Intermediate strategy for Jacks or Better video poker

Last update: July 18, 2008

Definitions:

• High Card = J to A
  
• Straight Flush draw (type 1) = Open ended straight flush draw, in which the number of high cards equals or exceeds number of gaps.
  
• Straight Flush draw (type 2) = Open ended straight flush draw, with one gap, or two gaps with one high card, any ace-low, or 234 suited.
  
• Straight Flush draw (type 3)= Straight flush draw with two gaps and no high cards.

The following stategy is not expressed in the usual order of value. Instead, this is a list of all the common conflict hands. I think the kind of list below is better suited to the way people actually think about video poker. The list is in the order of the hand strength of the better play.

1. 9♥ T♥ J♥ Q♥ K♥ — Pat straight flush or 4 to a royal: Keep the straight flush.
2. 2♣ T♣ J♣ Q♣ A♣ — Pat flush or 4 to a royal: Go for the royal.
3. T♥ J♥ Q♠ K♥ A♥ — Pat straight or 4 to a royal: Go for the royal.
4. T♠ J♠ Q♠ Q♥ K♠ — High pair or 4 to a royal: Go for the royal.
5. J♣ Q♥ Q♣ Q♠ K♣ — 3 of a kind or 3 to a royal: Keep the 3 of a kind.
6. 2♠ 6♠ J♠ Q♠ K♠ — Pat flush or 3 to a royal: Keep the flush
7. 3♥ 4♥ 6♥ 7♥ Q♥ Pat flush or 4 to a straight flush: Keep the flush
8. T♥ J♣ Q♥ K♠ A♥ — Pat straight or 3 to a royal: Keep the straight
9. 3♥ 4♥ 6♥ 7♥ Q♠ — Pat straight or 4 to a straight flush: Keep the straight
10. T♣ T♥ Q♣ A♥ A♣ — 2 pair or 3 to a royal: Keep the 2 pair.
11. 7♠ 8♠ 9♠ J♠ J♥ — 4 to a straight flush vs. any pair: Go for straight flush
12. 2♥ 5♥ 7♥ J♣ J♥ — High pair vs. 4 to a flush: Keep high pair
13. 8♣ 9♥ T♠ J♥ J♣ — High pair vs. 4 to a straight: Keep high pair
14. 3♥ T♠ J♠ Q♥ Q♠ — High pair vs. 3 to a royal flush: Keep high pair
15. 3♥ 9♠ J♠ Q♥ Q♠ — High pair vs. 3 to a straight flush: Keep high pair
16. 4♣ T♥ T♠ Q♥ A♥ — 3 to a royal vs. Low pair: Go for the royal.
17. 2♥ 5♣ T♥ Q♥ A♥ — 3 to a royal vs. 4 to a flush: Go for the royal
18. 2♥ T♣ J♥ Q♣ K♣ — 3 to a royal vs. 4 to a straight: Go for the royal
19. 3♠ 3♥ 5♠ 7♠ 9♠ — 4 to a flush vs low pair: Go for the flush
20. 4♠ 5♠ 6♥ 7♠ Q♠ — 4 to a flush vs. 4 to a straight: Go for the flush
21. 2♣ 6♥ 7♥ 8♥ K♥ — 4 to a flush vs. 3 to a straight flush: Go for the flush
22. 2♣ 7♣ 8♥ Q♣ K♣ — 4 to a flush vs. 2 to a royal flush: Go for the flush
23. 5♠ 6♥ 7♣ 7♥ 8♠ — Low pair vs. 4 to a straight: Keep the low pair
24. 7♠ 8♠ 8♥ 9♠ K♥ — Low pair vs. 3 to a straight flush: Keep the low pair
25. 3♠ 6♣ 6♥ J♠ Q♠ — Low pair vs. 2 to a royal: — Keep the low pair
26. 2♣ 7♥ 8♥ 9♥ T♠ — 4 to an outside straight vs. 3 to a straight flush: Go for the straight
27. 2♣ 9♣ T♠ J♥ Q♥ — 4 to an outside straight vs. 2 to a royal flush: Go for the straight
28. 4♣ 5♣ 6♣ J♥ Q♥ — 3 to a straight flush (type 1) vs. 2 to a royal flush: Go for the straight flush
29. 8♣ T♥ J♥ Q♠ A♥ — 3 to a straight flush (type 1) vs. 4 to an inside straight with 3-4 high cards: Go for the straight flush
30. 2♥ T♣ J♥ Q♠ A♥ — 2 to a royal flush (both high) vs. 4 to an inside straight with 3-4 high cards: Go for the royal
31. 2♠ 4♥ J♣ Q♥ K♣ — 2 to a royal flush (both high) vs. any 3 unsuited high cards: Go for the royal
32. 5♥ 6♥ 8♥ K♠ A♠ — 2 to a royal flush (both high) vs. 3 to a straight flush (type 2): Go for the royal
33. 7♥ T♥ J♥ K♣ A♠ — 4 to an inside straight with 3-4 high cards vs. 3 to a straight flush (type 2): Go for the straight
34. T♥ J♣ Q K♠ A♥ — 4 to an inside straight with 3-4 high cards vs. 2 to a royal (ten low): Go for the straight
35. 2♠ 4♥ 7♣ T♣ J♣ — 3 to a straight flush (type 2) vs. 2 to a royal flush (10 low): Go for the straight flush
36. 7♥ 8♥ T♥ J♣ A♠ — 3 to a straight flush (type 2) vs. 1-3 high cards: Go for the straight flush
37. 2♥ 5♠ J♣ Q♥ K♠ — KQJ vs. QJ: Play KQJ
38. 4♠ 6♥ T♥ J♥ Q♣ — QJ vs 2 to a royal flush (ten low): Keep QJ
39. 2♥ 4♥ 6♥ J♠ Q♣ — QJ vs 3 to a straight flush (type 3): Keep QJ
40. 3♥ 5♠ J♣ Q♥ A♠ — QJ vs 3 high cards A high: Keep QJ
41. 2♣ 3♥ T♥ J♥ A♣ — JT suited vs 2-3 unsuited high cards K or A high: Keep JT
42. 2♥ 4♥ 6♥ T♠ J♠ — JT suited vs 3 to a straight flush (type 3): Keep JT
43. 2♥ 4♠ T♥ J♥ K♣ — KJ vs JT suited: Keep KJ
44. 2♥ 4♥ 6♥ J♠ K♣ — KQ or KJ vs. 3 to a straight flush (type 3): Keep KQ or KJ
45. 3♥ 4♣ 5♥ T♠ K♠ — KT suited vs. K: Play KT suited
46. 2♥ 4♥ 6♥ T♠ K♠ — KT suited vs. 3 to a straight flush (type 3): Keep KT suited
47. 3♣ 5♣ 7♣ 8♥ J♥ — Single high card vs. 3 to a straight flush (type 3): Keep high card only

