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Evaluating Three-Card Royal Flush Draws

The machine deals you three to the royal. Now what?

A three-card royal flush is an exciting starting combination. After all, we are only two perfect cards away from a 4,000-or-more-coin jackpot. Most players have experienced drawing one or more royal flushes from this starting position. And the discussion in this article does not apply to the five-of-a-kind Joker Poker game found largely in Atlantic City where the royal flush, with or without a joker, is paid the same as a straight flush.

Still, it’s over a thousand-to-one against drawing two perfect cards THIS TIME. When you have enough of these draws, perfect draws sometimes emerge, but you’ll never know WHEN the royal will occur until it

actually happens. It’s always a very pleasant surprise.

In addition to completing a royal flush, a three-card royal can end up being a high pair, two pair, three of a kind, a straight, flush, and, for combinations not containing an ace, a straight flush. In 9/6 Jacks or Better, from about one third to over one half of the value of a three-card royal comes from “nonroyal” final hands.

Not all three-card royals are created equal. Some have more potential to create straights and straight flushes than others do. And some have more potential for high pairs than others do. Let’s look at what gives these combinations value.

Games where you get your

money back for a pair of jacks or better

There are a lot of these games. Some examples are Jacks or Better, Bonus Poker, Double Bonus Poker, Double Double Bonus Poker among many others. These games vary in how much you get for various four-of-a-kinds and in how much you get for two pair. The hierarchy of three-card royals is the same, though, for any of these games.

I. Includes ace and two other high cards: A-K-Q, A-K-J, A-Q-J

II. Includes ace and one other high card: A-K-10, A-Q-10, A-J-10

III. King is highest with two other high cards: K-Q-J

IV. King is highest with one other high card: K-Q-10, K-J-10

V. Queen is highest card: Q-J-10

In each of these games, the combinations in Category I (A-K-Q, A-K-J, and A-Q-J) are always superior to those in Category II

(A-K-10, A-Q-10, and A-J-10) because of the potential to get a high pair. It is easier, after all, to connect on a high pair when you have three targets to shoot at than when you only have two. Assuming high pairs return even money and you are playing five $1 coins per bet, Category I combinations are worth 50 cents more than those in Category II, no matter what the rest of the pay schedule is like.

Similarly, Category III (K-Q-J) combinations are always superior to Category IV (K-Q-10 and K-J-10) combinations, also by 50 cents. The only difference in these two categories is the number of high pairs you end up with.

Category III is also superior to Category I, even though the combinations have equal numbers of high cards. Here, the difference is “straight potential” and “straight flush potential”. Both K-Q-J and A-K-Q may end up as part of a royal or an A-high straight, but only the former may be part of a K-high straight or straight flush. How much is this worth? We can’t say unless we look at the pay schedule. The return for straights, flushes, and straight flushes all come into being in this calculation. Similarly, because of straight and straight flush potentials, Category V combinations (Q-J-10) are always worth more than those in Category IV (K-Q-10 and K-J-10).

How about comparing Category I with Category IV? We can’t do it unless we know the pay schedule. Category I has an extra high card and Category IV has extra straight potential. Same with comparing Category III with Category V. What we CAN say, independent of pay schedules, is

Category III > Category I > Category II

Category III > Category IV

Category V > Category IV.

Games where there are no high pairs

Most versions of Deuces Wild do not give you your money back unless you end up with three of a kind or better. Some versions of Joker Wild give you your money back only if you get two pair or better. For these games, the ranking of three-card royal flushes is different. Now the combinations in Category I are exactly equal to those in Category II, and Category III combinations are equal to those in Category IV.

The ranking of three-card royals in this game is strictly determined by the straight potential of the hands. Therefore

we have

Category V > (Category III = Category IV) > (Category I = Category II).

Games where you need kings

or better to get your money back

The most popular version of Joker Wild in Las Vegas has this type of structure, as does a game called Triple Bonus. Our former categories don’t work in this game, as A-K-J has two high cards and A-Q-J has only one. In this game we have,

a. Includes an ace and king: A-K-Q, A-K-J, A-K-10

b. Includes an ace without a king: A-Q-J, A-Q-10, A-J-10

c. King is the highest card: K-Q-J, K-Q-10, K-J-10

d. Queen is the highest card: Q-J-10

The logic that determines which category is higher than the other is the same in this game as it was for those in the Jacks or Better version, except now the categories are defined differently. So in this type game, no matter the pay schedule, we can make these judgments:

Category a > Category b because of the extra high card

Category c > Category b because of the extra straight potential

We can make no other absolute judgments unless we know the pay schedule.

Other considerations

Other than in this sentence, I’m not discussing penalty cards in this article, but they affect how a three-card royal is played. And nothing in this article tells you whether a particular three-card royal is better than a particular high pair or not. To decide that, you need to consider the specific game and pay schedule.

But what this article does do is explain in hopefully an easy-to-understand way just why not all three-card royals are played the same. If you learn these distinctions, it will make learning game strategies easier because now you’ll have enough knowledge that you can understand the “why.” ´

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