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 share their experience of being dealt four consecutive straight flushes, each worth a 40-1 payoff on the Pair Plus portion of the game. That might pale in comparison to the 1,000-1 bonanza for a royal in Let It Ride or a progressive jackpot that can reach hundreds of thousands of dollars in Caribbean Stud. But any frequent player of Three Card Poker will tell you that straight flushes, with 1-in-460 odds, do come around. For most players, royals in Caribbean Stud and Let It Ride are a once-in-a-lifetime—if ever—event, with odds of 1 in 649,740.
Four straight flushes in a row? Even in a game with frequent jackpots, that’s something truly special.
The player wrote, “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 the mathematical odds of this happening. How do you calculate this sequence of events?
“Needless to say, I was just overwhelmed—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?
To be precise: there are 22,100 possible three-card combinations in a 52-card deck. Of those, 48 are straight flushes—meaning we see a straight flush about once every 460.417 hands.
To get the odds of two consecutive straight flushes, multiply 460.417 by 460.417. That’s about 1 in 211,984 trials. Add a third straight flush, and you’re at 1 in 97.6 million. A fourth? Now you’re looking at 1 in 44.9 billion.
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 the same exact hand again are 1 in 22,100.
So, the odds of being dealt a straight flush followed by an identical straight flush are 1 in 460.417 × 22,100—that’s already over 10 million to 1. Add two more straight flushes after that, and we’ve left the billions behind. Try 1 in 2.16 trillion.
You might ask: “OK, so how often would a casino deal a streak like this?” It’s an extreme long shot for an individual player, but casinos deal a lot of hands—so is it inevitable that someone, sometime, will hit a streak like that?
Let’s put it this way: Royal flush jackpots in Caribbean Stud don’t hit every day, do they? Those progressive pots are usually months in the making. This Three Card Poker streak? It was more than 3 million times less likely than landing a royal flush in Caribbean Stud.
Say a casino has two Three Card Poker tables, always full, with seven players each, playing 50 hands per hour, 24/7, 365 days a year. That’s 876,000 hands per year. At that rate, a streak like this—a straight flush, followed by the same straight flush, followed by two more straight flushes—would happen about once every 2.5 million years.
Now, I don’t know how much the player was wagering, but I’m sure it made for a nice payday. On the Pair Plus portion of Three Card Poker, straight flushes pay 40-1, the highest payoff at the table. If the player bet $10 per hand, they would have won $400, then $400 again, and again, and again—for a total of $1,600. Not bad, even if it doesn’t quite reflect the astronomical odds.
Now imagine if they parlayed their winnings, betting all of it on each subsequent hand. While table limits would make this impossible, just for fun: they’d win $400 on the first hand, then $16,000, then $640,000, and finally $25.6 million.
That’s extreme, but wild turns of the cards do happen in Three Card Poker. I once had my first straight flush come on the very next hand after another player got three of a kind—the two highest-ranking hands, dealt back to back.
When I picked up my cards, I nodded toward the dealer and said, “She just dealt three of a kind and a straight flush back to back.”
No one thought I was serious. The dealer laughed. Another player said, “Sure—wouldn’t that be nice?” It wasn’t until the dealer turned my cards face up that everyone realized I wasn’t just joking.
And not long ago, I saw another kind of streak. It wasn’t in the league of the four straight flushes, but it was still a sight to behold.
Three women who clearly knew each other were sitting near third base. I was at first base, with an empty seat between me and a man in his 30s. Another empty seat was to his left.
The woman closest to the center of the table asked, “Does anyone ever win at this game?” as she pulled a $100 bill from her purse. She’d apparently taken some losses earlier.
She put $5 on the ante and $5 on Pair Plus—and then she was off and running.
First hand: a pair. Then a flush. Two more pairs. A straight. Then a pair, another flush, and another pair. Eight winning hands in a row, winning both on the ante bet and Pair Plus.
I don’t know exactly how much she won on the ante portion. On several hands, the dealer didn’t qualify, so she only won the ante and had her play bet returned. I wasn’t tracking closely enough to count how many times the dealer qualified with Queen-high or better.
But the Pair Plus streak was eye-catching. She bet $5 each time. She hit five pairs ($5 each), two flushes ($15 each), and a straight ($30)—for a total of $85.
We win Pair Plus bets about once every 3.9 hands, so winning eight in a row is rare. Two in a row comes about once in 15.2 trials; three in a row, once in 59.3. Eight in a row? Once in 53,320 trials. You’re 10 times more likely to draw a three-card straight flush (worth $200 on a $5 bet) than to win eight Pair Plus hands in a row—worth $85 in this case.
Along the way, the young man at mid-table asked her if she still thought no one could win. She laughed, they chatted. During her streak, I lost $25—and left shortly after her streak ended. I couldn’t leave sooner. I had to see how it played out—to add one more Three Card Poker oddity to my collection.
By John Grochowski