If you prefer to learn the usual way, here is a list of possible plays according to the strength of the hand. To use the strategy look up all viable ways to play an initial hand on the following list and elect that which is highest on the list. A "high card" means a jack or higher.

1. Four of a kind, straight flush, royal flush
2. 4 to a royal flush
3. Three of a kind, straight, flush, full house
4. 4 to a straight flush
5. Two pair
6. High pair
7. 3 to a royal flush
8. 4 to a flush
9. Low pair
10. 4 to an outside straight
11. 3 to a straight flush (type 1)
12. AKQJ unsuited
13. 2 suited high cards
14. 4 to an inside straight with 3 high cards
15. 3 to a straight flush (type 2)
16. KQJ unsuited
17. QJ unsuited
18. JT suited
19. KQ, KJ unsuited
20. QT suited
21. AK, AQ, AJ unsuited
22. KT suited
23. One high card
24. 3 to a straight flush (type 3)
25. Discard everything

Note: The number of high cards in holding 3 to a straight flush is roughly offset by the number of gaps. When evaluating 3 to a straight flush subtract the number of gaps from the number of high cards.

Terms:

High card: A jack, queen, king, or ace. These cards are retained more often because if paired up they return the original bet.

Outside straight: An open ended straight that can be completed at either end, such as the cards 7,8,9,10.

Inside straight: A straight with a missing inside card, such as the cards 6,7,9,10. In addition A,2,3,4 and J,Q,K,A also count as inside straights because they are at an extreme end.

Gap: The number of ranks needed to fill in the middle of a straight flush. For example a 6,7,8 would have 0 gaps, a 6,7,9 would have 1, and a 6,7,10 would have 2. The following are considered to have 2 gaps because they are at extreme ends: A,2,3; A,2,4; A,3,4; J,Q,A; J,K,A; and Q,K,A. The following are considered to have 1 gap because they are close to an extreme end: 2,3,4 and J,Q,K.

Example: Suppose you have the following hand.

The top two plays are (1) keep the three to a straight flush and (2) keep two to a royal flush. The number of gaps to the straight flush is 2 and the number of high cards is also 2, so it is a type 3 straight flush draw. The table shows that 3 to a straight flush (type 3), beats two suited high cards, so go keep the 3 cards to the straight flush.

Comparison to Optimal Strategy

The following table compares the probability and return of each hand under both the simple strategy and the optimal strategy.

The next table is a frequency distribution of the error, or difference in expected return, between the simple strategy and the optimal strategy.