Optimal Strategy for Full Pay Jacks or Better 9/6 Video Poker (paytable 800-50-25-9-6-4-3-2-1)

At Bits & Odds, we conducted a thorough mathematical analysis of all probabilities to determine the overall payout (expected value, or EV) and the optimal strategy for Full Pay Jacks or Better 9/6 video poker. This strategy is specifically tailored for the 9/6 payout table, which offers the best return for this variant. It’s important to note that payout tables can significantly impact both the EV and the optimal strategy, so always ensure you’re using the correct strategy for the machine you’re playing.

Payout table

Hand 1 Coin 2 Coins 3 Coins 4 Coins 5 Coins
Royal Flush 250 500 750 1000 4000
Straight Flush 50 100 150 200 250
Four of a Kind 25 50 75 100 125
Full House 9 18 27 36 45
Flush 6 12 18 24 30
Straight 4 8 12 16 20
Three of a Kind 3 6 9 12 15
Two Pair 2 4 6 8 10
Jacks or Better 1 2 3 4 5

Analysis

Jacks or Better (9/6 Paytable) – Overall EV: 99.54%
Hand Payout Probability Combinations EV
Royal Flush 800 0.000024758268 41,126,022 0.0198066144
Straight Flush 50 0.000109309090 181,573,608 0.0054654545
Four of a Kind 25 0.002362545686 3,924,430,647 0.05906364215
Full House 9 0.011512207336 19,122,956,883 0.103609866024
Flush 6 0.011014510968 18,296,232,180 0.066087065808
Straight 4 0.011229367241 18,653,130,482 0.044917468964
Three of a Kind 3 0.074448698571 123,666,922,527 0.223346095713
Two Pair 2 0.129278902480 214,745,513,679 0.25855780496
Jacks or Better 1 0.214585031126 356,447,740,914 0.214585031126
Nothing 0 0.545434669233 906,022,916,158 0
Total 1.000000000000 1,661,102,543,100 0.995439043694

Optimal Drawing Strategy

Want to know the absolute, undisputed best way to play Jacks or Better? Stewart N. Ethier’s “Doctrine of Chances: Probabilities in the Game of Poker” lays out the mathematically optimal strategy for maximizing your Expected Value (EV) on every single hand. But here’s the kicker: we didn’t just take his word for it. The team here at Bits & Odds actually coded and ran simulations on every possible hand to verify that this strategy is, in fact, the real deal. We’re talking about a verifiably optimal approach – the gold standard of poker theory. Now, while this level of perfect play is way too complex for a quick game at the casino, it’s an incredible testament to the power of math in poker, and something we’ve rigorously confirmed ourselves!

