hand odds
Royal flush odds.
There are 4 royal flushes in a deck of 52 cards, one for each suit, out of 2,598,960 possible five card hands. That is 1 in 649,740. In Texas Hold'em you get to use seven cards instead of five, and the odds shorten to 1 in 30,940. Everything below is counted from the deck rather than copied from somewhere, and the build stops if any of it stops adding up.
five cards dealt
1 in 649,740
4 of 2,598,960
seven cards, to the river
1 in 30,940
4,324 of 133,784,560
holding two of the five
1 in 1,960
1,081 of 2,118,760 boards
five cards
Every hand, and how rare it is.
This is the classic table: deal five cards from a full deck and see what you get. The order of the hands is not a convention someone agreed on, it is this column of counts sorted from small to large. If you want the order without the arithmetic, the hand rankings page lists all ten with an example of each.
| # | Hand | Example | Combinations | Chance | Odds |
|---|---|---|---|---|---|
| 01 | Royal flush Ten to ace in one suit. Nothing beats it and nothing ties it. | 4 | 0.00015% | 1 in 649,740 | |
| 02 | Straight flush Five in a row, one suit, not topped by the ace. | 36 | 0.00139% | 1 in 72,193 | |
| 03 | Four of a kind All four of one rank. | 624 | 0.024% | 1 in 4,165 | |
| 04 | Full house Three of one rank and two of another. | 3,744 | 0.144% | 1 in 694 | |
| 05 | Flush Five of one suit, in no particular order. | 5,108 | 0.197% | 1 in 509 | |
| 06 | Straight Five in a row, suits ignored. | 10,200 | 0.392% | 1 in 255 | |
| 07 | Three of a kind Three of one rank, and no pair beside it. | 54,912 | 2.11% | 1 in 47.3 | |
| 08 | Two pair Two pairs, highest pair compared first. | 123,552 | 4.75% | 1 in 21.0 | |
| 09 | One pair Two of a rank, three cards beside it. | 1,098,240 | 42.26% | 1 in 2.4 | |
| 10 | High card Nothing made. The highest card plays. | 1,302,540 | 50.12% | 1 in 2.0 |
counted at build time, and the ten counts add up to 2,598,960
seven cards
The table that applies at a Hold'em table.
The five card table is the one everybody quotes, and it is the wrong one for the game most people play. In Hold'em you make your best five out of two in your hand and five on the board, so you get 21 attempts at once. Every hand becomes more likely, and the ones that need five specific cards gain the most.
| Hand | Combinations | Chance | Odds | Versus five cards |
|---|---|---|---|---|
| Royal flush | 4,324 | 0.00323% | 1 in 30,940 | 21x |
| Straight flush | 37,260 | 0.028% | 1 in 3,591 | 20x |
| Four of a kind | 224,848 | 0.168% | 1 in 595 | 7.0x |
| Full house | 3,473,184 | 2.60% | 1 in 38.5 | 18x |
| Flush | 4,047,644 | 3.03% | 1 in 33.1 | 15x |
| Straight | 6,180,020 | 4.62% | 1 in 21.6 | 12x |
| Three of a kind | 6,461,620 | 4.83% | 1 in 20.7 | 2.3x |
| Two pair | 31,433,400 | 23.50% | 1 in 4.3 | 4.9x |
| One pair | 58,627,800 | 43.82% | 1 in 2.3 | 1.0x |
| High card | 23,294,460 | 17.41% | 1 in 5.7 | 0.3x |
counted at build time, and these ten add up to 133,784,560
reading the numbers
Rarity is the ranking.
A straight beats three of a kind because there are 10,200 straights against 54,912 sets of trips in five cards. A flush beats a straight because there are only 5,108 of them. Every line of the hand ranking is one of these comparisons, which is why the order never changes and why nobody has to remember it as a list of arbitrary rules. If you want to prove that to yourself instead of taking it on trust, the hand trainer deals real spots and keeps score.
Something interesting happens on the way from five cards to seven. In five cards, one pair is the most common made hand at 42.26 percent and two pair is rare at 4.75 percent. With seven cards two pair jumps to 23.50 percent, and a made hand of some sort becomes the norm rather than the exception: only 17.41 percent of seven card combinations make nothing at all, against 50.12 percent in five cards. That is the real reason ace high wins fewer showdowns than beginners expect.
Both tables answer the question of how often a hand appears if you see every card. They do not answer how often you will hold one, because you fold most of your starting hands and you rarely reach the river. The probability tables for the hands you are actually dealt take it from the other end: what you get before the flop, what the flop does to it, and how often a draw comes in. The two sets of numbers describe the same deck from opposite sides.
