What's with royals? Readers want to know

Video poker players love to talk about royal flushes --- the ones they hit, the ones they didn't, the ones that are still to come.

I had a couple of e-mails from players who were downright philosophical about their royals. One asked what the lack of royals did to the payback percentage, while the other wanted to know if expert strategy --- a term I use often in this column --- gives you a better chance at royals.

First things first. On most video poker games, royal flushes account for about 2 percent of your long-term return. When you read that 9-6 Jacks or Better returns 99.5 percent with expert play, royals account for about 2 percent of that. Between royal flushes, you're playing about a 97.5 percent game.

Within that 97.5 percent, of course, there's room for a whole lot of volatility. Sometimes you're going to hit a cluster of four of a kinds, and win big even without a royal. Sometimes you'll struggle to find anything better than two pair, and you'll have a session that doesn't begin to approach 97 percent. It happens.

I remember volatility taking a big swing in my favor in the early days of riverboat casinos in Illinois, back when the boats were required to leave the dock for two-hour sessions. I was playing 8-5 Jacks or Better --- as good as it got in the Chicago area at the time --- and hit a four of a kind, and then another.

Cruise time was almost over, so I pushed the button to cash out. The tokens started to pour into the tray … and then the hopper jammed. I waited, and waited, and waited some more. By the time an attendant came over to check, there were only about 10 minutes left until the doors would close and I'd be stuck for another cruise. He cleared the jam … and the hopper stopped again. This time it needed a fill.

There was no question of getting off the boat now. I was stuck. So while waiting for the hopper fill, I started playing the next machine. Within five hands, I had another four of a kind. A few minutes later, quads again.

Then again, and again. Within half an hour, I had six sets of quads to go with the two four of a kinds on the other machine.

If we'd had ticket in, ticket out payoffs in those days, I'd have been happily off the boat with profits from two quick four of a kinds. Instead, my bankroll was even happier with six more quads, although my wife was a little miffed that I was a couple of hours late.

That's a long tangent just to say big wins are possible without a royal. And, of course, large, fast losses are part of the game, too. But overall, your payback percentage is about 2 percent lower whenever your session doesn't include a royal flush.

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On to the second reader. "I read about expert strategy," she started, "and I was wondering. Does expert strategy help me hit more royals? I practice on the computer, and I try to play the right way, but it's been about a year and a half since I hit a royal. What's happening?"

Royal-less streaks happen, and they can get awfully lengthy --- "awful" being a key part of that phrase.

Given expert strategy, we'll hit a royal about once per 40,000 hands, a little more or less often depending on the game and its strategy adaptations. For someone who plays at a steady, but not really speedy, 500 hands an hour, that'll give us a royal about once per 80 hours of play.

But we can't count on that royal being there within 80 hours. With such a rare event, sometimes we'll go two or three times that long without seeing a royal flush. My reader seems to be in one of those streaks now.

Frustrating, but normal.

As for the question of whether expert strategy helps you hit more royals, the answer is not necessarily. Expert strategy is designed to maximize the average return on each decision you face, and sometimes that means we'll pass up the chance at a royal.

For example, playing 9-6 Jacks or Better and dealt Queens of clubs, diamonds and spades, along with a King and a 10 of diamonds, do you hold the three of a kind, or do you hold King-Queen-10 of diamonds?
If you hold the three Queens, you have no chance at a royal flush. If you hold the three diamonds, you'll draw a royal once per 1,081 hands. Still, holding the three Queens is a much, much better play. You're assured of three of a kind, and have a chance at a full house or four of a kind. Your average return is 21.5 coins per five wagered, compared with 6.7 coins if you hold the three diamonds.


You could hit more royals by using a "go for it" strategy in which you always discard cards that get in the way of royal possibilities. You'd also lose a lot of money using it.