9/6 Double Double Bonus strategy: the 39-line chart

The kicker is the whole game

Jacks or Better pays one price for four of a kind. Double Bonus pays three, split by rank. Double Double Bonus pays five — and the top two depend on the card you didn’t improve. Four aces alone pay 160 per coin; four aces with a 2, 3 or 4 sitting next to them pay 400, which is 2,000 coins off a five-coin bet. Four 2s, 3s or 4s pay 80, or 160 with an ace, 2, 3 or 4 alongside.

That one row is the reason players choose DDB over the flatter games, and the reason is arithmetic rather than folklore: under optimal play the 2,000-coin hand arrives more than twice as often as a royal flush. These frequencies are exact — every deal of the 52-card deck enumerated, with the best hold played each time:

You pay for those jackpots at the bottom of the table. Two pair returns your bet instead of doubling it — 1 per coin, exactly as in 10/7 Double Bonus and half of what 9/6 Jacks or Better pays. Nearly every DDB deviation from the Jacks or Better chart follows from those two edits: aces are worth far more than any other card, and pairs are worth less than they look.

9/6 or 10/6: read the glass before you sit

DDB machines are named after the same two rows as Jacks or Better — the full house and the flush, priced for one coin. The kicker rows never change between them. Only the full-house row moves, and it moves the whole game:

Both returns come from enumerating all 2,598,960 deals of a 52-card deck with the best hold played every time — not a simulation. One coin on the full-house row is worth 1.09 points of return: 10/6 crosses 100% and 9/6 does not. 10/6 is rare, and the trainer ships both. The chart below is the 9/6 order, but it transfers: dealt 40,000 hands on the 10/6 table, it gave up 0.0031% of coin-in against the solver, so a 10/6 machine played from this chart is still over 100%.

Hand 1 — four aces, and you throw a card away

Twelve of the 47 unseen cards are a 2, a 3 or a 4, and each of them turns 160 into 400. The other 35 leave the quad exactly as it was. The draw cannot cost you anything, so it is free money — 12/47 × 400 + 35/47 × 160 = 221.2766. This is chart line 3, “Four of a kind (draw for the kicker)” — and standing pat instead throws away 61.2766 coins for every coin bet, which is 306 coins at max bet. The same line applies to four 2s, 3s or 4s, where an ace-through-4 kicker doubles 80 into 160.

More on the play: four aces and the kicker draw.

Hand 2 — three aces and a 2, and you throw the kicker away

The kicker only pays once the fourth ace actually arrives, and two draws find that ace far more often than one does. So you discard the 2 — even though holding it would be worth 11.8298, nearly double the 6.7234 of holding the dead 8. The 2 is genuinely valuable; the extra draw is worth more. Chart line 6 is simply “Three aces,” sitting above the full house at line 7 for the same reason. The rule to memorize: hold the kicker only when the quad is already made.

More on the play: three aces with a kicker.

Hand 3 — you break two pair to keep the aces

Two pair pays 1 and a full house pays 9, so the eights add very little. Drawing three fresh cards keeps the whole ace ladder alive instead: trip aces, quad aces at 160, and quad aces with a 2, 3 or 4 in the last slot at 400. “Pair of aces” is line 12 of the chart and “Two pair” is line 13, and that one-line inversion is what makes DDB feel wrong to everyone arriving from Jacks or Better. The same five cards, solved on each of our three 52-card games:

On 10/7 Double Bonus the margin is 0.0025 of a coin — a genuine coin flip. On 9/6 Jacks or Better two pair wins by more than a full coin. Of the three, only DDB breaks two pair, and only for aces — with any other two pair you keep both. Note also that the aces are worth more alone on DDB (1.9159) than on Double Bonus (1.7635), even though Double Bonus pays more for the full house, the flush and the straight. The kicker is the whole difference.

More on the play: aces and eights on DDB.

One more reversal: low pairs get demoted

Two pair paying 1 instead of 2 also drains the follow-up value of every low pair, which pushes the four-card straight draws above them. Same five cards, two games:

The straight draw is worth exactly the same 0.8085 in both games — straights pay 4 either way. It is the pair that collapses, from 0.8237 to 0.7332. On the chart below, “4 to an outside straight with a high card” is line 20 and “Low pair” is line 21; the Jacks or Better chart has them the other way round, which is why that question has a different answer on each machine. Strip the high card out and the straight draw falls back below the pair, to line 22 — the reversal only applies to draws carrying a jack or better. Play the chart for the game in front of you, never the one you learned first.

The chart — all 39 lines

Read your dealt hand down the list and play the first line you can make. Every line names exactly which cards to hold, so there is nothing to interpret.

“High card” means a jack, queen, king or ace. “Outside straight” means four in a row that can complete at either end; “inside” means it can only complete one way, and A-K-Q-J counts as inside. The three straight-flush types split by how many high cards and how many gaps they contain. You never have to classify a hand alone: the trainer names the line you played and the line you should have played, by number, after every hand it grades.

Where this order comes from

The list is the published optimal exceptionless order for 9/6 DDB, re-encoded line by line and then checked against our own solver, with one change: the lower three-card royals (10-J-K, 10-Q-K and the ace-high triples) rank above “4 to a flush” here, where the printed charts put the flush draw first. We measured both orders on the hands where they actually disagree, using exact EVs from the same engine that produced every number on this page, and royal-first lost less. The full method — how the engine is built and how a chart order is scored — is in the solver write-up and the methodology page.

An exceptionless chart is not perfect play: perfect play needs penalty-card exceptions nobody memorizes at a machine. 98.9808% is the ceiling — what the solver returns when the best hold is played every single time. We measured the distance to it by dealing 40,000 hands and playing each one twice, once by the chart and once by the solver:

The chart chose a different hold than the solver on 138 of the 40,000 deals (0.34%), and on every single deal the solver’s best hold was somewhere on the list — the chart never has to reach for a play it doesn’t name. Its cost, about 0.003% of coin-in, is roughly three cents per $1,000 played, against the 1.09 points you give up by sitting at a 9/6 machine when a 10/6 is on the same floor. Choose the machine first; the chart is the cheap part. (Both mean EVs above are from a 40,000-deal sample, not an exhaustive enumeration — unlike the game’s 98.9808% ceiling, which is exact. The sample is seeded, so the run reproduces exactly: npx tsx scripts/list-gap.ts 40000 ddb-9-6 in the repository prints these two numbers and the 138 deviating hands.)

Practise it

The trainer deals DDB hands and prices every mistake in coins, naming the line you played and the line you should have. The analyzer solves any hand you type in and ranks all 32 holds, on either DDB paytable. All four charts — DDB, Jacks or Better, Double Bonus and 20/7/5 Joker Wild — live on the strategy page. If you are new to reading a machine’s glass, start with the paytable guide: choosing the machine is worth more than the last decimal of any chart. Training and math only; no real-money gambling, 18+.