The royal flush is the hand every poker player dreams about. Some regulars have played for years without making one, while others hit it in their first month. So how rare is a royal flush in reality? In this BC Poker guide we explain what the hand is, show how its probability is calculated and compare the odds of a royal flush in Five-Card Draw, Texas Hold’em, Omaha and Seven-Card Stud. We also answer how rare is a royal flush in texas holdem, the game most players meet first.
All figures below are based on a standard 52-card deck and simple combinatorics, so you can check every number yourself.
What Is a Royal Flush in Poker?
A royal flush is a straight from ten to ace in one suit: A, K, Q, J and 10 of spades, hearts, diamonds or clubs. It is the highest hand in poker, and the only one that can never lose. At most it can be tied, when all five cards are on the board. For a detailed overview of the hand, see our guide to the Royal Flush in Poker.
These four hands are the only royal flushes in the deck, and suits have equal value in poker, so all four are exactly as strong. If you ask how rare is a royal flush in poker, the answer starts here: four hands out of millions of possible ones.
How to Calculate the Probability of a Royal Flush
Before asking what are the odds of a royal flush in a specific game, it helps to know the formula. Any poker probability follows the same rule: the number of favorable outcomes divided by the number of all possible outcomes. For a royal flush, this means counting how many hands contain one and dividing by the total number of hands.
- Count all possible five-card hands. From a 52-card deck you can deal 2,598,960 different five-card hands.
- Count the hands that are royal flushes. There are only 4, one per suit.
- Divide. 4 / 2,598,960 = 1 / 649,740, or about 0.000154%.
The probability of royal flush in five cards is therefore 1 in 649,740. Poker players often state the same number as odds against, 649,739 to 1, because that compares the hands that miss with the one that hits.
In games where you see seven cards, the math changes. There are 133,784,560 possible seven-card sets. A set contains a royal flush when it includes all five royal cards of one suit plus any two of the other 47 cards. That gives 4 × 1,081 = 4,324 sets, so the probability of royal flush with seven cards is about 1 in 30,940, or 0.0032%. More cards mean more chances, which is why the hand appears far more often in Hold’em than in a five-card deal. The same figure gives the odds of royal flush in texas holdem for a player who sees the river.
What Are The Odds of a Royal Flush?
The answer depends on the game, because each variant gives you a different number of cards and different rules for using them. Here are the odds of getting a royal flush for a player who stays in the hand until the end.
| Game 🌟 | Cards you can use 🃏 | Probability 📊 | Odds 🎯 |
|---|---|---|---|
| 🎴 Five-card deal, no draw | 5 cards | 0.000154% | 1 in 649,740 |
| ♠️ Texas Hold’em | Best 5 of 7 cards | 0.0032% | 1 in 30,940 |
| ♦️ Omaha | 2 of 4 hole cards + 3 of 5 board cards | 0.0092% | 1 in 10,829 |
| ♣️ Seven-Card Stud | Best 5 of 7 cards | 0.0032% | 1 in 30,940 |
Real chances of a royal flush at the table are lower than these numbers, because players fold most hands before the river. Still, the table shows clearly how rare is a royal flush in poker: even in Omaha, the friendliest of these games, you need more than ten thousand complete hands on average to make one.
One legendary hand. Four poker formats. Different odds.
Royal Flush Odds
Royal Flush Probability in Five-Card Draw
In Five-Card Draw, you receive five cards and can replace some of them once. Being dealt a royal flush straight away is a 1 in 649,740 event. Drawing improves the odds of hitting a royal flush only when you already hold most of the required cards.
With K♥ Q♥ J♥ 10♥, discard the fifth card and draw one replacement. You need exactly the A♥ from the 47 unseen cards. If you hold only three royal cards, you must draw two specific cards instead.
Royal Flush Probability in Texas Hold’em
For a player who sees all five board cards, the odds of royal flush in texas holdem are 1 in 30,940. Your hole cards change the odds of hitting a royal flush significantly.
Starting with two suited royal cards, such as A♠ K♠ or J♠ 10♠, your chance to flop the exact three missing cards is 1 in 19,600. Your chance to complete the hand by the river is 1 in 1,960.
So how rare is a royal flush in texas holdem? Extremely rare; hands without two suited royal hole cards need even more help from the board.
Royal Flush Probability in Omaha Poker
Omaha gives every player four hole cards, but a final hand must use exactly two hole cards and exactly three board cards. The extra hole cards create more possible combinations, making the odds of getting a royal flush about 1 in 10,829 by the river.
In this example, the player uses A♥ K♥ from the hand and Q♥ J♥ 10♥ from the board. The remaining four cards are not part of the royal flush.
The two-card rule matters: even if the board shows A♥ K♥ Q♥ J♥, holding only 10♥ in your hand is not enough to make a royal flush.
Royal Flush Probability in Seven-Card Stud
In Seven-Card Stud, each player gets seven cards of their own, some face down and some face up. For a player who reaches seventh street, the probability of a royal flush is the same as for seven random cards in Hold’em: 1 in 30,940.
The key difference is visible information. Opponents’ exposed cards show which cards are no longer available. If another player has an exposed K♠, you cannot complete a spade royal flush in that hand, because you cannot have the same K♠ yourself.
The illustrated hand makes a club royal flush using five of the seven cards; the other two cards are excluded.
Royal Flush Probability in Five-Card Draw
In Five-Card Draw you get five cards and can replace some of them once. Being dealt a royal flush straight away is a 1 in 649,740 event. The draw improves the odds of hitting a royal flush, but only if you already hold most of it.
K♥ Q♥ J♥ 10♥ + one draw
With four cards to a royal flush, you discard the fifth card and need one exact card, here the A♥, from the 47 you have not seen. The chance is 1 in 47, about 2.1%. With three cards to a royal flush, you draw two and need two exact cards, which gives 1 in 1,081.
Royal Flush Probability in Texas Hold’em
For a player who sees all five board cards, the odds of royal flush in texas holdem are 1 in 30,940. Your hole cards change the odds of hitting a royal flush a lot here. With two suited royal cards, such as A♠ K♠ or J♠ 10♠, the chance to flop a royal flush is 1 in 19,600, and to make it by the river 1 in 1,960.
A♠ K♠ + Q♠ J♠ 10♠
Hands without two royal cards of one suit can still make a royal flush, but they need even more help from the board. So how rare is a royal flush in texas holdem for a typical player? Rare enough that many players see only a few in a year, even when they play a lot of hands at the BC Poker tables.
Royal Flush Probability in Omaha Poker
Omaha gives each player four hole cards, and the hand must use exactly two of them with exactly three board cards. More hole cards mean more possible combinations, so the odds of getting a royal flush rise to about 1 in 10,829 by the river.
A♥ K♥ 7♣ 7♦ + Q♥ J♥ 10♥ 4♠ 2♣
In this example the player uses A♥ K♥ from the hand and Q♥ J♥ 10♥ from the board. Remember the two-card rule: if the board shows A♥ K♥ Q♥ J♥ and you hold only the 10♥ in hearts, you do not have a royal flush, because you must play two cards from your hand.
Royal Flush Probability in Seven-Card Stud
In Seven-Card Stud each player gets seven cards of their own, some face down and some face up. The math matches Hold’em: a player who reaches seventh street makes a royal flush about once in 30,940 hands.
The difference is in what you can see. Your opponents’ upcards are visible, so you can tell when a card you need is already gone. If a K♠ is showing in front of another player, a spade royal flush is impossible for you in that hand, and your real chances drop.
