My Missing Royal Flush

8 January 2022

By Jerry Stickman

Regular readers of my articles know that I am very partial to low variance, high return video poker games. The game that I enjoy the most, and what I recommend for all serious beginner video poker players, is full-pay, 9/6 (full house pays 9-for-1, flush pays 6-for-1) jacks or better.

While this game is not nearly as common as it once was, it can still be found somewhere in most gambling destinations. This game returns 99.54 percent with optimum play. It also has a very low variance of only 19.5.

And there is more. As an added bonus, jacks or better has one of the most straightforward video poker playing strategies.

High return, low variance games level out your bankroll swings.

Because jacks or better has only one jackpot-sized winning hand (the royal flush), the remaining hands can all pay closer to the actual odds of hitting that particular winning hand. Your bankroll will tend to slowly decline until you hit a royal flush to replenish it.

The odds of being dealt a royal flush are one in 649,740 – not very likely. However, a video poker player has the opportunity to discard unwanted cards and replace them with different ones. Because of this, the odds of hitting a royal flush in full-pay jacks or better are one in 40,391.

This is much better, but still a rare occurrence.

In full pay jacks or better, the royal flush accounts for almost two percent of the total 99.54 percent return. This means that until you hit a royal flush, the house has about a two and one-half percent edge on your play. For every $100 played through the machine (80 hands at $1.25 on a quarter machine, 20 hands on a dollar machine), a full pay jacks or better player will lose $2.50 on average.

During the 40,391 hands on average between royal flushes, this amounts to $1,009.78 for the quarter player.

If the real world worked like the math, a full pay video poker player would need just slightly more than $1,000 to survive between royal flushes.

The real world can be very different from the mathematical average. Even though the math says you will get a royal flush every 40,391 hands, that number is based on an average of millions and millions of hands.

It is entirely possible to get back-to-back royal flushes. It is also possible to get three, four or more royal flushes in the span of a few thousand hands.

Unfortunately, it is also possible to go 50,000, 60,000 and even 100,000 or more hands before getting even one royal flush. This is the nature of a random game.

Because of these possible streaks, many video poker experts recommend having a bankroll of three to four times the amount of a royal flush; that is $3,000-$4,000 for play on a quarter machine, $12,000-$16,000 for play on a dollar machine. A bankroll of this size will allow the video poker player to weather all but the most severe royal flush drought.

While I am ahead in my total video poker play over several years. This includes cash back and free-play winnings as well as the actual video poker play.

While that sounds very good (and it is) there were some very long droughts. Over one very long period, I went just under 200,000 hands between royal flushes.

I keep some fairly detailed playing information. This helps me to see the big picture more accurately rather than relying on memory. Memory tends to ignore the usual and focus on the unusual.

Using a 2 percent average loss between royal flushes, my losses would have totaled almost $20,000 – 200,000 hands X $5 per hand X 2 percent.

This is significantly above the ballpark three to four times a royal ($12,000 - $16,000) for a bankroll. My actual losses, however, totaled only $12,169. Even though the royal flush eluded me for an extremely long time, I fared quite a bit better than average.

So, what does all of this mean?

Random is random. Sometimes you will do well, other times you will not do well, and other times you will just suck. Even while playing the lowest variance machine available, you will have long – sometimes ridiculously long – losing streaks. It is part of the game.

Expect it.

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