Ah, that royal flush!

One of the reasons for the popularity of video poker is it generally has a higher payback – sometimes even more than 100% for a skilled player – than slot machines. 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.

Most common video poker games return 98+% to more than 100% 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%) possible, thereby extending your bankroll for more hours of play.

For the most common machines currently available, the royal adds about 2% to the overall return of the machine. So, in effect, you are losing an additional 2% to the casino while playing and not getting a royal. That amounts to $2 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 5 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 four 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 2,598960 possible hands.

Of these 2,598,960 hands, exactly four are royal flushes. Dividing the total possible hands by four – a 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.

OK, so what does all this mean to you?

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 or 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 standard 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 fours-of-a-kind, 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 1 in 40,000+ 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.

• Play perfect strategy. It will help you extend your time playing at the machines.

• Plan your sessions. Have 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 because a bankroll is too precious to waste.

May all your wins be swift and large and all your losses 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 stickmanjerry@aol.com.

This article is provided by the Frank Scoblete Network. Melissa A. Kaplan is the network's managing editor. If you would like to use this article on your website, please contact Casino City Press, the exclusive web syndication outlet for the Frank Scoblete Network. To contact Frank, please e-mail him at fscobe@optonline.net.