Three-card poker and roulette

26 January 2014

By John Grochowski

QUESTION: I’ve been playing three-card poker for many years, ever since I first saw it on a trip to Biloxi. I think Mississippi had it even before Las Vegas or Atlantic City.

I read an article right at the beginning that said the best strategy is to bet whenever you have a queen or better, and fold if you have less. I was playing that way on a trip just before Christmas, and another player said his strategy was to bet on queen-6-4 or better, and fold on less. Is that right?

ANSWER: Optimal strategy on the ante-play portion of three-card poker is to bet with queen-6-4 or better, and fold with less. The difference is small. I’ll assume the casino offers the original version, in which winning bets are paid at even money but there also is a bonus payoff of 5-1 on straight flushes, 4-1 on three of a kind and even money on straights. Given that pay table, the house edge is 3.37 percent of your ante if you bet with queen-6-4 or better, and 3.45 percent with the queen or better strategy.

I sometimes get questions about ranking hands that don’t include a pair or better. Should you hold queen-7-2, with one card higher and one card lower than the queen-6-4 base for optimal strategy?

The answer is yes, you would hold queen-7-2. Hands with no pairs or better are ranked first by their high card, then by their second, and the third card matters only if the first two are tied. The second-highest card in queen-7-2 outranks the second-highest card in queen-6-4, so queen-7-2 is the higher-ranking hand. So we would bet with queen-7-2, but not with queen-6-3.

Michael Shackelford’s site, wizardofodds.com, tells the statistical story on the game. If you fold, you lose $1 for every $1 of your ante. If you bet with queen-6-3, that rises to $1.00255 per $1 of your ante. With queen-6-4, that average loss drops to $0.993378 per $1 of your ante.

At the borderline, your strategy can’t make you a winner, but your average loss is less when you bet than if you folded.

QUESTION: Please explain to me the effect of Atlantic City rules on roulette.

ANSWER: On double-zero wheels, Atlantic City casinos have a rules variation on even-money bets that I don’t think I’ve ever seen elsewhere in the United States. If you’re betting red/black, odd/even or first 18/last 18 and the ball drops in zero or double-zero, you get half your bet back.

That drops the house edge on those wagers to 2.63 percent, making them the best bets on the table. The house edge remains 7.89 percent on the five-number bet on 0, 00, 1, 2 and 3, and 5.26 percent on all other bets. At double-zero wheels elsewhere in the U.S., the wagers with even-money payoffs have a house edge of 5.26 percent, matching almost all of the other bets.

The Atlantic City rule is similar to the European “en prison” rule common on single-zero wheels overseas. When that rule is in effect, if the ball drops in the zero, even money bets are held for another spin. If the winning number or color comes up on the next spin, the player gets his bet back. There are no winnings, but no losses, either. That cuts the usual 2.7 percent house edge on single-zero games in half.

In rare cases, I have seen the en prison rule in high-limit rooms in U.S. casinos. On a walkthrough in Bellagio in Las Vegas several years ago, I did see a single-zero wheel with en prison for a 1.35 percent house edge. That’s a nice game for the well-to-do, but it was well beyond my budget.