Rank Hand to Hold Description Example
1 Pat Royal Flush, Straight Flush, Four of a Kind, or Full House Hold all five cards if you have a complete Royal Flush, Straight Flush, Four of a Kind, or Full House. These are the highest paying hands, so you should always keep them.
Dealt:
A♠ K♠ Q♠ J♠ T♠
Hold:
A♠ K♠ Q♠ J♠ T♠
Dealt:
7♥ 8♥ 9♥ T♥ J♥
Hold:
7♥ 8♥ 9♥ T♥ J♥
Dealt:
K♠ K♥ K♦ K♣ 2♠
Hold:
K♠ K♥ K♦ K♣ 2♠
Dealt:
A♠ A♥ A♦ K♣ K♠
Hold:
A♠ A♥ A♦ K♣ K♠
2 Three of a Kind Hold the three cards of the same rank and discard the other two. Drawing two cards gives you a good chance to improve to a Full House or Four of a Kind.
Dealt:
9♠ 9♥ 9♦ 3♣ 6♦
Hold:
9♠ 9♥ 9♦ 3♣ 6♦
3 Two Pairs or Four to a Royal Flush Hold all four cards if you have two pairs (discard the fifth card) or four cards of the same suit in sequence that could become a Royal Flush (Ten, Jack, Queen, King, Ace). Prioritize the higher payout of a potential Royal Flush.
Dealt:
5♠ 5♥ 8♣ 8♦ K♥
Hold:
5♠ 5♥ 8♣ 8♦ K♥
Dealt:
T♠ J♠ Q♠ K♠ 2♥
Hold:
T♠ J♠ Q♠ K♠ 2♥
4 Pat Flush or Pat Straight Hold all five cards if you have a complete Flush (five cards of the same suit) or a complete Straight (five cards in rank sequence, but not of the same suit).
Dealt:
A♦ T♦ 7♦ 4♦ 2♦
Hold:
A♦ T♦ 7♦ 4♦ 2♦
Dealt:
9♠ T♥ J♦ Q♣ K♥
Hold:
9♠ T♥ J♦ Q♣ K♥
5 Four to a Straight Flush Hold four cards of the same suit that are in rank sequence, needing one more card (either at the beginning or end of the sequence) to complete a Straight Flush.
Dealt:
6♥ 7♥ 8♥ 9♥ 2♠
Hold:
6♥ 7♥ 8♥ 9♥ 2♠
Dealt:
T♣ J♣ Q♣ K♣ A♦
Hold:
T♣ J♣ Q♣ K♣ A♦
6 High Pair Hold a pair of Jacks, Queens, Kings, or Aces. These pairs guarantee a payout in Jacks or Better video poker.
Dealt:
J♠ J♥ 3♦ 7♣ 9♠
Hold:
J♠ J♥ 3♦ 7♣ 9♠
Dealt:
A♦ A♣ 2♠ 5♥ 8♦
Hold:
A♦ A♣ 2♠ 5♥ 8♦
7 Four to a Flush with A, T, one high card (K, Q, or J), and one low card (2-9) of the same suit. Hold these if the fifth card (to be discarded) is a K, Q, J, or T of a different suit. Hold four cards of the same suit if the hand includes an Ace, a Ten, one high card (King, Queen, or Jack), and one low card (2-9), and the fifth card is a King, Queen, Jack, or Ten of a different suit. This specific four-flush ranks higher than other combinations.
Dealt:
A♠ T♠ J♠ 2♠ K♥
Hold:
A♠ T♠ J♠ 2♠ K♥
Dealt:
A♦ T♦ Q♦ 9♦ Q♣
Hold:
A♦ T♦ Q♦ 9♦ Q♣
8 Three to a Royal Flush Hold three cards of the same suit in sequence that could become a Royal Flush by drawing two specific cards (e.g., Jack, Queen, King of hearts – need Ten and Ace of hearts).
Dealt:
J♠ Q♠ K♠ 3♦ 7♥
Hold:
J♠ Q♠ K♠ 3♦ 7♥
Dealt:
T♥ J♥ Q♥ 2♣ 8♦
Hold:
T♥ J♥ Q♥ 2♣ 8♦
9 Four to a Flush Hold four cards of the same suit. Drawing one card gives you a chance to complete a Flush.
Dealt:
2♥ 5♥ 9♥ J♥ 4♠
Hold:
2♥ 5♥ 9♥ J♥ 4♠
Dealt:
3♣ 6♣ T♣ K♣ A♦
Hold:
3♣ 6♣ T♣ K♣ A♦
10 Four to a Straight (K, Q, J, T) Hold four cards in rank sequence King, Queen, Jack, and Ten, regardless of suit. Drawing one card can complete a Straight.
Dealt:
K♠ Q♥ J♦ T♣ 2♥
Hold:
K♠ Q♥ J♦ T♣ 2♥
Dealt:
K♣ Q♠ J♥ T♦ 5♣
Hold:
K♣ Q♠ J♥ T♦ 5♣
11 Low Pair Hold a pair of cards with ranks lower than Jacks (2 through 10). While these do not guarantee a payout, they offer a chance to improve to a higher paying hand.
Dealt:
7♠ 7♥ 3♦ J♣ 9♠
Hold:
7♠ 7♥ 3♦ J♣ 9♠
Dealt:
2♦ 2♣ A♠ 5♥ 8♦
Hold:
2♦ 2♣ A♠ 5♥ 8♦
