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Deuces Wild Video Poker

This strategy was designed to be used for a machine with the following payoff table, although it can be used without much error against any deuces wild machine. The table also shows the probability of forming each hand, assuming perfect play, the contribution to the expected return, and the overall expected return.

Basic Strategy

Following is a strategy for the payoff table above. To determine the best play look under the list given the number of deuces hold (you never discard a deuce). Then look for the highest playable hand on the list. For example if you have both a pair and four to a flush you would keep the pair because it is higher on the list. The numbers on the right represent the expected return, which can vary depending on the discards.

0 Deuces

1. Natural royal flush (800.0000)
2. 4 to a royal flush (19.574469)
3. Straight flush (9.0000)
4. Four of a kind (5.8510637)
5. Full house (3.0000)
6. Three of a kind (2.0175762)
7. Straight/Flush (2.0000)
8. 4 to a straight flush (1.3829787)
9. 3 to a royal flush (1.2719704)
10. Pair (0.560222)
11. Two pair (0.5106383)
12. 4 to a flush (0.5106383)
13. Four to an outside straight, except 3/4/5/6 (0.5106383)
14. 3 to a straight flush, spread 3 (0.50508785)
15. 3 to a straight flush, spread 4 (0.43755782)
16. 2 to a royal flush, jack highest (0.38815913)
17. 3 to a straight flush, spread 5 (0.35522664)
18. Four to an inside straight, except ace/3/4/5 (0.34042552)
19. Unsuited 3/4/5/6 (0.34042552)
20. 2 to a royal flush, queen highest^* (0.33851373)
21. 2 to a royal flush, king highest, no penalty cards (0.3278446)
22. Garbage, everything discarded (0.32552597)
23. 2 to a royal flush, king highest, 1 penalty card (0.3185939)
24. 2 to a royal flush, ace highest (0.29768732)

Notes:
* If two to a royal flush, queen highest vs. 4 to an inside straight then go for the straight unless there are no flush penalty cards to the royal and only a 9 straight penalty card.

1 Deuce

1. Wild royal flush (25.0000)
2. 5 of a kind (15.0000)
3. Straight flush (9.0000)
4. Four of a kind (5.8510637)
5. 4 to a royal flush (3.4042554)
6. Full house (3.0000)
7. 4 to an outside straight flush (2.255319)
8. 3 of a kind (2.01758)
9. Straight (2.0000)
10. Flush (2.0000)
11. 4 to an inside straight flush (1.9787234)
12. 3 to a royal flush, highest card king or less (1.1424607)
13. 2 consecutive suited cards, 6/7 or higher, + deuce (1.0952822)
14. 3 to a royal flush, ace highest card, no penalty cards (1.0462534)
15. Deuce only (1.0328652)
16. 3 to a royal flush, ace highest card, 1+ penalty card (1.0286771)
17. 2 consecutive suited cards, 5/6 or lower, + deuce (1.0166513)
18. 4 to an outside straight (1.0000)

2 Deuces

1. Wild royal flush (25.0000)
2. 5 of a kind (15.0000)
3. Straight flush (9.0000)
4. Four of a kind (5.8510637)
5. 4 to a royal flush (4.617021)
6. 2 consecutive suited cards, 6/7 or higher, + deuces (3.3404255)
7. 2 deuces only (3.2730188)
8. 2 consecutive suited cards, 5/6 of lower, + deuces (3.1276596)
9. Full house or less

3 Deuces

1. Wild royal flush (25.0000)
2. 3 deuces only, non-pair discarded (15.059204)
3. 3 deuces only, pair 9 or less discarded (15.057354)
4. 5 of a kind (15.0000)
5. 3 deuces only, pair 10 or greater discarded (14.938946)
6. 4 to a royal flush (11.829787)
7. Straight flush or less

4 Deuces

1. 4 deuces (200.0000)

Terms:

• Outside straight: An open ended straight that can be completed at either end, such as (7,8,9,10).
  
  
• Inside straight: A straight with a missing inside card, such as (6,7,9,10).
  
  
• Penalty card: Sometimes one must discard a potentially useful card. For example if you had one deuce and a suited queen and ace it is usually best to go for the royal. However if one of the discards were a non-suited 10, jack, or king that would be considered a penalty card because it makes the probability of forming a straight less. In this case it would be better to keep the deuce only.

Methodology

To determine the above strategy I created a program can determine the expected return of the best play of any hand. The way it works is to consider all 32 ways to play a hand. For every play the program systematically scores the held cards with every possible set of discards and averages the results. The play that yields the greatest average is determined to be the best play and the specific statistics for that play are displayed. The program can also show the statistics for non-optimal plays. Using this program it was then a time consuming task to try numerous borderline hands and rank them in order of expected return.

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