Should we expect a royal every 100 hours of play, every 48, or somewhere in between?
By John Grochowski
After more than 30 years of playing video poker, every royal ﬂush still gives me a jolt. My hands don’t shake while an attendant is counting out my $100 bills, as they did when I drew my ﬁrst at the Tropicana in Las Vegas many years ago, but I still get the butterﬂies in my stomach and a nice little head rush when those suited high cards all hit the screen.
Last year, I drew a royal in clubs and immediately reached for my phone. I was going to text Marcy, my wife, who was oﬀ playing penny slots. I’m not that quick on the texts though—I think my son can ﬁre oﬀ ﬁve or six in the time I do one—and before I could type “Royal!” Marcy was standing behind me to oooh and aaah.
They’re rare events, but royals also are on video poker players’ minds every time we play. Take the fellow who emailed, wondering if he was really getting his fair share:
“I play 10-7-5 Double Bonus video poker,” he wrote. “I kept track of how many hours I play before I get a royal and it seems that I get them about every 100–110-plus hours of play. What I read before was that it should happen in 48-plus hours of play. What are your thoughts on how many hours?”
I told him I don’t usually think about royals in terms of time, I think of them in terms of hands. And if we assume optimal play, each game and each pay table has its own average frequency of royal ﬂushes.
In this reader’s favorite game, 10-7-5 Double Bonus Poker, there’s a 1 in 48,048 chance of drawing a royal in any given hand. On 9-6 Jacks or Better, it’s 1 per 40,391, and it moves to 1 per 40,799 in 9-6 Double Double Bonus and 1 in 42,077 in 9-6 Bonus Poker Deluxe.
Those are all high-paying games, with the lowest payer in the bunch being 9-6 Double Double Bonus, clocking in at a 98.98 percent return with optimal play. What if we graze a little lower on the food chain, with some reduced-pay table games commonly available through most of the country? Then, the average hands between royals are 40,864 in 9-6-5 Double Bonus, 40,170 in 8-5 Jacks or Better, 40,066 in 8-5 Double Double Bonus and 40,527 in 8-5 Bonus Deluxe.
I’ve received many questions over the years about what drives the diﬀerences in royal ﬂush frequency. Do you get royals less often in 10-7-5 Double Bonus because the game needs to make up for the bigger payoﬀs on other hands? Are royals a little more frequent in 9-6 Jacks or Better than on other high-payers because it doesn’t have big payoﬀs on four Aces? Does the machine deal Aces needed for royals more often in Jacks or Better because it doesn’t have to worry about four- Ace bonanzas?
The short answer to all of that: No.
What changes with the diﬀerent games and pay tables isn’t the frequency with which cards are dealt, it’s your strategy.
In 10-7-5 Double Bonus Poker, the 10-for-1 payoﬀ on full houses makes minimal impact on your strategy, but the 7-for-1 payoﬀ on ﬂushes vs. 6-for-1 on 9-6 Jacks or Better makes an enormous diﬀerence. That payoﬀ enhances the value of ﬂush and straight ﬂush draws so much that we hold extra suited cards that eliminate some royal draws.
One example comes when we’re dealt four parts of a ﬂush, including three parts of a royal. If the deal brings 6, Jack, Queen, King of diamonds and 5 of clubs in 10-7 Double Bonus Poker, the average return for holding all four diamonds is 7.66 coins, and that beats the 7.59 for holding Jack- Queen-King and leaving open the royal shot. In 9-6 Jacks or Better, the average return is 7.41 on Jack-Queen-King, and only 6.70 if you hold all four diamonds.
You make more plays in Double Bonus that preclude chances of a royal, so royals happen less often. It’s your strategy that changes the frequency of royals, not any need for the game to make up for pay table diﬀerences.
But to get back to the reader’s original question about average time between royals, that’s partly dependent on how fast you play. Remember the number he suggested, that he should get a royal once per 48 hours? That would take exceptionally fast play.
At one royal per 48,000-plus hands, as in the reader’s game of 10-7- 5 Double Double Bonus Poker, it would take 1,000 hands per hour to average a royal per 48 hours. I know people who play that fast, but they are exceptions. When I try to move at that speed, I make mistakes. When I start to see cards I should have held disappearing from my screen on the draw, I know it’s time to slow down, get some rest, or both.
At more normal levels, if you play fast, 800 hands per hour, that’s about one royal ﬂush per 60 hours. If you play at moderate speed, 600 hands per hour, that’s 1 per 80 hours. If you play slow, 400 hands per hour—that’s 1 per 120 hours.
Beyond that, royals are such rare hands, you can appear to be far above or below normal for fairly lengthy periods. The expectation for any given session is that you will not draw a royal, and playing 48,000 hands is no guarantee that a royal will come. Sometimes, you’ll draw two, three or more with that much play, but it’s not unusual to go hundreds of thousands of hands without one.
But of course, it always feels like it should be royal time. And when the royals come, they’re worth the wait.