Beginner's luck

Given enough trials, anything that can happen eventually will. A Megabucks slot jackpot can be years in the making, but eventually there will be a new multimillionaire. A craps shooter holding the dice for a couple of hours? It happens.

And then there's the best streak of beginner's luck I've ever heard.

A father called me to tell me he'd taken his wife, daughter and son to the Hollywood Casino in Joliet on the son's 21st birthday. Father and son sat down to play Triple Play Poker together, playing on a combined bankroll and alternating hands.

"I played the first hand, then on the second he was dealt three parts of a royal flush," the dad told me. "Then on the draw, would you believe it, the other two parts came up. The first hand he ever played in his life, and he had a royal flush."

Since they'd combined money, father and son split the $1,000 payoff, and left the machine a couple of hands later. After an evening of splitting play with his dad, with his sister, and with his mom and sister, the son still had nearly all of his $500.

"The next night," the dad said, "he realized he'd never played on his own, that he'd split play all night. Before long, my cell phone went off. He'd sent me a picture of him at a single-hand Bonus Poker machine. Another royal flush."

This time, the son cashed out immediately. That $1,000 and $400 from the previous night went directly into the bank account. But he wasn't finished.

"He's going to Las Vegas in a couple of weeks, seven buddies and three dads," the father said. "He wants to play blackjack and roulette, so he went back to Joliet to get his feet wet."

This time, he won $200 for four 3s with an ace kicker on a video poker game, and decided to use that at roulette. Betting $10 a spin on red or black, he quickly lost $150. That was enough of that.

So it was back to video poker. And as impossible as it may seem, he drew ANOTHER royal flush.

The dad was flabbergasted: "If I hadn't seen the pictures AND the money, I wouldn't believe it myself."

How unbelievable was it? Let's do some quick calculation. The chance of finishing with a royal flush in five-card draw video poker is about 1 in 40,000. It's different depending on game and strategy. Expert strategy in 9/6 Jacks or Better will bring a royal an average of once per 40,391 hands, while it's 1 in 48,048 in 10/7/5 Double Bonus Poker and in 9/6 Double Double Bonus Poker it's 1 in 40,799.

It is possible to increase the frequency of royals with non-expert play, but you lose more than you gain by trying to force the pace. Let's say you're playing 9/6 Double Double Bonus Poker and the deal brings queen of clubs, jacks of spades, 8 of diamonds, 6 of hearts and 2 of diamonds. The expert play is to hold queen-jack, which brings an average return of 2.33 credits per five credits wagered.

But holding the two high cards of different suits means it's impossible to draw a royal flush. If you hold just the queen, or just the jack, you open the royal possibility. It's a long shot. Holding a single high card will bring a royal only once per 178,365 hands. And the average return for holding just the jack drops to 2.15 credits per five wagered, while holding the queen alone has an expected value of 2.13.

The bottom line is that a player who is very aggressive in chasing royals and makes many plays such as the one above can increase the chance of drawing a royal to better than 1 in 40,000. However, those plays also increase average losses, so that's not the way good players go.

We don't know what strategy the newly legal player was using, so let's just use 1 in 40,000 for easy arithmetic. The chance of hitting three royals in a row is 1 in 40,000 x 40,000 x 40,000, or 1 in 64 trillion. From the amount of time he spent in the casino, I estimate he played about 1,000 hands. Divide the 64 trillion by 1,000, and that makes his chance of those hands including three royal flushes about 1 in 64 billion. His dad thinks he played only about 300 total hands. That would take it to about 1 in 213 billion.

"No doubt, it's the streak of a lifetime," his dad told me. "Now I just have to make him understand it's not that easy. Don't want him to get the bug."

Look for John Grochowski on Facebook (http://tinyurl.com/7lzdt44); Twitter (@GrochowskiJ) and at casinoanswerman.com.