Short answer: with five random cards, the odds of a royal flush are exactly 1 in 649,740, about 0.00015 percent. In Texas Hold'em, where you make the best hand out of seven cards, they are roughly 1 in 30,940, about 0.0032 percent.
What is a royal flush?
A royal flush is the highest form of the straight flush: ten, jack, queen, king and ace, all in the same suit. There are exactly four in the whole deck, one each in spades, hearts, diamonds and clubs. No other hand beats it.
The math with five cards
A 52-card deck makes 2,598,960 different five-card hands. Only four of them are a royal flush. 2,598,960 divided by 4 is 649,740.
So the odds are exactly 1 in 649,740. If you kept drawing five completely random cards from a full deck, you would statistically need almost 650,000 hands before one of them was a royal flush.
Royal flush odds in Texas Hold'em
In Texas Hold'em things look friendlier at first. At the end of a hand played all the way through, you have seven cards: your two hole cards plus the five community cards on the board. The best five-card hand is built from those seven, which pushes the probability up considerably.
| Situation | Odds |
|---|---|
| Five-card hand | 1 in 649,740 |
| Seven cards through the river (Texas Hold'em) | about 1 in 30,940 |
How long until your first royal flush?
30,940 hands sounds doable. So let us convert it into real time. At an ordinary full live table, roughly 25 to 30 hands are dealt per hour. For 30,940 hands you would sit somewhere between about 1,030 and 1,240 hours at the table.
If you play four hours a week, that comes to roughly five to six years of regular poker.
Why it takes even longer in practice
The 1 in 30,940 figure assumes you actually see all seven cards, in other words that you play every hand to the river. Nobody does. You fold most hands long before that: preflop, on the flop or on the turn.
So if you want to actually experience a royal flush at the table, not just be dealt one in theory, the real wait is considerably longer. Maybe ten years. Maybe twenty. Maybe an entire poker life. Some players who have played for decades never see a single one.
That is why almost every poker player remembers their first royal flush, whether the pot was enormous or everybody had already folded on the turn.
Royal flush against four aces
A straight flush, and with it the royal flush, is the only hand that beats four aces. How that happened on camera at the 2008 World Series of Poker is in What beats four aces?
Sources in the book: Wizard of Odds, poker probability tables. This article is based on chapter 10, "Five Years at the Table for One Royal Flush", which is also part of the free sample.