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In the previous post, we discussed the odds of completing royal flushes in 9/6 Jacks or Better. Today, we will explore the same topic for the NSU Deuces Wild game.

NSU Deuces Wild pays 99.73%. The pay schedule is 800/200/25/16/10/4/4/3/2/1 from top payline to bottom. The analysis is based on the perfect strategy.

Enumerate Potential Holdings for Achieving a Royal Flush

In Deuces Wild, unlike Jacks or Better, there are no high or low cards. Generally, you don’t hold a single card other than the wild card deuce, which is why the list is shorter.

Note: By examining the combination of suited royal cards, you can notice several interesting aspects that may help you correct your strategy.

1. There is no scenario where you should hold a suited Ace and King/Queen/Jack. For Jacks or Better players, this might seem counterintuitive.
2. There is indeed a rare scenario where you should hold a suited Ace and Ten. We will discuss this in a future post.
3. According to my calculations, in NSU Deuces Wild game, there are 451,260 hands out of the total 2,598,960 where you should discard all 5 cards. This accounts for approximately 17.36% of the hands.  In comparison, only 3.25% of the hands in the 9/6 Jacks or Better game require discarding all 5 cards. This highlights how NSU Deuces Wild can be streaky.

Summarize the numbers

Category	Count	Odds (1/p)
5RF 4RF 3RF 2RF 1RF Discard all 5 cards	4 860 33660 93168 0 958452	649740 3022.046512 77.21212121 27.89541473 N/A 2.711622491

Same as Jacks or Better as well as all other video poker games based on 52-card deck, there are a total of 2,598,960 possible ways to deal a hand of 5 cards from a 52-card deck. Among these, there are exactly 4 ways to get a dealt Royal Flush, making the odds of getting such a hand 1 in 649,740.

There are 860 ways to get a dealt hand where you should hold four-to-royal. To complete the Royal Flush. The odds of getting such a dealt hand are 1 in about 3,022 hands. The number is lower than the same category in Jacks or Better because you always hold the wild card deuces in Deuces Wild games.

Note: Since you never hold a single card other than the wild card, the number of hands in the category 1RF is 0.

Category	Odds (1/p)	Odds to draw a royal flush (1/p)	Combined Odds (1/p)
5RF 4RF 3RF 2RF 1RF Discard all 5 cards	649740 3022.046512 77.21212121 27.89541473 N/A 2.711622491	1 47 1081 16215 178365 1533939	649740 142036.186 83466.30303 452324.1499 N/A 4159463.493

Category	Combined Odds Deuces Wild (1/p)	Combined Odds Jacks or Better (1/p)
5RF 4RF 3RF 2RF 1RF Discard all 5 cards	649740 142036.186 83466.30303 452324.1499 N/A 4159463.493	649740 130503.3333 102192.4836 205912.9112 1186106.165 13970584.89

I hope that all readers now understand how to read this chart. If not, please refer to the previous post for clarification.

Notes:

1. Similar to the odds in Jacks or Better, holding three royal cards and successfully drawing the needed two cards is still the easiest way to complete a royal flush in Deuces Wild, the odds of completing a royal flush this way are 1 in 83,466.
2. Getting a royal flush by discarding all cards has a probability of 1 in 4,159,463. This is approximately three times more likely than achieving a royal flush in Jacks or Better in the same way. Intuitively, this is because you discard all cards about three times more often in this scenario compared to Jacks or Better.

Overall odds of getting a royal

Category	Combined Odds (1/p)	Combined Odds
5RF 4RF 3RF 2RF 1RF Discard all 5 cards	649740 142036.186 83466.30303 452324.1499 N/A 4159463.493	1.53908E-06 7.04046E-06 1.19809E-05 2.2108E-06 0 2.40416E-07
TOTAL		2.30116E-05 (1 in 43456.27018)

The overall odds of getting a royal flush in Jacks or Better, when summing up all the odds in the table, is 1 in approximately 43457. You hit royal flush a bit slower in Deuces Wild compared with Jacks or Better.

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