Royal Flush in Poker: How It Compares and How to Calculate the Odds

A royal flush is A-K-Q-J-10 of one suit: nothing beats it, and an equal royal flush splits the pot. Its probability depends on your question: 1 in 649,740 for five dealt cards; 1 in 30,940 for the best five of seven if you see all five board cards in Hold'em; and 1 in 1,960 by the river with A♠K♠ if only your hole cards are known and you see the full board. The three figures answer different questions.

These calculations use a standard 52-card deck with no jokers or wild cards. Moving from five cards to seven changes 1 in 649,740 to 1 in 30,940. With A♠K♠, knowing two unrelated opponent cards changes 1 in 1,960 to 1 in 1,730. If you fold on the flop, your chance of completing the hand is 1 in 19,600.

If your hole cards make a royal flush, you have the nuts: focus on getting paid rather than protecting against a better hand. If the board itself is a royal flush, every remaining player has the same best hand. Folding to a bet gives up your share of a pot you cannot lose at showdown.

How does a royal flush compare with other hands?

A royal flush beats every other standard poker hand, including four of a kind and every lower straight flush. Suits do not break ties.

A straight does not wrap around the ace: K-A-2 is not part of a straight. These ranking and suit rules are described in Pagat, “Ranking of Poker Hands”, domain pagat.com, viewed 17 October 2026.

In Hold'em, you choose the best five of seven cards and need not use either hole card. That is why a board of A♠ K♠ Q♠ J♠ T♠ gives everyone the same royal flush. Source: Pagat, “Texas Hold'em”, domain pagat.com, viewed 17 October 2026.

Two royal flushes of different suits cannot occur in one Hold'em deal: each would need at least three community cards, and 3 + 3 > 5. A royal-flush tie in Hold'em therefore requires the royal flush to be on the board.

The collision of two specific hands is a separate calculation. Our quad aces vs royal flush guide covers a two-player model at about 1 in 165 million; that figure does not describe a nine-player table. A bad beat jackpot may reward a qualifying losing hand, but each cardroom sets its own terms—the hand name alone does not establish eligibility.

Which denominator should you use?

Use the denominator that matches what you are counting: five random cards, seven available cards, a specified starting hand or an entire table.

The last denominator counts something different: all possible placements of the five needed cards in a 52-card deck. The 724 favourable placements put them entirely on the board or among the board and one player's hole cards, within the 23 dealt cards.

The five-card and seven-card frequencies are listed in Wikipedia, “Poker probability”, domain en.wikipedia.org, viewed 17 October 2026. Percentages here are rounded; the “1 in” figures are rounded to whole numbers.

Probability is not the same as odds against. For five cards, there are 4 favourable hands out of 2,598,960. The probability is 1 in 649,740, while the odds against are 2,598,956 to 4, or 649,739 to 1. Odds against compare failures with successes; “1 in N” compares all outcomes with successes.

You cannot divide the five-card figure by the number of Hold'em players: they share a board rather than receive independent five-card hands. Doing so gives about 72,000 for a nine-player table, which is wrong; the correct figure is 1 in 3,590.

For a rarity comparison, five-card hands include 4 royal flushes, 36 other straight flushes and 624 four-of-a-kind hands. Other straight flushes occur 9 times as often, and four of a kind occurs 156 times as often. Among seven-card sets, a royal flush appears in 4,324 sets versus 4,140 for each individual lower straight flush; royal flushes account for 10.4% of straight flushes.

How do your starting hand and the street change the probability?

A♠K♠ and K♠Q♠ have the same chance of making a royal flush using your hole cards. For this one event, suited cards from ten through ace give the best chance; that says nothing about whether to play the hand.

Each row below has 2,118,760 possible boards. “Using your hole cards” means the royal flush includes at least one of them; royal flushes entirely on the board are listed separately.

Only suited cards from ten through ace contribute directly to a royal flush. A♠5♠ and T♠9♠ each contribute just one useful card; chasing a royal flush is not a sound reason by itself to hold or play them.

A♠K♠ by street

Seeing fewer community cards gives you fewer opportunities to complete the royal flush. 1 in 1,960 is the chance when the full board is dealt, not a promise that you will reach the river.

How many outs does a royal flush draw have?

With A♠K♠ on Q♠ J♠ 7♦, you have four to a royal and need exactly T♠ to complete it: one out. If only your hole cards and the flop are known, the chance is 2.1% on the next card and 4.3% by the river. That is the chance of making the royal flush, not of winning the hand.

You can check the one-out result in the outs chart. In “Outs to percentage chart (1 to 20)”, the one-out row shows “2.1%” under “Turn (1 card)” and “4.3%” under “By river (2 cards)”.

