Jacks or Better optimal strategy

Last Update: Dec. 11, 2011

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The following strategy is for full pay Jacks or Better video poker. "Full Pay" designates the following paytable, per coin based on five coins bet, which returns 99.54% of money bet assuming optimal strategy.

To use this strategy, look up all reasonable ways to play a hand, and choose the play that is highest on the list. If a play isn't on the list then it should never be played. The numbers on the right represent the average return. These numbers can vary depending on the discards.

Let's try an example. Suppose you have both four to a flush and a low pair. Should you sacrifice the low pair to complete the flush or sacrifice the possible flush and keep the low pair? From the list below 4 to a flush has a higher ranking and thus is the better play. To test yourself on other hands try my video poker quiz.

I admit this is a long and rather difficult strategy but I believe it correctly advises every possible hand. If used correctly it should yield perfect play.

1. Dealt royal flush (800.0000)
2. Dealt straight flush (50.0000)
3. Dealt four of a kind (25.0000)
4. 4 to a royal flush (18.3617)
5. Dealt full house (9.0000)
6. Dealt flush (6.0000)
7. 3 of a kind (4.3025)
8. Dealt straight (4.0000)
9. 4 to a straight flush (3.5319)
10. Two pair (2.59574)
11. High pair (1.5365)
12. 3 to a royal flush (1.2868) ^A
13. 4 to a flush (1.2766)
14. Unsuited TJQK(0.8723)
15. Low pair (0.8237)
16. 4 to an outside straight with 0-2 high cards(0.6809)
17. 3 to a straight flush (type 1) (0.6207 to 0.6429)
18. Suited QJ (0.6004)^B
19. 4 to an inside straight, 4 high cards (0.5957)
20. Suited KQ or KJ (0.5821)
21. Suited AK, AQ, or AJ (0.5678)
22. 4 to an inside straight, 3 high cards (0.5319)
23. 3 to a straight flush (type 2) (0.5227 to 0.5097)^C
24. Unsuited JQK (0.5005)
25. Unsuited JQ (0.4980)
26. Suited TJ (0.4968) ^D
27. 2 unsuited high cards king highest (0.4862)
28. Suited TQ (0.4825) ^E
29. 2 unsuited high cards ace highest (0.4743)
30. J only (0.4713)
31. Suited TK (0.4682) ^F
32. Q only (0.4681)
33. K only (0.4649)
34. A only (0.4640)
35. 3 to a straight flush (type 3) (0.4431)
36. Garbage, discard everything (0.3597)

Card Abreviations
Letter	Card
T	10
J	Jack
Q	Queen
K	King
A	Ace

Rare Exceptions

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.

Hands that are never played:

By request I have removed hands that are never played from the list. Either some subset of these hands are better than the larger hand, or discarding everything is better. In parenthesis I put what you should do with these hands.

• Suited 10 and ace (keep the ace only)
• 3 unsuited high cards, ace highest (keep the lowest two high cards)
• 4 to an inside straight, 2 high cards (keep the two high cards)
• 4 to an inside straight, 1 high card (keep the single high card)
• 4 to an inside straight, 0 high cards (discard everything)

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 6-7-8-9.

Inside straight: A straight with a missing inside card, such as 5-6-7-9. Note that A-2-3-4 and J-Q-K-A are considered inside straights because only one rank will complete them.

Penalty card: Sometimes one must discard a potentially useful card. In rare situations cards you would never keep can still tip the scales in favor of one play over another. For example, take the situation in footnote F. The player has a king of clubs, 10 of clubs, 9 of spades, 6 of clubs, and a 3 of diamonds. The best options are to either keep the suited 10 and king or the king only. The suited 10 and king is usually the better option. However in this scenario two potentially useful cards would be discarded, the 9 (lowering the odds of forming a straight), and the 6 of clubs (lowering the odds of forming a flush). These two penalty cards degrade the value of the suited 10 and king to below that of keeping the king only.

It should be mentioned that this strategy is mainly for academic interest or only the most avid video poker players. For practical purposes I recommend my simple strategy with a return of 99.46% or my intermediate strategy with a return of 99.52%.

Methodology

To determine the above strategy I created a program that 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 9/6 Jacks or Better 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 .