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# Probability of Getting a Video-Poker Royal Flush

30 April 2022

One of the reasons for the popularity of Video Poker is it generally has a high payback – sometimes even more than 100 percent for a skilled player.

Regardless of which Video Poker game you play, achieving the long-term payback percentage is dependent on getting your fair share of “natural” (those without the aid of a wild card) royal flushes. These generally pay about 4,000 coins for a five-coin bet or 800-for-1.

Common video poker games return 98+ percent to more than 100 percent with perfect play. I define perfect play as holding for the maximum average return on each hand you are dealt. This means holding cards that will give you the most money for any possible hand you could make starting with the cards you have been dealt.

You could hold some cards in the hope of getting a straight, or a flush, or a high pair. You do not always try for a royal on every hand.

With perfect play you lose the least (or win the most if the machine pays more than 100 percent) possible, thereby extending your bankroll for more hours of play.

For the most common machines currently available, the royal adds about two percent to the overall return of the machine. So, in effect, you are losing an additional two percent to the casino while playing and not getting a royal. That amounts to two dollars for every 100 dollars played through the machine – not an insignificant amount.

So just how elusive are these lucrative royal flushes? How frequently can you expect to be blessed by their appearance? Let’s look into the math of it.

In a game using a 52-card deck with no wild cards each hand will be made up of:

Any of five out of 52 for the first card of the hand.

Any of four out of 51 (there are 51 cards remaining after drawing the first card and four cards left to draw for the hand) for the second card of the hand.

Any of three out of 50 for the third card.

Any of two out of 49 for the fourth card.

And, one out of 48 for the fifth and final card of the hand.

That means that there are (52 divided by 5) times (51 divided by 4) times (50 divided by 3) times (49 divided by 2) times 48 – or 2,598,960 possible hands.

Of these 2,598,960 hands, exactly four are royal flushes. Dividing the total possible hands by four – a dealt royal flush is one out of 649,740 possible hands.

Your odds of being dealt a royal are one in almost two-thirds of a million hands!

Fortunately, you don’t need to be dealt a royal to cash in on a royal – you can discard some of cards that are dealt and have the discards replaced by new cards.

This increases the probability of getting a royal to:

One in approximately 40,000 in Jacks or Better, Bonus Poker or Double Double Bonus Poker

One in approximately 45,000 in the common Deuces Wild games

One in approximately 48,000 in Double Bonus Poker

These numbers are based on perfect play. As mentioned above, perfect play will maximize the payback of each hand. If you were to change the style of play to favor saving for royals at the risk of losing other more common (but lower) paybacks, the frequency of hitting a royal would increase. Your losses however would also increase dramatically.

Assuming an even distribution of all the possible hands you should receive a royal every 40,000 to 48,000 hands or so. Some advanced players can play over 1,000 hands per hour with great accuracy.

The recreational player probably plays closer to 400 – 500 hands per hour. At that pace it will take somewhere between 80 to 120 hours to play the 40,000 to 48,000 hands. That is two to three 40-hour work weeks of play between royals.

You can do the math on your own play to see how many playing sessions it will take to play 40,000 to 48,000 hands, but no matter how you look at it you are in for a lot of sessions.

There is another fact you must also consider. royals (or straight flushes, or four-of-a-kinds, etc.) do not appear in an even distribution. You could get two royals back-to-back, or it might take three, four, five, or more times the average before you see a royal.

The only thing the remains constant is you have a one-in-40,000 plus chance of getting a royal on each and every hand you play.
As an average recreational player here is what this means to you:

Be patient – it may be a long time before you see a royal.

Plan your sessions. Have a large enough bankroll to tide you over the losing cycles.

By doing these, you will have many rewarding hours, days, weeks and months playing video poker.

Playing video poker instead of slot machines is a smart move. Even though a royal flush is a rare occurrence, playing using the proper strategy and having an adequate bankroll is an even smarter move.

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

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. 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
Recent Articles
Best of Jerry Stickman
Jerry Stickman

Jerry "Stickman" is an expert in dice control at craps, blackjack, advantage slots and video poker. He is a regular contributor to top gaming magazines. The "Stickman" is also a certified instructor for Golden Touch Craps dice control classes and Golden Touch Blackjack's advantage classes. He also teaches a course in advantage-play slots and video poker. For more information visit www.goldentouchcraps.com or www.goldentouchblackjack.com or call 1-800-944-0406 for a free brochure. You can contact Jerry "Stickman" at stickmanGTC@aol.com.

#### Jerry Stickman Websites:

www.goldentouchcraps.com
www.goldentouchblackjack.com
Jerry Stickman
Jerry "Stickman" is an expert in dice control at craps, blackjack, advantage slots and video poker. He is a regular contributor to top gaming magazines. The "Stickman" is also a certified instructor for Golden Touch Craps dice control classes and Golden Touch Blackjack's advantage classes. He also teaches a course in advantage-play slots and video poker. For more information visit www.goldentouchcraps.com or www.goldentouchblackjack.com or call 1-800-944-0406 for a free brochure. You can contact Jerry "Stickman" at stickmanGTC@aol.com.

#### Jerry Stickman Websites:

www.goldentouchcraps.com
www.goldentouchblackjack.com