What are the odds of completing a royal flush?

2 August 2025

By Jerry Stickman

Any video poker player who plays the game regularly has been dealt four cards of a royal flush. When this happens, the player will carefully select each of the four cards to be saved – sometimes even (properly) discarding the fifth card of a flush. Then, while holding their breath, the “deal” button is pressed. Most often disappointment is the result. No royal flush, no flush, and no straight. Usually not even a high pair.

This same scenario can happen five times, 10 times, 20 times or more. It sems that one time out of twenty should produce a royal flush. After all, it is rare to be dealt four of a royal flush.
It sometimes seems that players are looking for proof that the game they love to play is rigged. Let’s look at the actual odds of completing several hands from powerful, but not winning, dealt hands.

First, we will look at four cards of a royal flush. Yes, it is rare to be dealt four of a royal. The odds of this happening are about one in 2,765 or roughly once every three to six hours of play depending on your speed.

After your initial five cards are dealt, there are 47 cards left in the deck. Only one of these remaining cards will complete the royal so you have a one in 47 chance of completing the jackpot hand. Keep in mind that this is an average over time. It could take 200, 300, or more times being dealt four of a royal before you complete one. it could also happen immediately or even two or three times in a row, but on average you will complete a royal flush from four cards of a royal once every 47 times.

Looking at it another way, it takes a player playing 600 hands per hour almost 217 hours to play enough hands to complete one four card royal – on average.

Not every failure to produce a royal flush will end with a loss.

There is a two in 47 chance of a straight flush (one of them being a royal flush) if the ace is the only missing card of the royal.

In the remaining 47 cards there are eight or nine cards of the same suit that will complete a flush (depending on whether a card of the same suit was discarded in pursuit of the royal). That is about a one in five chance if a like suit was not discarded and just under a one in six chance if the same suit was discarded.

Assuming the fifth card of a straight was not discarded in the attempt to produce a royal, there is about a one in eight shot of completing a straight. If it was discarded there is still about a one in nine shot of scoring a straight.

There is also the possibility of a high pair when saving four of a royal. If the 10 is not one of the saved cards, there are 12 cards in the 47 that will match one of the saved cards for a little better than a one in four shot at getting your bet back. If the 10 was saved there are only nine possibly high pair matches remaining for a little worse than one in five odds of returning your bet.

How about the odds of completing other four card hands such as four of a straight flush, four of a flush, four of a straight, or two pair making a full house?

The odds of completing a straight flush when dealt four are the same as completing a straight flush when dealt four of a royal. If the four cards dealt are all together with no gaps (this is called an open straight or an open straight flush) the odds of completing the straight flush are two in 47. If there is a gap, the odds are one in 47.

When four cards of a flush are dealt, there are nine cards that will complete a flush in the 47 remaining cards – or about a one in five chance of completing the flush.

How about a dealt four cards of a straight? Like the straight flush, the odds of drawing the correct card to complete a straight depends on whether the cards are together (open) or have a gap (inside). If it is four cards of an open straight, there are eight cards out of 47 that complete the straight for just under a 1 in 6 chance. When there is a gap (or the ace – either high or low – is one of the cards), the odds of completing the hand are cut in half as there are only four cards that will do the trick. There is a one in almost 12 chance of completing the hand in this case.

The last four-card dealt hand is two pairs. The best possible outcome when holding two pairs is a full house. Since there are two more of each of the two pair’s rank in the remaining 47 cards, there is a one in almost 12 chance of completing the full house – the same as completing four of an inside straight.

While being dealt four of any potential high paying hand is an exciting proposition, completing the hand is still far from common. Don’t let your hopes and expectations blind you to the reality of the math. The math will win out in the end.

As always, may all your wins be swift and large, and your losses be slow and tiny.

Jerry “Stickman”

Jerry “Stickman” is an expert in craps, blackjack and video poker and advantage slot machine play. He is a regular contributor to top gaming magazines and 888casino.com. He authored the video poker section of Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo, and Pai Gow Poker! You can contact Jerry “Stickman” at stickmanjerryg@gmail.com