The total to divide by
Five-card poker starts from one number. The count of different five-card hands in a 52-card deck is 2,598,960, from choosing 5 cards out of 52 when order does not matter. Every one of those hands is equally likely, so the probability of a category is simply the number of hands in it divided by 2,598,960.
This article covers the dealt five-card hand only. It does not cover the chances of improving after a draw, or the 7-card and Texas hold ’em situations, which are different calculations.
The full table
Categories are counted in the usual way: each hand is placed in the highest category it qualifies for, so a flush does not also count as a high-card hand, and a straight flush is not counted as a flush.
| Category | Number of hands | Approximate probability |
|---|---|---|
| Royal flush | 4 | 0.00015% (about 1 in 649,740) |
| Straight flush (excluding royal) | 36 | 0.0014% (about 1 in 72,193) |
| Four of a kind | 624 | 0.024% (about 1 in 4,165) |
| Full house | 3,744 | 0.14% (about 1 in 694) |
| Flush (excluding straight flush) | 5,108 | 0.20% (about 1 in 509) |
| Straight (excluding straight flush) | 10,200 | 0.39% (about 1 in 255) |
| Three of a kind | 54,912 | 2.1% (about 1 in 47) |
| Two pair | 123,552 | 4.8% (about 1 in 21) |
| One pair | 1,098,240 | 42.3% (about 1 in 2.4) |
| High card | 1,302,540 | 50.1% (about 1 in 2) |
| Total | 2,598,960 | 100% |
The counts add up exactly to the total, which is a useful check: 4 + 36 + 624 + 3,744 + 5,108 + 10,200 + 54,912 + 123,552 + 1,098,240 + 1,302,540 = 2,598,960.
Where the numbers come from
Each count follows from a short argument. Using combinations, written C(n, k) for choosing k items from n, a few examples show the pattern.
Four of a kind (624). Choose the rank for the four cards (13 ways), take all four of that rank (1 way), and then choose any fifth card from the remaining 48. That is 13 x 48 = 624.
Full house (3,744). Choose the rank of the three (13 ways) and which three of its four cards (4 ways), then choose a different rank for the pair (12 ways) and which two of its four cards (6 ways). That is 13 x 4 x 12 x 6 = 3,744.
Flush (5,108). Choose a suit (4 ways) and five of its 13 cards. C(13, 5) is 1,287, so there are 4 x 1,287 = 5,148 hands with all five cards in one suit. Of these, 40 are straight flushes, including the 4 royal flushes, so a plain flush leaves 5,148 - 40 = 5,108.
Straight (10,200). A straight uses five consecutive ranks, and there are 10 possible sequences (ace-high down to five-high, counting the ace as either high or low). Each of the five ranks can be in any of 4 suits, giving 10 x 4^5 = 10,240. Remove the 40 straight flushes: 10,240 - 40 = 10,200.
Three of a kind (54,912). Choose the rank (13), three of its four suits (4), then two other cards of two different ranks from the remaining 12 ranks (C(12, 2) = 66) with 4 suit choices each (4 x 4 = 16). That is 13 x 4 x 66 x 16 = 54,912.
Two pair (123,552). Choose two ranks for the pairs (C(13, 2) = 78), pick two suits for each (6 x 6 = 36), then a fifth card of a third rank (11 ranks x 4 suits = 44). That is 78 x 36 x 44 = 123,552.
One pair (1,098,240). Choose the pair’s rank (13) and its two suits (6), then three other cards of three different ranks (C(12, 3) = 220) with 4 suit choices each (4^3 = 64). That is 13 x 6 x 220 x 64 = 1,098,240.
High card (1,302,540). What is left: the hands with five different ranks that are neither a straight nor a flush. Choose five different ranks (C(13, 5) = 1,287), remove the 10 sequences that form straights to get 1,277, assign suits in 4^5 = 1,024 ways, and remove the 4 all-one-suit choices to get 1,020 valid suit patterns. 1,277 x 1,020 = 1,302,540.
These calculations rely on counting methods and on the multiplication principle, and the combinations notation is explained in more detail under binomial coefficients.
Why rarer ranks higher
In standard five-card poker, the ranking follows rarity: the fewer hands there are in a category, the higher it ranks. That is a design choice, and it makes sense because a rarer hand is harder to beat. If rankings ignored rarity, ordinary hands would beat unusual ones and the game would feel arbitrary.
In five-card poker the order matches rarity all the way up: a straight (about 0.39%) is less rare than a flush (about 0.20%), a flush is less rare than a full house (about 0.14%), and so on. The match breaks in variants that change the deck or the hand size. With jokers, a shorter deck or more cards per hand, the counts shift and the standard order may no longer follow rarity, which is why some games adjust the rankings.
Reading the table sensibly
- Most hands are small. About 92% of dealt hands are a pair or worse (42.3 + 50.1 = 92.4). Strong hands are exciting precisely because they are uncommon.
- Rarity is not value in a bet. How likely a hand is does not tell you how much a hand is worth in a betting situation. That depends on opponents, pot size and the chance of improving, which is the territory of hand equity and poker math.
- Past deals do not matter. Seeing a flush does not make another flush less or more likely on the next deal.
- Money warning. Where poker is played for money, outcomes are uncertain, and games with a rake or house edge lose over time for the typical participant. Do not stake money you cannot afford to lose, and if gambling is causing harm, a local support service can help.