On a full pay 9/6 Jacks or Better machine, perfect strategy returns 99.54% of money wagered, a house edge of 0.46%. Reaching that figure depends on two things: playing the five coin maximum, and holding cards in the fixed priority order below. The order matters most on a handful of hands where the intuitive hold is wrong, and those are worked through in the derivation.
Rule assumptions
| Rule | Setting |
|---|---|
| Game | Jacks or Better, single hand, 52 card deck, no wild cards |
| Paytable | 9/6 (full house 9, flush 6, per coin) |
| Royal flush | 800 per coin at five coins (4,000 total) |
| Coins played | Five |
| Draw | One draw from the 47 unseen cards |
Every figure below assumes this exact paytable. A machine paying 8 for a full house and 5 for a flush is a different game with a different chart and a lower return.
The paytable and where the return comes from
The table lists each hand's payout per coin, its frequency under optimal play, and its share of the total return. Frequencies are the standard computed values for this paytable.
| Hand | Pays | Probability | Adds to return |
|---|---|---|---|
| Royal flush | 800 | 0.0025% | 1.98% |
| Straight flush | 50 | 0.011% | 0.55% |
| Four of a kind | 25 | 0.236% | 5.91% |
| Full house | 9 | 1.151% | 10.36% |
| Flush | 6 | 1.101% | 6.61% |
| Straight | 4 | 1.123% | 4.49% |
| Three of a kind | 3 | 7.445% | 22.33% |
| Two pair | 2 | 12.928% | 25.86% |
| Jacks or better | 1 | 21.459% | 21.46% |
The point most players miss is in the last three rows. Two pair, three of a kind and a high pair together supply about 70% of the return. The royal flush, which arrives about once in 40,391 hands, supplies under 2%. Strategy is therefore mostly about small, frequent decisions, not about chasing royals.
The hold order
Find every way to hold the dealt hand that appears in this list, then hold the one that ranks highest. Cards not covered by the chosen line are discarded.
- Royal flush, straight flush, four of a kind
- Four to a royal flush
- Full house, flush, three of a kind, straight
- Four to a straight flush
- Two pair
- High pair (jacks, queens, kings, aces)
- Three to a royal flush
- Four to a flush
- Unsuited 10, J, Q, K
- Low pair (twos to tens)
- Four to an outside straight
- Suited Q J
- Suited K Q or K J
- Suited A K, A Q or A J
- Unsuited J Q K
- Unsuited J Q
- Suited 10 J
- Two unsuited high cards (if three, keep the lowest two)
- Suited 10 Q
- One high card
- Discard everything
This is a simplified list. The full computer strategy adds a few rare lines for three to a straight flush and inside straights with high cards. Leaving them out costs a small amount of return against the full strategy; the hands they cover are rare.
Derivation
Every line in the order comes from one comparison: the expected value of each possible hold, in coins returned per coin bet. The hold with the higher value ranks higher.
Four to a royal over a pat flush
Hold A K Q J of hearts and throw a dealt 4 of hearts, giving up a flush already worth 6. Of the 47 unseen cards, 1 completes the royal for 800, 7 more hearts make a flush for 6, 3 other tens make a straight for 4, and 12 cards pair a high card for 1. That totals 866 coins across 47 equally likely draws, an expected value of 18.43. The pat flush is worth exactly 6. Breaking it is correct by more than 12 coins per coin bet.
High pair over four to a flush
A pair of jacks or better is worth about 1.54. Four to a flush with no high cards is worth 9 flush cards out of 47, times 6, or 1.15. The pair wins clearly, and the margin is why line 6 sits two places above line 8.
Four to a flush over a low pair
A low pair is worth about 0.82. The same four flush cards at 1.15 beat it, which is why line 8 sits above line 10. This is the most common misplay at the machine: players see a pair and keep it.
Unsuited 10 J Q K over a low pair
Four to an open ended straight usually ranks below a low pair, as the next comparison shows. This hand is the exception. Holding 10 J Q K leaves 8 cards, the four nines and four aces, that complete a straight for 4. Another 9 cards pair the jack, queen or king for 1. That is 41 coins over 47 draws, about 0.87, just above the low pair at 0.82. The three high cards are what tip it.
Low pair over four to an outside straight
An open ended straight draw has 8 outs out of 47, paying 4, for about 0.68 with no high cards. The low pair at 0.82 is higher, so the pair is kept.
No kickers
Holding an ace with a pair of jacks never improves the value. The kicker takes up a slot that a fresh card could fill, reducing the chances of trips or a full house.
Why five coins
At one to four coins, the royal pays 250 per coin rather than 800. Its share of the return falls from about 1.98% to about 0.62%, and the machine's total return drops by more than one percentage point even after the strategy adjusts. On this paytable, a smaller bet is better played as five coins on a lower denomination machine than as one coin on a higher one.
Paytable sensitivity
Each unit cut from the full house or flush payout costs about 1.1 percentage points of return. Under optimal play for each version, 9/6 returns 99.54%, 8/5 returns 97.30%, and 7/5 returns 96.15%. That gap is larger than any strategy error on this list.
What strategy changes, and what it does not
Correct holds move the result from whatever a player's instinct produces up to 99.54%. They do not change the card distribution, and they do not remove the edge. Under perfect play on a full pay 9/6 machine, the house retains 0.46% of every coin wagered. Over 1,000 hands at five 20 cent coins, that is an expected cost of 4.60 euro on 1,000 euro wagered, and the actual result will swing well above and below that figure in either direction.
Responsible gambling
Video poker at MGA licensed operators is restricted to players aged 18 and over. Video poker hands take a few seconds each, so a game with a small edge can still cost real money through volume. Set a deposit limit before playing. The Responsible Gaming Foundation's national helpline is 1777, and Appoġġ Supportline is 179.