Three royals in a row astounding

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Richard Marx

I don’t really believe in beginner’s luck. The odds don’t change just because you’re a newbie.

Nonetheless, a father’s tale of his son’s first, second and third times in a casino might make the phrase “beginner’s luck” ring through your brain at megadecibels.

The short version: On his 21st birthday, playing at Hollywood Casino in Joliet, the son drew a royal flush on a video poker machine on the first bet he ever made in a casino. That’s roughly a 1 in 40,000 shot, more or less depending on game and strategy. He played the next day, and drew another royal flush. And he did it again the next day.

His total winnings, $2,500, aren’t astounding. Players hit bigger slot jackpots than that every day. But the way he did it goes beyond uncanny to unbelievable. As a starting point, we need to look at the odds of hitting three consecutive royal flushes. That would be 1 in 40,000 times 40,000 x 40,000 and that comes to 1 in 64 trillion.

Next, we need to divide by the number of hands played. An average player gets in 400 or 500 hands an hour, and a veteran can play 700, 800 or more. Complicating this is that the new player was splitting play, alternating hands with his dad, sister and mother. Days 2 and 3 were very short sessions.

The dad thinks his son played only about 300 hands. I suspect it was more like 1,000. Divide 64 trillion by 300 hands, and it’s a 1 in 213 billion shot. Make it 1,000 hands, and it’s a mere 1 in 64 billion.

How unlikely is that? Let’s do a table comparison, and look at Caribbean Stud Poker. The odds of being dealt a royal flush and winning a big progressive jackpot are 1 in 649,740. If you played two hours a day, 365 days a year, it’d take nearly 18 years to play that many hands.

Video poker royals are a lot more common. But three in the first 1,000 hands are 98,501 times less likely than the Caribbean Stud royal. It’s a once in hundreds of thousands of lifetimes shot.

The dad was flabbergasted: “If I hadn’t seen the pictures and the money, I wouldn’t believe it myself.”

John Grochowski is a local free-lance writer. His “Casino Answer Man” tips air at
5:18 p.m. Tuesday-Friday on WLS-AM (890).