Odds of a Royal Flush: 1 in 649,740 — or 1 in 30,940?

The two numbers, and why they're both right

People quote wildly different royal flush odds because there are two different questions:

• •Five random cards (e.g. 5-card draw, or 'what fraction of all 5-card hands are royals'): there are C(52,5) = 2,598,960 possible hands and exactly 4 royal flushes — one per suit. 4 ÷ 2,598,960 = 1 in 649,740.
• •Texas Hold'em by the river: you hold 2 cards and share 5 board cards — 7 cards total. Of the C(52,7) = 133,784,560 seven-card combinations, exactly 4,324 contain a royal flush. That's 1 in 30,940 — about 21x more likely, because 7 cards give you many more ways to catch the exact five you need.

Flopping a royal flush: the same 1 in 649,740

Here's a neat identity from our cooler odds data (computed for /odds/royal-flush-flop): the chance of flopping a royal in Hold'em — being dealt two of the five royal cards in one suit (40 of the 1,326 possible starting hands) and then hitting the exact three-card flop that completes it (1 of 19,600) — multiplies out to exactly 1 in 649,740. It's the same number as the 5-card figure and it isn't a coincidence: flopping a royal means your first five cards are one specific 5-card hand, and any specific 5-card combination has identical probability.

How often will you actually see one?

Per-player, per-hand numbers from our computed odds pages:

• •You make a royal by the river: 1 in 30,940 — but only if you see all five board cards. Since you fold most hands preflop, your real-life rate is several times rarer.
• •Someone at a full 9-handed table flops a royal: 1 in 72,193 deals (players' flopped royals are mutually exclusive, so the individual chances simply add).
• •Any straight flush by the river, royal included: 1 in 3,178 per player — roughly 10x more common than the royal specifically.
• •Volume check: an online regular playing 60,000 hands a year would make about two royals a year if they never folded. Realistically, expect one every year or two — and a live 1-table player might wait a decade.

Can two players have a royal flush at once?

Only if the royal is entirely on the board — in that case everyone 'has' it and the pot is split. Two different players can never each make their own royal in Hold'em, because two royals would require ten distinct cards of two suits, and only five community cards exist. If you hold even one card of a completed royal, you have the absolute nuts and cannot be tied.