What Are The Odds of a Royal Flush?

What Are The Odds of a Royal Flush?

The royal flush stands as the rarest of hands in poker. In any game that uses standard poker hand rankings, the royal flush beats out all other hands.

A royal flush is made when you have a ten-to-ace straight (aka a broadway straight) with all five cards the same suit. The royal flush represents the top-ranking straight flush you can possibly make.

This hand is so rare that you might only make it once or twice in a lifetime. What are the odds of a royal flush hitting in poker? Let’s take a quick look:

Odds of Royal Flush

A 52-card standard poker deck produces only one distinct way to draw a royal flush. Here’s an example of what a spade royal flush looks like:

What Are The Odds of a Royal Flush?

When we say there’s only one distinct way to make a royal flush, we mean there’s no way to mix and match suits and still get the same hand. Only a monotone ten-to-ace straight qualifies as a royal flush.

The four suits give you a total of four possible total ways to make a royal flush. The four ways to make a royal flush come out of 2,598,960 different five-card hands that can come out of a 52-card poker deck.

The odds of making a five-card royal flush out of a 52-card deck are 4/2,598,960. This translates to a 0.000154% chance of making poker’s ultimate hand. The odds against making a royal flush are 649,739-to-1.

By comparison, the odds of making a straight flush, poker’s second strongest hand, are 0.00139%, with the odds against at 72,192.3-to-1.

Calculating the odds of royal flush for Texas Hold’em requires different mathematics, as Texas Hold’em hands are made by choosing the best five-card hand out of seven total cards. 

That does make the royal flush easier to make in Texas Hold’em, but it’s still an exceedingly rare occurrence. Your odds of a royal flush are 0.0032% in Texas Hold’em, with the odds against making a royal flush at 30,939-to-1.

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About the Author

Geoffrey Fisk

Freelance writer and poker player based in San Diego, California.

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