12 Four to an Outside Straight (5, 4, 3, 2 up to Q, J, T, 9) Hold four cards in rank sequence with the lowest being 2 and the highest being Queen (e.g., 5-4-3-2, 6-5-4-3, …, Q-J-T-9), regardless of suit. Drawing one card can complete a Straight.
Dealt:
Q♠ J♥ T♦ 9♣ 2♥
Hold:
Q♠ J♥ T♦ 9♣ 2♥
Dealt:
5♣ 4♠ 3♥ 2♦ K♣
Hold:
5♣ 4♠ 3♥ 2♦ K♣
13 Three to a Straight Flush (s + h ≥ 3) Hold three cards of the same suit. Here, ‘s’ is the number of possible 5-card straights that include the ranks of these three suited cards (disregarding suits), and ‘h’ is the number of high cards (Ace, King, Queen, Jack) among these three suited cards. Hold these three cards if the sum of ‘s’ and ‘h’ is 3 or more.
Dealt:
4♥ 5♥ 6♥ A♠ K♦
Hold:
4♥ 5♥ 6♥ A♠ K♦
Explanation: Three hearts (4, 5, 6). Possible 5-card straights including these ranks: 2-3-4-5-6, 3-4-5-6-7, 4-5-6-7-8 (s=3). High cards: None (h=0). s + h = 3 + 0 = 3.
Dealt:
J♦ 9♦ T♦ 2♠ 3♥
Hold:
J♦ 9♦ T♦ 2♠ 3♥
Explanation: Three diamonds (9, T, J). Possible 5-card straights including these ranks: 9-T-J-Q-K, 8-9-T-J-Q, 7-8-9-T-J (s=3). High cards among these three: J (h=1). s + h = 3 + 1 = 4.
Dealt:
8♠ 9♠ J♠ 2♦ 3♥
Hold:
8♠ 9♠ J♠ 2♦ 3♥
Explanation: Three spades (8, 9, J). Possible 5-card straights including these ranks: 7-8-9-T-J, 8-9-T-J-Q (s=2). High cards among these three: J (h=1). s + h = 2 + 1 = 3.
14 Four to a Straight (AKQJ) if QJ flush penalty or 9 straight penalty Hold four cards to a Straight (Ace, King, Queen, Jack) if the hand also contains a Queen and a Jack of the same suit, along with at least one other card of that suit, OR if the hand contains a 9 of any suit, and the hand does not contain three cards to a Royal Flush of the same suit.
Dealt:
A♦ K♠ Q♦ J♦ 2♦
Hold:
A♦ K♠ Q♦ J♦ 2♦
Explanation: The hand contains an Ace, King, Queen, and Jack. It also has a Queen and a Jack of the same suit (diamonds), and there is another diamond (2♦). This triggers the Queen-Jack flush penalty, so we hold AKQJ. This hand does not contain three cards of the same suit that could lead to a Royal Flush.
Dealt:
A♠ K♥ Q♦ J♣ 9♦
Hold:
A♠ K♥ Q♦ J♣ 9♦
Explanation: The hand contains an Ace, King, Queen, and Jack. It also contains a 9. This triggers the 9 straight penalty, so we hold AKQJ. This hand does not contain three cards of the same suit that could lead to a Royal Flush.
15 Two to a Royal Flush (Q, J of the same suit) Hold a Queen and a Jack of the same suit, hoping to draw a Ten, King, and Ace of that suit to complete a Royal Flush.
Dealt:
Q♠ J♠ 3♦ 7♣ 9♥
Hold:
Q♠ J♠ 3♦ 7♣ 9♥
16 Four to a Straight (A, K, Q, J) Hold four cards in rank sequence Ace, King, Queen, and Jack, regardless of suit. Drawing one card can complete a Straight.
Dealt:
A♠ K♥ Q♦ J♣ 2♥
Hold:
A♠ K♥ Q♦ J♣ 2♥
17 Two to a Royal Flush (AH or KH) Hold an Ace with a Ten, Jack, Queen, or King of the same suit (Ace-High), OR hold a King with a Ten, Jack, or Queen of the same suit (King-High), toward a Royal Flush.
Dealt:
A♥ T♥ 3♦ 7♣ 9♠
Hold:
A♥ T♥ 3♦ 7♣ 9♠
Dealt:
K♠ Q♠ 4♦ 8♣ 2♥
Hold:
K♠ Q♠ 4♦ 8♣ 2♥
18 Three to a Straight Flush (s + h = 2, no sp) Hold three cards of the same suit if the sum of ‘s’ (number of possible 5-card straights including these 3 ranks) and ‘h’ (number of high cards among these 3) is exactly 2, and discarding the other two cards does not create a straight penalty. A straight penalty occurs if a discarded card is one rank away from any of the held cards, and those four ranks could form part of a straight.
Dealt:
2♥ 3♥ 5♥ K♠ Q♣
