In Deuces Wild video poker, when to discard a deuce

Video poker is a passion for Pam, a regular reader who phoned for some Deuces Wild advice.

"Is there ever a time when I should discard a deuce?" she wondered.

There's an easy answer to that one: No.

"OK," she said. "I thought you might say that. But think about this for a minute. What if I have four parts of a natural royal plus a deuce. If I discard the 2, I'm giving up a sure 125 credits, but I have a chance at drawing a natural royal, and that's worth 4,000.

"If I'm playing quarters, I'm giving up $31.25 for a shot at $1,000. A thousand dollars. Isn't that worth the risk?"

By the percentages, no it's not. Your best play is to hold the wild royal with its 125-coin payback for a five-coin wager, and it's not close.

Here's the way it works, using the common "Illinois" version of Deuces Wild. For a five-coin bet, that version pays 4,000 for a natural royal, 1,000 on four 2s, 125 on a royal with wild cards, 75 on five of a kind, 45 on a straight flush, 20 on either four of a kind or a full house, 15 on a flush, 10 on a straight, and 5 on three of a kind.

Let's say you're dealt 10-J-Q-K of the same suit, along with a deuce. If you discard the 2 to give yourself a shot at drawing the ace for a natural royal, there are 47 possible one-card draws.

Thirty of those draws would leave you with a non-paying hand. Six draws would bring straights, and another six would bring flushes, each worth 15 coins. One, the 9 of your suit, would bring a straight flush, worth 45. Any of the other three 2s would bring you back to your starting point with a wild royal worth 125.

And one draw, the ace of your suit, would give you that 4,000-coin bonanza for a natural royal.

Average all that out and your per hand return is 97.23 coins. Even though once per 47 hands you'll hit the big one, on a per draw basis you cost yourself nearly 28 coins by discarding the 2.

If you start with a wild royal that includes the ace and one 2, such as suited A-K-Q-J and a deuce, your average return drops to 95.97 coins if you discard the 2.

That's because there are fewer straight possibilities and no chance of a non-royal straight flush if your hand is ace-high.

Either way, your average return can't touch the sure 125 coins for holding the wild royal.

Pam sighed.

"I knew you were going to say something along those lines. It sure is exciting when the natural royals come. It's tempting to ignore those percentages and go for it."

That's up to each player. But to get the most out of the game, resist the temptation.

** * ** * **

As an addendum to all that, I focused on wild royals with a single deuce because with more than one 2, it's nowhere near a close call. When you need two cards, or three to complete a natural royal, that 125-coin sure thing looks even better.

Dealt 2-2 along with a suited 10-J-Q, the average return on holding just the high cards drops to 5.89 per five coins wagered. Dealt 2-2-2 with 10-J of the same suit, the average return for holding 10-J is 0.896 coins.

It becomes more interesting to turn it around and ask how low on the pay table you have to go before it becomes more profitable to hold three deuces and hope for the 1,000-coin jackpot on the fourth rather than take the guaranteed win.

It's not close at a wild royal, where the average return of 70.95 coins for holding just the three 2s can't compare to the 125-coin sure thing.

It tightens up at five of a kind. At the pay table described above, five of a kind pays 75 coins for a five-coin bet. Holding 2-2-2 and tossing away a pair of 7s brings an average return of 71.49 coins — close, but not enough to break up the winner. (Returns are slightly different if your pair is made of 3s, or 10s, or other denominations because of their effects in straight, straight flush or royal flush possibilities. The changes are not enough to call for a strategy switch.)

But what if you find yourself at a machine that pays only 12-for-1 on five of a kind, a 60-coin payoff for a five coin bet instead of 75. I recommend that you not play that machine, but if you do, it's a better play to hold just the 2s. If the only change in the above pay table is that lower payoff on five of a kind, the average return for holding 2-2-2 and tossing two 7s becomes 70.56 coins, and that beats the sure 60 for holding all five cards.

Drop one more step down the pay table to a straight flush with no royal possibilities, and holding three 2s becomes far the better play. Dealt 2-2-2 plus a suited 7-8, the average payoff of 71.47 coins for holding three 2s far exceeds the 45-coin pay for keeping the hand intact.