# Deuces Wild video poker strategy

## Introduction

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

### "Full Pay" Deuces Wild — 100.76%

Hand Payoff Combinations Probability Return
Natural royal flush 800 440202756 0.000022 0.017667
Four deuces 200 4060462824 0.000204 0.040741
Wild royal flush 25 35796957696 0.001796 0.044896
Five of a kind 15 63818309856 0.003202 0.048024
Straight flush 9 83087969280 0.004168 0.037515
Four of a kind 5 1294427430576 0.064938 0.324691
Full house 3 423165297240 0.021229 0.063687
Flush 2 334561280724 0.016784 0.033568
Straight 2 1117664265756 0.056070 0.112141
Three of a kind 1 5674784779512 0.284690 0.284690
Nothing 0 10901423560980 0.546897 0.000000
Total 0 19933230517200 1.000000 1.007620

## Optimal Strategy

Following is I believe the optimal 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

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 an outside straight flush (1.65958)
9. Suited 10-J-Q (1.3987)8
10. 4 to an inside straight flush (1.3829787)
11. 3 to a royal flush, except 10-J-Q (1.2719704)
12. Pair (0.560222)
13. Two pair (0.5106383)
14. 4 to a flush (0.5106383)
15. 4 to an outside straight (0.5106383)
16. 3 to a straight flush, spread 3-4, suited 345(0.5051-0.3959)
17. 2 to a royal flush, jack highest1(0.38815913)
18. 3 to a straight flush, spread 5 and suited 346,3562,3,4 (0.35522664)
19. 4 to an inside straight, except missing deuce (0.34042552)
20. 2 to a royal flush, queen highest5(0.33851373)
21. 2 to a royal flush, king highest, no penaltycards6 (0.3278446)
23. 2 to a royal flush, king highest, 1 penaltycard7 (0.3185939)
24. 2 to a royal flush, ace highest (0.29768732)
25. 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. 2: Three to a straight flush, spread 5, with one straight penalty card is exactly equivalent in expected value to an inside straight. For example5♥,6♠,8♥, 9♥,K♣ (three to a straight flush with two gaps with a straight penalty card). See more on this hand below.
3. 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.
4. Play 2 to a royal, queen high, over 3 to a straight flush, spread 5, when 6 or 7 high.
5. 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. Also play suited Q/10, with 6/7/8, with a suited 6 or 7.
6. 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.
7. 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.
8. With a suited 8, and off-suited K, play the four to the inside straight flush.

## 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. 3 consecutive suited cards 5-6-7 or greater(2.21277)
8. 3 of a kind (2.01758)
9. Straight (2.0000)
10. Flush (2.0000)
11. All other 4 to a straight flush (1.70213 to1.97872)
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 card8 (1.0286771)
17. 2 consecutive suited cards, 5-6 or lower, + deuce(1.0166513)
18. 4 to an outside straight (1.0000)

Note:
8: 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

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) This hand should never be played
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). 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.

5 ,6♠,8,9,K♣

It is common in video poker, especially deuces wild, for two plays to have the exact same expected value. For example in this game with two pair the player should only keep one of them, which one makes no difference. However it is rare for two plays to have the same expected value but a different distribution of possible hands on the draw. Full pay deuces wild is one of the few games that has such a hand. Three to a straight flush, with two gaps, and one straight penalty card has an expected value of 0.340425532 whether going for the straight flush or the straight. The following table shows the number of possible outcomes of both plays.

### Borderline Hand AnalysisExpand

Hand Pays Combinations Four to the Straight Combinations Three to the Straight Flush Probability Four to the Straight Probability Three to the Straight Flush Return Four to the Straight Return Three to the Straight Flush
Straight Flush 9 0 15 0 0.013876 0 0.124884
Flush 2 0 63 0 0.058279 0 0.116559
Straight 2 8 31 0.170213 0.028677 0.340426 0.057354
Three of a Kind 1 0 45 0 0.041628 0 0.041628
Nothing 0 39 927 0.829787 0.857539 0 0
Total   47 1081 1 1 0.340426 0.340426

As the above table shows the expected values are the same. However the standard deviation of playing four to the straight is 0.751639223, while playing three to the straight flush is 1.182169177. This hand, and all similar, happen 8,712 times out of 2,598,960. The return table listed in my return tables is based on playing four to the straight. By always playing three to the straight flush in this situation the standard deviation of the entire game goes up from 5.181690 to 5.181960, an increase of 0.000269.

## 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.

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