Hold:
2♥ 3♥ 5♥ K♠ Q♣
Explanation: Three hearts (2, 3, 5). Possible 5-card straights including these ranks: A-2-3-4-5, 2-3-4-5-6 (s=2). High cards: None (h=0). s + h = 2. The discarded King and Queen are not adjacent in rank to 2, 3, or 5, so no straight penalty.
Dealt:
A♦ 2♦ 4♦ 7♠ 8♣
Hold:
A♦ 2♦ 4♦ 7♠ 8♣
Explanation: Three diamonds (A, 2, 4). Possible 5-card straights including these ranks: A-2-3-4-5 (s=1, Ace as low). High cards: A (h=1). s + h = 2. The discarded 7 and 8 are not adjacent in rank to Ace, 2, or 4, so no straight penalty.
19 Four to a Straight (A, H, H, T or K, Q, J, 9) Hold four cards that could form a straight in the following combinations: Ace with two other high cards (King, Queen, or Jack) and a Ten (e.g., A-K-Q-T, A-K-J-T, A-Q-J-T), or King, Queen, Jack, and a 9.
Dealt:
A♠ K♥ Q♦ T♣ 2♥
Hold:
A♠ K♥ Q♦ T♣ 2♥
Dealt:
K♣ Q♠ J♥ 9♦ 5♣
Hold:
K♣ Q♠ J♥ 9♦ 5♣
20 Three to a Straight Flush (s + h = 2) Hold three cards of the same suit if the sum of ‘s’ (number of possible 5-card straights including these 3 ranks) and ‘h’ (number of high cards among these 3) is exactly 2, and discarding the other two cards creates a straight penalty. A straight penalty occurs if a discarded card is one rank away from any of the held cards, and those four ranks could form part of a straight. This hand would not fall under Rule 18 because of the straight penalty.
Dealt:
A♠ 2♠ 3♠ 4♦ J♥
Hold:
A♠ 2♠ 3♠ 4♦ J♥
Explanation: Three spades (A, 2, 3). Possible 5-card straight including these ranks: A-2-3-4-5 (s=1, Ace low). High cards: A (h=1). s + h = 2. The discarded 4♦ is adjacent in rank to the held 3♠, and the ranks A, 2, 3, 4, 5 can form a straight. This incurs a straight penalty, so we follow Rule 20. This hand would not fall under Rule 18 because of this straight penalty.
21 Three to a Straight (K, Q, J) Hold three cards in rank sequence King, Queen, and Jack, regardless of suit. Drawing two cards gives you a chance to complete a Straight.
Dealt:
K♠ Q♥ J♦ 2♣ 3♥
Hold:
K♠ Q♥ J♦ 2♣ 3♥
Dealt:
K♣ Q♠ J♥ 4♦ 8♣
Hold:
K♣ Q♠ J♥ 4♦ 8♣
22 Two to a Straight (Q, J) Hold a Queen and a Jack of any suit, hoping to draw a Ten and a King or a Ten and an Ace to complete a Straight.
Dealt:
Q♠ J♥ 3♦ 7♣ 9♠
Hold:
Q♠ J♥ 3♦ 7♣ 9♠
Dealt:
Q♣ J♠ 2♥ 8♦ A♣
Hold:
Q♣ J♠ 2♥ 8♦ A♣
23 Two to a Straight (King, Jack) if Jack-Ten flush penalty Hold a King and a Jack if your hand also contains a Ten, and there is a Jack and a Ten of the same suit with at least one other card of that suit in your hand, AND the King in your hand is not of that same suit. This rule prioritizes a two-card straight (KJ) when there’s a “Jack-Ten flush penalty” and the King isn’t part of that penalized flush draw.
Dealt:
K♦ J♠ T♠ 2♠ 7♥
Hold:
K♦ J♠ T♠ 2♠ 7♥
Explanation: The hand contains a King (K♦), a Jack (J♠), and a Ten (T♠). The Jack and Ten are suited (spades), and there is another spade (2♠), triggering the Jack-Ten flush penalty. The King (K♦) is not a spade. Therefore, hold the King and Jack. This hand does not contain four cards of the same suit.
24 Two to a Royal Flush (J, T of the same suit) Hold a Jack and a Ten of the same suit, hoping to draw a Queen, King, and Ace of that suit to complete a Royal Flush.
Dealt:
J♠ T♠ 3♦ 7♣ 9♥
Hold:
J♠ T♠ 3♦ 7♣ 9♥
25 Two to a Straight (K, High Card) Hold a King and another high card (Queen or Ace) of any suit, hoping to draw the two middle cards to complete a Straight (e.g., King and Queen need a Jack and a Ten).
