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.
Full Pay Jacks or Better
Hand Payoff
Royal flush 800
Straight flush 50
Four of a kind 25
Full house 9
Flush 6
Straight 4
Three of a kind 3
Two pair 2
Jacks or better 1
To use this strategy look up all reasonable ways to play a hand and choose the play that is highest on the list. If your hand 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.
Pat royal flush (800.0000)
Pat straight flush (50.0000)
Pat four of a kind (25.0000)
4 to a royal flush (18.3617)
Pat full house (9.0000)
Pat flush (6.0000)
3 of a kind (4.3025)
Pat straight (4.0000)
4 to a straight flush (3.5319)
Two pair (2.59574)
High pair (1.5365)
3 to a royal flush (1.2868) A
4 to a flush (1.2766)
4 to an outside straight with 3 high cards (0.8723)
Low pair (0.8237)
4 to an outside straight with 0-2 high cards (0.6809)
3 to a straight flush, spread 5, 2 high cards (0.6429)
3 to a straight flush, spread 4, 1+ high card (0.6392)
3 to a straight flush, spread 3, 0+ high 789Bet cards (0.6207)
Suited jack and queen (0.6004) B
4 to an inside straight, 4 high cards (0.5957)
2 suited high cards, king highest (0.5821)
2 suited high cards, ace highest (0.5678)
4 to an inside straight, 3 high cards (0.5319)
3 to a straight flush, spread 5, 1 high card (0.5227) C
3 to a straight flush, spread 4, 0 high cards (0.5097)
Unsuited JQK (0.5005)
Unsuited JQ (0.4980)
Suited TJ (0.4968) D
2 unsuited high cards king highest (0.4862)
Suited TQ (0.4825) E
2 unsuited high cards ace highest (0.4743)
J only (0.4713)
Suited TK (0.4682) F
Q only (0.4681)
K only (0.4649)
A only (0.4640)
3 to a straight flush, spread 5, 0 high cards (0.4431)
Garbage, discard everything (0.3597)
Rare Exceptions:
A
4 to a flush beats 3 to a royal if royal includes a ten and ace, and the unsuited card is a 10 or straight penalty card.
B
4 to an inside straight beats suited jack and queen with 9 or flush penalty card.
C
3 to a straight flush, spread 5, with 1 high card vs. 4 to an inside straight, with 3 high cards: Play the straight flush if there is no straight penalty card.
D
Suited 10 and jack vs. an unsuited jack and king: If there is no flush penalty card then keeping the 10 and jack then that is the better play, otherwise keep the jack and king.
E
Suited 10 and queen vs. an unsuited queen and ace: If there is no flush penalty card then keeping the 10 and queen then that is the better play, otherwise keep the queen and ace.
F
Suited 10, king vs. king only: Normally the suited ten and king is better than the king alone, however if you must discard a 9 and a flush penalty card then hold the king only.
Key:
T
10
J
Jack
Q
Queen
K
King
A
Ace
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 (discarding 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 (7,8,9,10).
Inside straight: A straight with a missing inside card, such as (6,7,9,10).
Spread: This refers to the number of ranks spread apart the cards are toward a potential straight, straight flush, or royal flush. The smaller the spread the better the odds are for the player. For example a suited 5, 6, an 8 would be 3 to a straight flush with a spread of 4 because they cards span 4 ranks.
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 hand 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 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.
