Deuces Wild and royal flushes

19 May 2013

By John Grochowski

QUESTION: I have a question about Deuces Wild. I love the full-pay game. It’s the one I first played in Las Vegas in the ’80s and it’s still the game I play whenever I can find it. I find it less and less, however.

I find myself more and more settling for the games that reduce the four-of-a-kind pays to 4-for-1, but also pay 4 on the full houses and pay 3 instead of 2 on flushes.

One hand troubles me. If I’m dealt a five-of-a-kind with three deuces, like 2-2-2-6-6, I’m used to holding the 2s and throwing away the other two, knowing I have at least four-of-a-kind. In the Deuces games I see now, where I get less on four-of-a-kind, that drops my guaranteed payoff if make my usual draw. Instead of 25 coins for a five-coin bet for four-of-a-kind, my guarantee is only 20 coins.

Does that change your strategy? Should I be holding the five-of-a-kind now?

ANSWER: You were making the correct play in full-pay Deuces, which returns 100.8 percent with expert play. The chance to draw a fourth Deuce for a 1,000-coin bonanza with a five-coin bet is a powerful incentive to break up a five-of-a-kind. In the full-pay game, your average return for a five-coin wager when you hold 2s alone is 75.32 coins, a shade better than the 75 coins you’d get for keeping all five cards.

In most Deuces games today, the situation is as you’ve described. Four-of-a-kind hands and full houses all return 20 coins for five-coin wager, and flushes return 15 instead of the 10 you get on full-pay Deuces.

Those changes force a number of alterations in strategy. For the hand you describe, it depends on the rest of the pay table. There are three common versions. One, nicknamed “Illinois Deuces” or “Airport Deuces” has the same wild royal, five-of-a-kind and straight flush pays as full-pay Deuces, so that for a five-coin wager you’re getting back 125, 75 and 45 respectively. Another, which players have come to call “Not So Ugly Deuces,” increases the five-of-a-kind payback to 80 and the straight flush to 50. And a third, which I see as a game to avoid, reduces wild royals to 100, five-of-a-kind to 60 and leaves straight flushes at 45.

In Illinois Deuces, a 98.9 percent game with expert play, the drop in the four of a kind return means the average payback for holding just the 2s drops to 71.5 coins. You’re better off holding the five-of-a-kind. And in Not So Ugly Deuces, that increase to 80 on five-of-a-kind means it’s not a close call. Holding 2-2-2 brings just a 72.4-coin expectation.

But in the reduced pay version, a 97.1 percent game that is all too common in modern casinos, five of a kind brings only 60 coins. The 69.7-coin average return isn’t as strong as the paybacks for holding the 2s on other versions, but it’s far better than the five-of-a-kind pay.
So the best percentage play is to hold 2-2-2 in full-pay or reduced pay Deuces Wild, but hold five of a kind in the Illinois or Not So Ugly versions.

QUESTION: You’ve said that in Caribbean Stud and in other five-card stud poker games, the chance of getting a royal flush is 1 in 649,740. How do you get that? I thought you had to take 52 to the fifth power, which is 380,204,032, to get the number of five-card poker hands. Then you divide by four, so the chance of getting a royal is 1 in 95,051,008 chance of a royal. That’s a lot longer odds than you say.

ANSWER: Your calculation assumes a 1 in 52 chance of any given card being dealt into your hand, and it assumes cards must be in specific order, that Ace-King-Queen-Jack-10 of spades is a different hand than Jack-10-King-Ace-Queen of spades.

Actually, there’s a 1 in 52 chance of any card being dealt on the first card, but the remaining cards then have a 1 in 51 chance of being dealt, then 1 in 50, 1 in 49 and 1 in 48. So the number of possible five-card hands dealt in any specific order is 52 x 51 x 50 x 49 x 48, or 311,875,200. Any five cards can be arranged in 120 different ways, and when we divide 311,875,200 by 120 we get 2,598,960 possible hands in which order doesn’t matter.

Divide that by four possible royals -- one in each suit -- and there is a 1 in 649,740 chance of being dealt a royal in five-card stud poker.