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Which One Is Worth More?

In both situations, you have five cards that will give you a wild royal flush -- two high diamonds and three deuces in the first case, and three high diamonds and two deuces in the second. In both situations, drawing any of the seven diamonds in the range of 3d through 9d will give you a flush. And in both situations drawing any of the three tens or three jacks that don't happen to be diamonds will give you a straight. So far, everything points towards the two starting combinations being worth the same.

Each of the other 29 cards you can draw (i.e., every card that is not a diamond and/or a deuce, a jack or ten) yields a hand that is worth more in the two-deuce starting position than the one-deuce starting position. Three of these are non-diamonds queens (which yield a straight rather than 3-of-a-kind), six of these are non-diamond aces or kings (which yield 4-of-a-kind rather than 3-of-a-kind), and the other twenty cases are "nothing much" which yield nothing at all in the first case and 3-of-a-kind in the second.

It's actually not a close decision. The pay schedule affects "by how much" the two-deuce 4-card royal is preferable to the 1-deuce 4-card royal, but not that fact that it is preferable. In full pay Deuces Wild, the two-deuce version is worth an even five coins (i.e., $1.25 in a quarter game) more than the one-deuce version. In the NSU Deuces Wild, the difference is "only" about 4.4 coins.

Now for a similar kind of choice, except we are talking about 3-card royals rather than 4-card royals, and comparing them with no deuces and 1 deuce. That is, which is better between Ac Kc Qc 6h 7s and W Ac Kc 6h 7c?

As before, having a deuce gives you a lot more scoring hands. With the no-deuce 3-card royal, you will end up with a zero-score 85% of the time, whereas with the 1-deuce 3-card royal, you will end up with a zero score "only" 52% of the time. Those players who spend time worrying about whether or not they score points on this particular hand should probably choose the combination with the deuce.

But this increase in the probability of success comes at a HUGE cost. Why? Because once in 1,081 times you draw to a suited AKQ you end up with a natural royal flush 4,000 coins. When you draw to WAK, the best you can do is end up with a wild royal flush, worth 125 coins.

Not that I would recommend you ever do it, but if you were betting 1 coin instead of 5, WAK would be better than AKQ. Now the bonus for the royal flush is reduced from 800-for-1 to 250-for-1 and the greater flexibility from having the deuce pays dividends.

Betting less than max coins in the first example above will not affect which is the best play. Why? Because betting less than max coins only affects the return on the natural royal flush, and since you have at least one deuce in each hand, a natural royal flush is out of the question.

The value of a 3-card royal in Deuces Wild is determined by it highest card, so QJT is the most valuable, KQJ, KQT, KJT are all worth the same and are slightly less valuable, and AKQ, AKJ, AKT, AQJ, AQT, AJT are all worth the same and are less valuable yet. Similarly, with a wild card WJT is more valuable than the 3-card royals with a Q-high, which is more valuable than those with a K-high, which is more valuable than those with an A-high.