Those three-card royals

24 March 2019

By John Grochowski

A Three Card Poker player named Jill e-mailed in late February to say she’d just played at a table that included mini-royals in its Pair Plus payoffs.

“It paid 50-1, so just a little more than the 40-1 on other straight flushes,” she wrote. “Someone even got one while I was playing. Not me, unfortunately. I mostly lost this time.

“But it got me to thinking. This must be the easiest royal flush to get, right? The others pay so much more, and I never saw one when I used to play Caribbean Stud.”

Three-card royals are easier to come by than five-card royals, so yes, your chances of being dealt a royal are greater in Three Card Poker than in other games.

Let’s look at a sample of royal frequency in several casino games.

THREE CARD POKER: There are four potential mini-royals, consisting of A-K-Q of the same suit. Given the 22,100 possible hands in Three Card Poker, you’ll see a mini-royal an average of once per 4,420 hands.

Most Three Card Poker tables don’t differentiate between mini-royals and other straight flushes. Usually, all pay the same 40-1. Should you find a table with mini-royals, they usually pay 50-1, though sometimes pay 100-1.

CARIBBEAN STUD; LET IT RIDE: Neither game is as common in casinos as they used to be, but they’re still around. Both are based on five-card stud, so there is no draw. A royal consists of A-K-Q-J-10 of the same suit.

In five-card stud, there are 2,598,960 possible hands in which card order doesn’t matter. Four of those are royal flushes, so you’ll see a royal an average of once per 649,740 hands. Most players will never see one.

In Let It Ride, royals pay 1,000-1 on the main game and usually 20,000-1 on a five-card bonus bet. In Caribbean Stud, royals pay only 100-1 if the dealer qualifies in the main game, but can pay much more separate bet on a progressive jackpot.

ULTIMATE TEXAS HOLD’EM: Royals come into play in a Trips bonus bet, where they pay 50-1, or in a bet on a progressive jackpot.

Ultimate Texas Hold’Em is a seven-card game in which your final hand is your best five cards. Since you have seven cards to make a five-card hand, your chances of making suited A-K-Q-J-10 for a royal are greater than in the five-card stud-based games.

There are 133,784,560 possible combinations, and with the extra cards taken into account, there are 4,324 seven-card hands that will include a five-card royal. That means you’ll see a royal an average of once per 30,940 hands – more than 20 times as often as you’ll get royals in Caribbean Stud or Let It Ride.

VIDEO POKER: Because this is draw poker, you see as many as 10 cards per hand. However, optimal strategy sometimes requires you to discard royal cards, so the frequency isn’t quite as high as in Ultimate Texas Hold’em.

Your strategy affects the royal frequency. In 9/6 Jacks or Better, you’ll average a royal about once per 40,391 hands, while it’s once per 48,035 in 9/7/5 Double Bonus Poker or once per 43,456 for natural royals in Not So Ugly Deuces Wild.

Royals usually pay 4,000 coins for a five-coin bet — $1,000 for five quarters.

Video poker players see 10 times or more hands per hour than table players, so they also see more royals. But on a per-hand basis, Three Card Poker mini-royals are by far the most frequent, followed by seven-card stud based games such as Ultimate Texas Hold’em, then video poker, with five-card stud-base games far behind.


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