What are the odds of getting a royal flush in poker?

The odds of being dealt a royal flush in a standard five-card poker hand are 649,739 to 1 against.

A royal flush is the ace-high straight flush: 10, jack, queen, king, and ace, all in the same suit. There are only four possible royal flushes, one for each suit. A standard deck produces 2,598,960 different five-card hands, so the probability is 4 divided by 2,598,960, or 1 in 649,740.

That probability converts to odds against of 649,739 to 1. This distinction causes a frequent mix-up: “1 in 649,740” describes the chance of success, while “649,739 to 1” describes the ratio of failures to successes.

The calculation assumes a single five-card hand from a 52-card deck, without wild cards. In Texas hold’em, players receive seven cards from which to make their best five-card hand, so the chance of completing a royal flush is higher than in a single five-card deal.