Poker: Unusual Streaks
Of all the poker-based games that have carved out niches in table pits, Three Card Poker pays out its top jackpot the most often. That makes some unusual streaks not only possible, but inevitable given enough play.
Take the reader who once emailed to tell of being dealt straight flushes on four consecutive hands, each worth a 40-1 payoff on the Pair Plus portion of the game. That may pale in comparison to the 1,000-1 bonanza for a royal in Let It Ride or a progressive jackpot that can run into hundreds of thousands of dollars in Caribbean Stud. But any frequent player of Three Card Poker will experience straight flushes, with 1-in-460 odds. For most, royals in Caribbean Stud and Let It Ride are a none-in-a-lifetime occurrence, a 1-in-649,740 super long shot.
The four straight-flush streak? Even with frequent Three Card Poker jackpots, that was something really special.
The player emailed to say, “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? 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?
To be precise on the odds, a, there are 22,100 possible three-card combinations in a 52-card deck. 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.
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 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.
Thatâ??s extreme, but odd turns of the cards happen in Three Card Poker.
By:Â John Grochowski