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Improbable things happen in casinos every day, just because there are so many trials. And with the growth of online gaming meaning millions are playing every day, the improbable becomes the likely.
Being dealt blackjacks on consecutive hands is a 440-1 shot, but it’ll happen pretty often in an offline casino that deals tens of thousands of hands a day, and is common online. Drawing a royal flush in video poker is about a 40,000-1 shot, but that’s a drop in the bucket compared with millions of hands played a day.
Still, there’s improbable, and then there’s improbable. An and e-mail from a reader brought a tale that seems nearly impossible. It happened on April 1, but the reader says it’s no April Fool’s joke.
“I was playing Three Card Poker and was dealt four consecutive straight flushes,” he reported. “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 to this player, to anyone the player knows, nor to anyone the players friends and relatives know, nor is it likely to happen again.
It reminded me of the first big record-setting Caribbean Stud Poker jackpots when the game started to spread among offline casinos in the mid-1990s. A man hit one for more than $400,000, then came a year laterr for more than $660,000.
Caribbean Stud is five-card stud poker, meaning a royal is a 1 in 649,740 shot. When the second record-setter happened, I phoned 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 this 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. That’s 3 million times less likely than landing a royal flush at Caribbean Stud.
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 $160,000 on his $400 wager, followed by $64 million on the $160,000 bet and $25.6 billion on the last go-around.
Even the biggest Caribbean Stud jackpots couldn’t come close to that. But then again, compared with this streak, Stud royals are almost a common occurrence.
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