Probability of Being Dealt a Royal Flush in Poker

A royal flush (A-K-Q-J-10 of the same suit) is the highest-ranking hand in poker and the rarest to be dealt naturally. In a standard 5-card poker deal from a 52-card deck, the probability is exactly 4 in 2,598,960, or 1 in 649,740.

There are only 4 possible royal flushes in a standard deck (one for each suit). The calculation comes from the total number of possible 5-card combinations: C(52,5) = 2,598,960. In Texas Hold'em (the most popular poker variant), where you have 7 cards to work with (2 hole cards plus 5 community cards), the odds of making a royal flush by the river improve to approximately 1 in 30,940.

For context, a straight flush (which includes the royal flush) has odds of about 1 in 72,193 for a 5-card hand. A regular flush has odds of about 1 in 509. Professional poker players may play millions of hands in their careers and still count their royal flushes on one hand. In casino poker, many rooms offer a special jackpot bonus for being dealt a royal flush.