Three-card poker oddities

16 May 2013

By John Grochowski

I don’t play three-card poker very often. Blackjack and video poker are my games of choice, though I do spread my time around to nearly all casino games. I spend the most time on the games that give me the best chance to win, and three-card poker moved down the list when it became common for casinos to pay only 3-1 instead of the original 4-1 on flushes in the Pair Plus portion of the game.

Nonetheless, when I have played, I’ve seen some odd turns of the cards, and I’ve heard of some strange ones from readers. I once saw another player collect a 30-1 payoff on three-of-a-kind, then collected 40-1 myself for a straight flush on the next hand. I couldn’t convince the fellow next to me that’s what was happening, until the dealer turned up my cards. He thought I was playing at “what ifs” when I mentioned the straight flush and three-of-a-kind coming on different hands.

Then there was the reader who told me about being dealt straight flushes on four consecutive hands. Not only that. The first two were identical, 3-4-5 of hearts. The date of his record streak was April 1, and the more I read, the more it looked like a ridiculous April Fool’s joke, but I verified it with the casino.

There’s a 1 in 460.417 shot of being dealt a three-card straight flush, making it one of the more easily attainable big hits in the casino. But four in a row? Try 1 in 44.9 billion. And the chances of straight flush No. 2 being identical to No. 1, followed by two more straight flushes take us to 1 in 2.16 trillion. That’s right in slim and none territory.

The latest three-card poker tale on my list isn’t that extreme, but it was pretty incredible to watch. I wish I could say it happened to me, but no such luck.

Three women who obviously knew each other were occupying the three seats that ended at third base. I was at first base, with an empty seat between me and a man in his 30s. There was another empty seat to his left.

The woman closest to the center of the table asked, “Does anyone ever win at this game?” She reached into her purse for a $100 bill. Apparently she’d lost some money before I arrived at the table.

She then put $5 down on the ante, and $5 more on Pair Plus. And she was off and running.

First hand, a pair. Then a flush. Two more pairs. A straight. Then a pair, a flush and a pair to finish off a streak of eight hands in a row, winning both on ante-bet and Pair Plus.

I don’t know precisely how much she won on the ante-bet portion. On several hands, the dealer didn’t qualify, so she won only the ante and got her bet back. I don’t track the play of others closely enough to know just how many times the dealer qualified by having a queen or better.

But the Pair Plus streak made me take notice. She bet $5 each time, and her winnings were $5 on each of the five pairs, $15 on each of the two flushes, and $30 on the straight, for a total of $85.

We win Pair Plus bets about once per 3.9 hands, so winning eight in row is a rarity. Two winners in a row come up about once per 15.2 trials, and for three in a row it’s once per 59.3.

You see where this is going. Eight in a row is really rare, on the order of once per 53,320 trials. You’re more than 10 times as likely to draw a three-card straight flush, worth $200 for a $5 bet, than to win eight Pair Plus wagers in a row, which in this case were worth $85.

Along the way, the younger man at mid-table asked if she still thought no one could win at this game, she laughed, they chatted some more. During her winning streak, I’d lost $25 and left soon after her streak ended. I couldn’t leave any sooner -- I had to see how the streak turned out, to add one more three-card poker oddity to my collection.

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