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Improbable Things Happen in Casinos

23 August 2005

Improbable things happen in casinos every day, just because there are so many trials.

Being dealt blackjacks on consecutive hands is a 440-1 shot, but it'll happen pretty often in a casino that deals tens of thousands of hands a day. Drawing a royal flush in video poker is about a 40,000-1 shot. But casinos pay off several royals a day, because customers pay hundreds of thousands, even millions of hands per day.

Still, there's improbable, and then there's improbable. And from an Indiana reader comes a tale that seems nearly impossible. It happened on April 1, but the reader says it's no April Fool's joke.

"I went to the Blue Chip Casino in Michigan City, Ind., on April 1," he said in an e-mail. "I was playing Three Card Poker and was dealt four consecutive straight flushes. The first two were identical, 3, 4, 5 of hearts. I would like to know what the mathematical odds of this happening. How do you calculate this sequence of events?

"Needless to say I was just overwhelmed, and floating in the clouds. I was surprised the casino didn't really acknowledge that it was a big deal. I wasn't looking for anything, but I thought it would be good advertisement for them. Guess I was wrong."

How big a deal was it? Let's put it this way. Nothing so improbable has ever happened at Blue Chip before, nor is it likely to happen again. It reminded me of the first big record-setting Caribbean Stud Poker jackpots at Empress Joliet. A man hit one for more than a record $400,000 when Caribbean Stud was new to the Midwest in 1995, then came back in 1996 and hit another for more than $660,000, another record-breaker.

Caribbean Stud is five-card stud poker, meaning a royal is a 1 in 649,740 shot. When the second record-setter happened, I phone Las Vegas Advisor publisher Anthony Curtis, who couldn't believe it. He in turn phoned mathematician and blackjack expert Stanford Wong, then phoned me back. "Wong says it didn't happen," Curtis said. It was just too improbable.

Three Card Poker is a different animal. A three-card straight flush happens A LOT more often than a five-card royal. Dealing three-card hands from a standard 52-card deck, there are 22,100 possible combinations. Of those, 48 are straight flushes --- we see a straight flush about once per 460.417 hands.

To get the chances of two consecutive straight flushes, multiply 460.417 by 460.417. We'll see back-to-back straight flushes about once per 211,984 trials.

A third straight flush? Multiply by 460.417 again, and up to once per 97.6 million trials. A fourth? How about a 1 in 44.9 BILLION shot.

But the Blue Chip streak was even more improbable than that astronomical long shot. Remember, the first two straight flushes were identical. After any hand, your chances of receiving identical cards on the next hand are not 1 in 460.417, they're 1 in 22,100.

Chances of being dealt a straight flush followed by an identical straight flush are 1 in 460.417 times 1 in 22,100 --- we're already at more than 10 million to 1. Follow that up with two more straight flushes and we're even out of the billions. Try 1 in 2.16 TRILLION.

I can hear the wheels turning. OK, you might ask, how often would a casino deal such a streak? It's a long, long, shot for an individual player, but don't casinos deal enough hands that it's inevitable that some player, some time, will hit a streak like that?

Let's put it this way. Royal flush jackpots at Caribbean Stud don't hit every day, do they? Those progressive pots are usually months in the making. This Blue Chip player's Three Card Poker streak was more than 3 million times less likely than landing a royal flush at Caribbean Stud.

If a casino has two Three Card Poker tables, always full with seven players at each table playing 50 hands an hour, 24 hours a day, 365 days a year, the casino will deal 876,000 hands of Three Card Poker a year. And they'll deal a straight flush, followed by an identical straight flush, followed by two more straight flushes, about once every two-and-a-half million years.

Now, I don't know how much the player was wagering, but I'm sure it all made for a nice payday. On the Pair Plus portion of Three Card Poker, straight flushes pay 40-1, the biggest payoff at the table. If the player was betting $10 a hand, he'd have won $400, then $400 again, and again, and again, for a total of $1,600. Nice, even if it doesn't come close to measuring up to the odds against the streak.

What if he parlayed it all, betting his winnings on the next hand each time? Table limits on maximum bets would have made that impossible, but leaving that issue aside, he'd have won $400 on his initial wager, then he'd have won $16,000 on his $400 wager, followed by $640,000 on the $1,600 bet and $25.6 million on the last go-around.

Even the biggest Caribbean Stud jackpots couldn't match that. But then again, compared with this streak, Stud royals are almost a common occurrence.

Listen to John Grochowski's "Beat the Odds" tips Saturdays at 6:20 a.m., 2:50 p.m. and 7:41 p.m. and Sundays at 8:20 a.m., 2:50 p.m. and 10:42 p.m. on WBBM-AM, News Radio 780 in Chicago, streaming online at www.wbbm780.com.

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Best of John Grochowski
John Grochowski

John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.

John Grochowski Websites:

www.casinoanswerman.com

Books by John Grochowski:

Winning Tips for Casino Games

> More Books By John Grochowski

John Grochowski
John Grochowski is the best-selling author of The Craps Answer Book, The Slot Machine Answer Book and The Video Poker Answer Book. His weekly column is syndicated to newspapers and Web sites, and he contributes to many of the major magazines and newspapers in the gaming field, including Midwest Gaming and Travel, Slot Manager, Casino Journal, Strictly Slots and Casino Player.

Listen to John Grochowski's "Casino Answer Man" tips Tuesday through Friday at 5:18 p.m. on WLS-AM (890) in Chicago. Look for John Grochowski on Facebook and Twitter @GrochowskiJ.

John Grochowski Websites:

www.casinoanswerman.com

Books by John Grochowski:

> More Books By John Grochowski