Dueces Wild Optimal Play

Written July 21, 2008 by Jack Jones

The following strategy is based on the “full pay” deuces wild paytable below.

Full Pay Deuces Wild
Hand	Payoff	Probability	Return
Royal flush (natural)	800	0.00002208	0.01766709
Four deuces	200	0.00020342	0.04068426
Royal flush (wild)	25	0.00179518	0.04487958
Five of a kind	15	0.00320057	0.04800855
Straight flush	9	0.00413697	0.03723269
Four of a kind	5	0.06492502	0.32462510
Full house	3	0.02122914	0.06368741
Flush	2	0.01658389	0.03316779
Straight	2	0.05659214	0.11318429
Three of a kind	1	0.28451355	0.28451355
Non-winner	0	0.54679803	0.00000000
Total		1.00000000	1.00765031

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.

The player should evaluate straight flush draws carefully. Usually the number of ranks the straight flush spans determines the spread. However if the straight flush is on the low end this can reduce the number of ways to complete it. For example suited 3-4-5

0 Deuces

Natural royal flush (800.0000)
4 to a royal flush (19.574469)
Straight flush (9.0000)
Four of a kind (5.8510637)
Full house (3.0000)
Three of a kind (2.0175762)
Straight/Flush (2.0000)
4 to an outside straight flush (1.65958)
Suited 10-J-Q (1.3987)
4 to an inside straight flush (1.3829787)
3 to a royal flush, except 10-J-Q (1.2719704)
Pair (0.560222)
Two pair (0.5106383)
4 to a flush (0.5106383)
4 to an outside straight (0.5106383)
3 to a straight flush, spread 3-4, suited 345 (0.5051-0.3959)
2 to a royal flush, jack highest¹ (0.38815913)
3 to a straight flush, spread 5 and suited 346,356 ^2,3 (0.35522664)
4 to an inside straight, except missing deuce (0.34042552)
2 to a royal flush, queen highest⁴ (0.33851373)
2 to a royal flush, king highest, no penalty cards⁵ (0.3278446)
Garbage, everything discarded (0.32552597)
2 to a royal flush, king highest, 1 penalty card⁶ (0.3185939)
2 to a royal flush, ace highest (0.29768732)
3 to a straight flush, A low (0.2729)

Notes:
1: Suited 7-10-J beats suited 10-J if either (1) king and ace discards, or (2) queen discard without 8

2: Play 4 to an inside straight over 3 to a straight flush, spread 5, if there is a straight penalty card to the straight flush.

3: Play 2 to a royal, queen high, over 3 to a straight flush, spread 5, when 6 or 7 high.

4: Play 2 to a royal, queen high, over 4 to an inside straight if there are no flush penalty cards and a fully open straight possibility. A fully open straight possibility means that there exists some possible straight with no penalty cards discarded. For example with suited 10-Q and unsuited 5-K-A the player has a full chance at a Q-J-10-9-8 straight. However with suited 10-Q and unsuited K-9-5 the player should go for the inside straight because the K and 9 block any fully open straight possibility.

5: There are some rare exceptions in which it is better to discard everything rather than keep two to a royal, king high, with no penalty cards. See my deuces wild appendix 1 for a list of these exceptions.

6. There are some rare exceptions in which it is better to keep the two to a royal, king high, despite a 9 or ace straight penalty card. See my deuces wild appendix 3 for a list of these exceptions.

1 Deuce

Wild royal flush (25.0000)
5 of a kind (15.0000)
Straight flush (9.0000)
Four of a kind (5.8510637)
4 to a royal flush (3.4042554)
Full house (3.0000)
3 consecutive suited cards 5-6-7 or greater (2.21277)
3 of a kind (2.01758)
Straight (2.0000)
Flush (2.0000)
All other 4 to a straight flush (1.70213 to 1.97872)
3 to a royal flush, highest card king or less (1.1424607)
2 consecutive suited cards, 6-7 or higher, + deuce (1.0952822)
3 to a royal flush, ace highest card, no penalty cards (1.0462534)
Deuce only (1.0328652)
3 to a royal flush, ace highest card, 1+ penalty card³ (1.0286771)
2 consecutive suited cards, 5-6 or lower, + deuce (1.0166513)
4 to an outside straight (1.0000)

Note:
3: There are some rare exceptions to this rule that cut both ways. Sometimes with two a royal with no penalty cards it is better to hold the deuce only, and sometimes with a penalty card you should go for the royal. See my deuces wild appendix 2 for a list of these exceptions.

2 Deuces

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

3 Deuces

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

4 Deuces

4 deuces (200.0000)

Terms:

Outside straight: An open ended straight that can be completed at either end, such as (7,8,9,10). A wild card shall not be used to complete an outside straight. For example 2,5,7,8 is not 4 to an outside straight because of the missing 6. However 2,5,6,7 is 4 to an outside straight.
Inside straight: A straight with a missing inside card, such as (6,7,9,10).
Penalty card: A penalty card is a potentially useful discarded card. For example if the player had 3 to a royal and 4 to a flush the correct play is to keep three to the royal, discarding the fourth suited card. The discarded suited card would be called a flush penalty card because it could have been used to complete a flush. By discarding it the players odds of forming a flush are “penalized.” Sometimes penalty cards can affect borderline plays. For example if the player had a suited 10 and king, with no other cards of that suit, nor a 9, jack, queen, or ace, then the player should keep the two to a royal flush. However this is only marginally better than discarding everything. If the player had just one suited card, or any card that could be used to complete a straight, then the odds of forming a flush or straight would be depressed, lowering the overall expected return below that of discarding everything. So in that situation the player should be mindful of the effect of penalty cards.

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. I used Bob Dancer’s Deuces Wild Video Poker report to verify my strategy. There I found some obscure exceptions that I did not notice, which I used to correct my strategy. So I would like to thank Bob Dancer for his help. You may order his software and strategy cards here.

Better known as “The Wizard of Odds”, Michael Shackleford uses math and computer analysis to determine optimal playing strategy for all casino games. His work can be found on his website, WizardofOdds.com with player strategies and probabilities on most of the casino games. Michael lives in Las Vegas and in his spare time likes to college license plates and gamble.