One warning about the shortcut everybody uses at the table. Multiplying your outs by four with two cards to come is close enough for a flush draw, where it says 36 percent against a real 35.0 percent, and badly wrong for a big draw, where fifteen outs give 54.1 percent and the shortcut claims 60. The gap grows exactly where the pot is biggest. The outs calculator prints the shortcut and the real number side by side so you can see how far apart they drift.
And none of this is advice about whether to play a hand. A probability tells you how often something happens; it says nothing about the price you are being asked to pay for it. That second half is what pot odds are for, and a hand can be rare, beautiful and still a fold.
the royal flush, in detail
Four hands in a deck of 2.6 million.
The royal flush is and its three siblings in the other suits. There is no ranking between them, so two royal flushes split the pot, and it is the only hand in poker that cannot be beaten by anything. Here is what that rarity looks like from every angle worth asking about.
| The question | Ways | Out of | Odds |
|---|---|---|---|
| Dealt in five cards | 4 | 2,598,960 | 1 in 649,740 |
| Somewhere in seven cards, any two hole cards | 4,324 | 133,784,560 | 1 in 30,940 |
| Holding two of the five, by the river | 1,081 | 2,118,760 | 1 in 1,960 |
| Holding two of the five, straight off the flop | 1 | 19,600 | 1 in 19,600 |
Turned into time at the table, 1 in 30,940 is about 1,031 hours of live poker at 30 hands an hour, or about 97 hours online across four tables at 320 hands an hour. Both figures assume you play every hand to the river, which nobody does, so the honest version is longer. Most players who have one have it because they were dealt two of the cards and the board did the rest, which is the 1 in 1,960 line.
where these numbers come from
Nothing on this page is typed in. When the site is built, two separate pieces of arithmetic count the deck. The first walks through every rank pattern a hand can have, three of one rank and two of another and so on, and works out how many ways there are to pick the ranks and how many ways to give them suits. The second deals all 2,598,960 five card hands one by one and sorts them into the nine categories.
The two have to agree to the last hand, and both have to add up to 2,598,960. If they ever disagree, this page does not get published. The seven card table uses the first method only, because dealing all 133,784,560 combinations would slow the build down for no gain, and its total is checked against 133,784,560 in the same way. On top of that, every example hand in the tables is run through the same hand evaluator the rest of the site uses, and the ten rows have to beat each other in the order shown.
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Your spot is not in this table.
These are the odds for the whole deck. The odds you need at the table are for the cards you can still see coming, with the ones you already hold taken out. That is a different sum, and it is the one the calculator does.
questions about hand odds
What are the odds of a royal flush?
In five cards there are exactly 4 royal flushes among 2,598,960 hands, one per suit, which is 1 in 649,740. In Texas Hold'em you see seven cards, and then 4,324 of the 133,784,560 seven card combinations contain one: 1 in 30,940. Both numbers are counted on this page rather than quoted.
How often will I actually hit a royal flush?
At 1 in 30,940 hands, a live player seeing about 30 hands an hour is looking at roughly 1,031 hours at the table. Online across four tables at about 320 hands an hour it is closer to 97 hours. That assumes you play every hand to the river, which nobody does, so in practice it takes longer.
What are the odds of a royal flush if I hold two of the cards?
Much shorter, and this is the number worth knowing. Holding two suited broadway cards that belong to the same royal, the board has to bring the other three: 1,081 of the 2,118,760 possible boards do, which is 1 in 1,960. Flopping it outright is 1 in 19,600.
Why are the odds different for five cards and seven?
Because seven cards give you more chances to hold five good ones. A five card deal is one shot; a Hold'em hand is the best five out of seven, which is 21 different five card hands at once. That is why a flush goes from 0.197 percent to 3.03 percent, and why one pair stops being the common result and two pair takes over.
Is a royal flush rarer than four of a kind?
Yes, by a long way. With seven cards there are 224,848 four of a kind combinations against 4,324 royal flushes, so quads turn up about 52 times as often. That ratio is the whole reason the ranking puts the royal flush on top.
Do these odds mean I should chase a royal flush?
No. Every number on this page is the chance of the hand appearing, not the chance of it making money. A draw is worth chasing when the price you are paying is smaller than your share of the pot, which is a different sum entirely, and a royal draw is almost never priced right on its own. It is worth something because it is also a flush draw and a straight draw.
Back to poker hand rankings.