Online Poker Cab 026
Odds of a Royal Flush: Five Cards, Seven Cards and Video Poker
- Reading minutes4 min
Dealt five cards from a shuffled deck, you will hold a royal flush once in every 649,740 hands on average. With seven cards to choose from, as in Texas Hold'em when a player sees all five community cards, the odds improve to about 1 in 30,940. Video poker, which lets you redraw, lands in between, at roughly one royal per forty thousand hands when a full strategy is followed.
Here is where each number comes from, and why "on average" is doing a great deal of work in that first sentence.
Five-card odds: 1 in 649,740
A royal flush is the ace, king, queen, jack and ten of one suit, so exactly four exist, one per suit. The number of different five-card hands that can be dealt from 52 cards, ignoring order, is 2,598,960. Divide one by the other:
- 4 royal flushes ÷ 2,598,960 hands = 1 in 649,740.
- As a percentage, about 0.000154%.
- Counting every straight flush (40 of them, royals included), about 1 in 64,974.
The 2,598,960 figure comes from the combination formula, choosing 5 cards from 52. Our article on poker combinatorics shows how that formula works with smaller, friendlier numbers.
Seven-card odds: about 1 in 30,940
In Hold'em you build the best hand from two hole cards plus five on the board, seven cards in all. A royal only needs five of them, so the count changes:
- Total seven-card sets: choosing 7 from 52 gives 133,784,560.
- Sets containing one particular royal: the five royal cards are fixed, and the remaining two can be any pair from the other 47 cards, which is 1,081 pairs.
- Four suits give 4 × 1,081 = 4,324 sets. Seven cards cannot hold two different royals, so nothing is counted twice.
- 133,784,560 ÷ 4,324 ≈ 30,940.
That figure assumes a player who stays in until the river every single time, which nobody does. Hands get folded early, so the practical rate at which a seated player completes a royal is lower again. Omaha shifts the count once more, because a finished hand must use exactly two hole cards and three from the board, as set out in our Omaha rules guide.
What are the odds of flopping one?
If you already hold two suited royal cards, say the ace and king of spades, the flop must bring exactly the queen, jack and ten of spades. There are 19,600 possible flops from the 50 unseen cards and only one of them works: 1 in 19,600. Our chart of flop odds in Hold'em covers the more everyday hits.
Video poker: the draw changes the maths
Video poker deals five cards, lets you hold any of them and replaces the rest from the same deck. That second chance is why royals appear far more often than in a plain five-card deal, and also why the result depends on how you play.
| You hold | Cards you still need | Chance on the draw |
|---|---|---|
| Four to a royal | 1 specific card from 47 | 1 in 47 |
| Three to a royal | 2 specific cards from 47 | 1 in 1,081 |
| Two to a royal | 3 specific cards from 47 | 1 in 16,215 |
Combine every possible starting hand with the best hold for each and the long-run rate for a classic game works out at around one royal per forty thousand hands. Paytables matter here. Many classic machines pay a much larger multiple for a royal when the maximum number of coins is staked, so the royal's share of the game's return depends on stake size as well as strategy. The help screen of each game lists its own paytable, and its return figure works in the same way as the one described in our RTP explainer.
What 1 in 649,740 does not mean
- It is not a countdown. No hand brings you closer to a royal; every deal starts fresh.
- It is not a promise within that many hands. Over 649,740 five-card deals, the chance of seeing at least one royal is only about 63%.
- Two in a short spell is not suspicious. Rare events bunch together by chance more often than intuition expects.
Royal flush side bets
Some table poker variants offer side bets or progressive prizes that pay out on a royal. The size of the prize reflects how rarely it lands. Before staking extra on such a bet, set the payout beside the odds above and read the game's rules on qualifying hands, because a large printed number is not the same thing as good value. The general counting rules behind every figure here are in our card probability primer.
Poker and video poker for real money are restricted to adults. Keep the stake to an amount you regard as the price of the evening, and find out whether online poker is lawful in your area first.