Dealt:
K♠ Q♥ 3♦ 7♣ 9♠
Hold:
K♠ Q♥ 3♦ 7♣ 9♠
Dealt:
K♣ A♠ 2♥ 8♦ 5♣
Hold:
K♣ A♠ 2♥ 8♦ 5♣
26 Two to a Straight (Ace, Queen) if Queen-Ten flush penalty Hold an Ace and a Queen if your hand also contains a Ten, there is a Queen and a Ten of the same suit in your hand, and there is at least one other card of that same suit (excluding a Queen, Ten, or Ace), AND the Ace and Queen in your hand are not of that same suit. This rule prioritizes a two-card straight (AQ) when there’s a “Queen-Ten flush penalty” and the Ace and Queen are not part of that penalized flush draw.
Dealt:
A♠ Q♦ T♦ 2♦ 3♥
Hold:
A♠ Q♦ T♦ 2♦ 3♥
Explanation: The hand contains an Ace (A♠), a Queen (Q♦), and a Ten (T♦). The Queen and Ten are suited (diamonds). There is another diamond (2♦), triggering the Queen-Ten flush penalty. The Ace of spades and Queen of diamonds are not of the same suit. Therefore, hold the Ace and Queen.
27 Two to a Royal Flush (Q, T of the same suit) Hold a Queen and a Ten of the same suit, hoping to draw a Jack, King, and Ace of that suit to complete a Royal Flush.
Dealt:
Q♥ T♥ 3♦ 7♣ 9♠
Hold:
Q♥ T♥ 3♦ 7♣ 9♠
28 Two to a Straight (AH) Hold Ace and a high card (Queen or Jack) toward a Straight.
Dealt:
A♣ Q♠ 2♥ 8♦ 5♣
Hold:
A♣ Q♠ 2♥ 8♦ 5♣
Dealt:
A♥ J♦ 3♠ 7♣ 9♥
Hold:
A♥ J♦ 3♠ 7♣ 9♥
29 One to a Royal Flush (King) if King-Ten flush penalty and 9 straight penalty Hold a King if your hand also contains a Ten and a Nine, the King and Ten are of the same suit, and there is at least one other card of that same suit in your hand. The presence of the Nine in the hand represents the “9 straight penalty”.
Dealt:
K♠ T♠ 9♦ 2♠ 3♥
Hold:
K♠ T♠ 9♦ 2♠ 3♥
Explanation: The hand contains a King (K♠), a Ten (T♠), and a Nine (9♦). The King and Ten are suited (spades). There is another spade (2♠), triggering the King-Ten flush penalty. The presence of the Nine indicates the 9 straight penalty. Therefore, hold only the King.
30 Two to a Royal Flush (K, T of the same suit) Hold a King and a Ten of the same suit, hoping to draw a Queen, Jack, and Ace of that suit to complete a Royal Flush.
Dealt:
K♠ T♠ 3♦ 7♣ 9♥
Hold:
K♠ T♠ 3♦ 7♣ 9♥
31 One High Card (A, K, Q, or J) Hold one high card (Ace, King, Queen, or Jack) if none of the better options listed above apply. This gives you a chance to draw a pair or better.
Dealt:
Q♠ 2♥ 4♦ 6♣ 8♠
Hold:
Q♠ 2♥ 4♦ 6♣ 8♠
Dealt:
A♥ 3♦ 5♣ 7♠ 9♥
Hold:
A♥ 3♦ 5♣ 7♠ 9♥
32 Three to a Straight Flush (s + h = 1) Hold three cards of the same suit if the sum of ‘s’ (number of possible 5-card straights including these 3 ranks) and ‘h’ (number of high cards among these 3) is exactly 1.
Dealt:
4♥ 5♥ 8♥ 9♠ T♣
Hold:
4♥ 5♥ 8♥ 9♠ T♣
Explanation: Three hearts (4, 5, 8). Possible 5-card straight including these ranks: 4-5-6-7-8 (s=1). High cards: None (h=0). s + h = 1.
33 Discard All If none of the above rules apply to your dealt hand, it is statistically best to discard all five cards and draw new ones.
Dealt:
2♠ 4♦ 6♣ 8♥ 9♦
Hold:
2♠ 4♦ 6♣ 8♥ 9♦

Understanding Payout Tables in Jacks or Better

Different payout tables can affect the optimal strategy and expected return in video poker. For a comprehensive comparison of various payout tables and their respective strategies, check out our Payout Tables Comparison Guide. This will help you choose the best machine and strategy for your gameplay.