0%, suited hands 17.4%, offsuit hands 18.9%.
| Starting hand | High card by the river | 1 in |
|---|---|---|
| K2o | 20.2% | 5 |
| K3o | 20.0% | 5 |
| Q2o | 20.0% | 5 |
| A9o | 19.8% | 5 |
| A6o | 19.8% | 5 |
| K8o | 19.8% | 5 |
| 72o | 19.8% | 5 |
| AKo | 19.7% | 5 |
| A2o | 19.7% | 5 |
| K4o | 19.7% | 5 |
| … | ||
| 22 | 0% | never |
| 33 | 0% | never |
| 44 | 0% | never |
High card beats
Nothing. It only wins when nobody has a pair or better.
High card 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
- One pair 43.8% by the river
- 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.