How Rare a Royal Flush Is in a Five-Card Hand
In a five-card hand, a royal flush is 4 combinations out of 2,598,960. The count, and what it does not predict.
A royal flush is the highest straight flush: ace, king, queen, jack, and ten of one suit. There are four of them in a 52-card deck, one in each suit. People call the hand one in a million. The real count, for five-card combinations, is more common than one in a million and still very rare. This page shows the arithmetic. It does not say you should play in order to see one. A royal flush is a curiosity of the rankings. It is not a financial plan.
The order of categories is in Poker Hand Rankings Explained. How to keep a fraction from being misread as odds against is in Odds and Probability Are Not the Same Number. The figure below is about five-card hands dealt from the full deck. It is not the chance that your two Hold'em cards will become a royal by the river. That is a different problem, and this article does not pretend to solve it in a footnote.
How many five-card hands exist
The number of ways to choose five cards from 52, ignoring order, is 52 times 51 times 50 times 49 times 48, divided by 120. The divisor is 5 times 4 times 3 times 2 times 1, because order does not matter. The product before dividing is 311,875,200. Divided by 120 it is 2,598,960. Every distinct set of five cards is one of those hands, equally likely if the deck is shuffled and five cards are dealt.
How many of them are royal
Each suit can contribute exactly one royal: the ace, king, queen, jack, and ten of that suit. Four suits, four royals. No other five cards have that name. Four divided by 2,598,960 is 1 divided by 649,740. So a random five-card hand is a royal flush once in 649,740 hands, not once in a million. One in a million would be rarer. The casual phrase overstates the rarity. It does not matter for how you should spend an evening. It matters if you are repeating a number.
Straight flushes that are not royal exist as well. Each suit has ten possible five-card straight flushes, from ace through five up to ten through ace, and the top one of those ten is the royal. Four suits give forty straight flushes in total, including the four royals. Thirty-six are straight flushes below the royal. That side count is here so the four does not look arbitrary. The royal is the top case of a family.
What the fraction refuses to do
649,740 is not a debt. If you have seen a vast number of five-card hands without a royal, the next hand is not close. Each fairly dealt five-card hand has the same chance if the deck is complete and shuffled. In Hold'em you are not dealt a finished five-card hand at the start. You see two cards, then a board, and you share the board with opponents who can beat you. A royal can still sit inside a night that cost more time and money than you planned. The rarity is a fact about combinations. It is not a trophy you are owed for patience.
Quote 4 out of 2,598,960, or 1 in 649,740, or do not quote a figure. Invented round numbers belong with the other myths. And if you do see the hand, enjoy the oddity. Do not let it reset your loss cap. The cap was never about collecting rare cards.
Frequently asked questions
Is a royal flush the same as a straight flush? A royal is the highest straight flush, ace through ten of one suit. Lower straight flushes are still straight flushes. They are not royals.
Does this probability apply to my two hole cards? No. Two cards cannot be a five-card royal. This count is for five-card combinations from a full deck.
Will I see one if I play long enough? Long enough is not a schedule. You might never see one. You might see one early. Neither result is a reason to extend a session.