How Rare Is Your Hand, Really?
There are 2,598,960 five-card hands. Knowing how the good ones are distributed across that number is the difference between a read and a guess.
· 7 min read
The ranking of poker hands is not a convention someone chose. It is a frequency table: hands are ranked in the exact order of how rarely they occur, from the 4 ways to make a royal flush to the 1,302,540 ways to make nothing at all. Everything about how the game is scored falls out of one number.
2,598,960
The number of distinct five-card hands from a 52-card deck. Every hand ranking in poker is simply this number partitioned by frequency
Wikipedia, poker probability
The full table
| Hand | Probability | Roughly once in |
|---|---|---|
| Royal flush | 0.000154% | 649,740 |
| Straight flush (excluding royal) | 0.00139% | 72,192 |
| Four of a kind | 0.024% | 4,165 |
| Full house | 0.144% | 694 |
| Flush | 0.197% | 509 |
| Straight | 0.393% | 255 |
| Three of a kind | 2.11% | 47 |
| Two pair | 4.75% | 21 |
| One pair | 42.26% | 2.4 |
| High card | 50.12% | 2 |
Probabilities for a random five-card hand from a 52-card deck, from the Wikipedia article on poker probability. These are the frequencies that generate the hand ranking: rarer beats commoner, without exception.
Read the bottom two rows first. More than 92% of random five-card hands are a single pair or nothing. The entire hierarchy that gets people excited — flushes, full houses, quads — occupies under 8% of the space between them, and the top three categories together account for less than three hundredths of a percent.
Hold’em: 1,326 deals, 169 hands
Two hole cards can be dealt in 1,326 distinct combinations, but most of those differences do not matter. Before any community cards are out, the suits are interchangeable — the ace and king of hearts play identically to the ace and king of spades. Collapse them and 1,326 combinations become 169 effectively different starting hands: thirteen pairs, seventy-eight suited non-pairs and seventy-eight offsuit non-pairs.
| Category | Distinct hands | Combinations | Share of deals |
|---|---|---|---|
| Pairs | 13 | 78 | 5.9% |
| Suited non-pairs | 78 | 312 | 23.5% |
| Offsuit non-pairs | 78 | 936 | 70.6% |
| Total | 169 | 1,326 | 100% |
The 169 figure and its breakdown are from the Wikipedia article on Texas hold ’em. Combination counts follow from it: 13 × 6 pairs, 78 × 4 suited, 78 × 12 offsuit. The Wizard of Odds lists each individual pair at 0.45% of deals, which across thirteen ranks gives the 5.9% total.
A specific pair — pocket aces, say — arrives 0.45% of the time, once in about 221 deals. Any pair at all arrives about once in seventeen. At a table dealing thirty hands an hour, aces show up roughly every seven hours of play, which is a useful calibration for how often the game hands you something obviously good.
Draws, and where the numbers come from
After the flop, five cards are known and 47 are not. A flush draw has nine of those 47 helping you, which is 19.1% on the next card. Over two cards the calculation runs through the complement — the probability of missing twice — and lands at about 35%.
| Draw | Outs | By the river | By the turn |
|---|---|---|---|
| Inside straight | 4 | 17% | 9% |
| Open-ended straight | 8 | 32% | 17% |
| Flush draw | 9 | 35% | 19% |
Figures as given in the Wikipedia outs chart for Texas hold ’em. The same article notes the rule of four and two — outs × 4 for two cards, × 2 for one — as a reasonable approximation.
The number that matters most is not on this page
Every figure here describes a hand in isolation, and poker is not played in isolation. A flush is rare in the abstract and unremarkable on a board showing four hearts. Pocket aces are the best starting hand in hold’em and still lose regularly, because five community cards are five chances for someone else to make something these tables say is rarer.
What the frequency table gives you is a baseline: how surprised to be, and how surprised your opponent should be. Knowing that two pair arrives once in twenty-one hands tells you something real about how often anyone at the table has one. It does not tell you whether the person betting into you does, and no table can.
The one practical takeaway
Fold more. The distribution says that most of the time neither you nor anyone else has anything — half of all five-card hands are high card, and another 42% are one pair. A player who acts as though a pair is a strong holding is misreading a table that says a pair is the ordinary case. The frequencies are public, they have not changed since the deck was standardised, and they are the least controversial edge available in the game.
