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Jacks or Better optimal strategy
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
|Four of a Kind||25|
|Three of a Kind||3|
|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 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.
- Dealt royal flush (800.0000)
- Dealt straight flush (50.0000)
- Dealt four of a kind (25.0000)
- 4 to a royal flush (18.3617)
- Dealt full house (9.0000)
- Dealt flush (6.0000)
- 3 of a kind (4.3025)
- Dealt 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)
- Unsuited TJQK(0.8723)
- Low pair (0.8237)
- 4 to an outside straight with 0-2 high cards(0.6809)
- 3 to a straight flush (type 1) (0.6207 to 0.6429)
- Suited QJ (0.6004)B
- 4 to an inside straight, 4 high cards (0.5957)
- Suited KQ or KJ (0.5821)
- Suited AK, AQ, or AJ (0.5678)
- 4 to an inside straight, 3 high cards (0.5319)
- 3 to a straight flush (type 2) (0.5227 to 0.5097)C
- 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 (type 3) (0.4431)
- Garbage, discard everything (0.3597)
Three to a Straight Flush Key
Straight Flush draw (type 1): Straight flush draw in which the number of high cards equals or exceeds number of gaps.
Straight Flush draw (type 2): One of the following straight flush draws.
- One gap and no high cards
- Two gaps and one high card
- Ace low
Straight Flush draw (type 3): Straight flush draw with two gaps and no high cards.
|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. Knowing this exception will add 0.00000021 to the game return.|
|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 3 to a straight flush if there is no straight penalty card. Knowing this exception will add 0.00000020 to the game return.|
|D||Suited 10 and jack vs. an unsuited jack and king — If there is no flush penalty card, then keeping the 10 and jack 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 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.|
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)
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%.
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