On Q♠ J♠ 7♦, 12 cards immediately give you at least a flush or straight: the remaining spades, including T♠, and the other tens. Only T♠ makes a royal flush. Hold'em pays the best hand, with no separate royal-flush bonus, so assessing the draw only through T♠ misses other ways to win.

Those 12 improving cards are not a guarantee of winning by showdown. Later board cards and the opponent's hand still matter; unlike a royal flush, an ordinary flush can lose to a straight flush.

How often does a royal flush occur at a nine-player table?

At a nine-player table, the frequency is 1 in 3,590 deals, assuming everyone receives cards and folded hands count. Folded hands are counted, so this is how often a royal flush is dealt, not how often one is shown at showdown.

Diagram: three ways a royal flush forms at a nine-player table — two hole cards plus three board cards, one hole card plus four board cards, or the whole board; 181 ways per suit and 724 for four suitsTeaching diagram from our calculation, not a game interface: every card dealt to nine players counts, even folded ones. 724 of 2,598,960 placements of the five needed cards is one chance in 3,590.

For a table with n players, the number of favourable placements is 4 × (1 + 20n) out of 2,598,960. This covers a royal flush entirely on the board, one hole card plus four board cards, or two hole cards plus three board cards. For n = 1 this gives 84 out of 2,598,960, the same probability as 4,324 out of 133,784,560 for seven cards.

The calculation uses exact enumeration of 133,784,560 seven-card sets and 2,118,760 boards for a specified holding. A simulation of 3,000,000 nine-player deals gave 0.0289% against the exact 0.0279%, about one standard deviation above the exact value and within expected noise.

At an assumed pace of 25 live deals per hour, the average interval is 144 hours; at 60 online deals per hour, it is 60 hours. The hourly pace is an assumption. The results are averages, not measured waiting times.

How can you check the draw in the calculator?

Check winning equity against a specific hand separately from the probability of making a royal flush. With A♠K♠ against 7♣7♥ on Q♠ J♠ 7♦, the equity calculator gives A♠K♠ a 33.8% chance of winning. The opponent's exact hand, a set of sevens, drives the result, and the 33.8% counts every way to win, not only the royal flush.

ToolsGambling equity calculator: A♠ K♠ on a Q♠ J♠ 7♦ flop against 7♣ 7♥ — win 33.8%, lose 66.2%Real frame of the ToolsGambling calculator, 17 October 2026: four to a royal flush plus 11 more cards to a flush or straight against a set of sevens. The hand wins 33.8%, not 4.3%, so do not price the draw on the T♠ alone.

To reproduce the calculation:

1. Set Hero's hole cards to A♠K♠ and Villain's to 7♣7♥.
2. Set the flop to Q♠ J♠ 7♦, leaving the turn and river unknown.
3. Press “Calculate equity”.
4. Check Hero's result: “Win 33.8% · Tie 0.0% · Lose 66.2%”.
5. Check Villain's result: “Win 66.2% · Tie 0.0% · Lose 33.8%”.

This is an exact calculation over 990 possible board runouts; displayed percentages are rounded. Unlike the one-out chart, this calculation also knows the opponent's cards, so its unknown-card pool is different.

For the general seven-card frequency, the bad beat calculator has a row labelled “Making a royal flush by the river (one hand)” with the value “~1 in 30,940”. That describes one random seven-card hand, not an entire table or a specified A♠K♠ holding.

Which assumptions change the result most?

Known cards and the streets you see determine which boards remain possible. Unrelated known cards raise the chance by shrinking the pool, while a known unavailable card needed for the royal flush rules it out.

A dead out is a specific known unavailable target card. Do not subtract unknown folded or burned cards from the 47- or 46-card pool. Remove only a card you know is unavailable, and if it is one of your target cards, remove it from the out count too.

Where do these calculations stop applying?

These tables do not transfer directly to wild-card games, Omaha or video poker: the hand-building rules or the draw process change.

In video poker, four to a royal with one replacement from 47 cards gives 1 in 47, or 2.1%. With four cards to a royal flush, one replacement card gives a chance of 1 in 47; with three to a royal and two replacement cards, the chance is 1 in 1,081. The video poker trainer is for choosing which cards to hold, and the pay table sets the value of that decision.

Our video poker bankroll guide gives an average royal flush cycle of about 40,390.55 hands for 9/6 Jacks or Better with optimal play. The game, pay table and strategy define that figure, which describes play with chosen holds and draws, not five randomly dealt cards. An average interval is not a deadline, and a drought does not make the next independent royal flush more likely.