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Long odds to be dealt a royal flush

By John Grochowski


If you’re a video poker player, you know that any royal flush is a cause for celebration. When I drew my first, way back in December of 1989, the 10 $100 bills handed to me by the slot attendant at the Tropicana in Las Vegas made for a merry Christmas indeed.

When the royal comes on the first five cards in a multi-hand game, well, that takes things to a whole new level. It’s party time for sure.

So, you can imagine the excitement of an old acquaintance, a player who phoned to say she has been dealt a royal flush in Ten Play Poker.

“It was a quarter machine, and I was betting the max,” Barb told me. “I hit the max bet button, and up popped the five high clubs. I couldn’t believe it. I screamed, everyone around me gave me high fives and congratulations, and someone from the casino took my picture next to the machine with the royal showing. It was incredible.”

In Ten Play, the royal coming on the deal means the player gets the royal flush in all 10 hands on the screen. The max-coins bet cost $12.50, but the royal wasn’t worth $1,000, as it would be if drawn in one hand. It was worth $10,000.A tax form came before the payoff, but Barb wouldn’t throw it back by any means.

“I couldn’t believe it she said. “I’ve had a lot of royals, and in Ten Play I’ve even drawn two and three at once when I started with four high cards. But what amounts to 10 royals at once? Never?’

Any video poker regular will get a royal every now and then. In five-card draw poker, they come along about once every 40,000 hands. The frequency varies a little as we change games and adapt our drawing strategies to the pay tables. In 9-6 Jacks or Better, for example, we’ll draw a royal about once per 40,390 hands, while in 9-6 Double Double Bonus Poker, with a different drawing strategy, the royals will come about once per 40,799 hands.

But a royal on the initial deal is a much rarer treat. That happens with the same frequency as royals are dealt in five-card stud games such as Caribbean stud and let it ride – once per 649,740 hands.

That’s an easy number to calculate. There’s a 1 in 52 chance of any card being dealt on the first card, but the remaining cards then have a 1 in 51 chance of being dealt, then 1 in 50,1 in 49 and 1 in 48. So, the number of possible five-card hands dealt in any specific order is 52*51*50*49*48, or 311,875,200.

Unless you’re playing either the rare game with a big jackpot for sequential royals or ACES$ Bonus Poker, with a 4,000-coin payoff if four aces appear in the designated sequence, card order doesn’t matter. As far as you and the machine are concerned, Jack of clubs, 8 of hearts, 2 of diamonds, 10 of spades, Jack of diamonds is the same hand as 8 of hearts, Jack of clubs, 2 of diamonds, Jack of diamonds, 10 of spades. Any five cards can be arranged in 120 different orders, and since the order doesn’t matter we can divide the 311,875,200 possible hands by 120. That leaves 2,598,960 possible hands in which order doesn’t matter.

Divide that by four possible royals – one in each suit – and there is a 1 in 649,740 chance of being dealt a royal in five-card stud poker.

But even though the odds of a royal being dealt in five cards are the same as in stud games, we’re much more likely to see a royal in the first five cards in video poker than we are in Caribbean stud or let it ride. That’s simply because we play video poker much faster than we play the table games.

If you’re playing 50 hands an hour or so at Caribbean stud, you’ll see a royal flush an average of once per 12,994.8 hours. If you played one four-hour session a week, you’d see a royal about once every 62.5 years. If you just want to SEE a royal and don’t worry that you’re not the one getting the payback, and are always playing at a full seven-player table and count the dealer’s hand, on the average you’ll see one in a little less than eight years.

Video poker is played much faster than 50 hands an hour. I’ve been clocked at a bit more than 700 hands an hour, and I have friends and acquaintances who play 800 hands an hour or more. Those are at the fast end, but 400 to 500 hands an hour is a nice, easy pace. At 500 hands an hour, you can divide all those Caribbean stud times by 10 – we see a dealt royal not once per 12,994.8 hours, but once per 1,299.48. At one four-hour session a week, we’ll see it once per 6.25 years. Those who play more will see dealt royals more often.

When it happens on the deal, it’s extra-exciting, even if it’s only on a single-hand game. I remember a Super Bowl weekend when my father, brother and I were in Las Vegas. My brother had a phone call to make, so my dad and I split a session of 25-cent 8-5 Bonus Poker. We both put in money, and one would play until he had a losing hand, then the other would take over. On one of my turns, all five high hearts came up, and we had $1,000 to split – which more than made up for backing the wrong football team.

That was memorable. For it to happen on Ten Play – well, I can understand if my caller is still celebrating.



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