A Double Bonus chart that beats the published one
10/7 Double Bonus is the famous over-100% game — if you play it perfectly. The strategy charts everyone memorizes are hand-derived and decades old. We pointed an exact solver at them and found money on the table.
Measured returns (48,000-hand paired studies, fresh-seed holdouts)
The line the books miss: break the pair for the royal draw
Deal: Q♠ J♠ 10♠ J♥ 3♦. Every published chart says keep the jacks. The solver disagrees:
Why the flip: Double Bonus pays two pair just 1-for-1 (Jacks or Better pays 2), which quietly guts a pair’s follow-up value. When one of your royal cards is paired — Q-J-10 or K-Q-J with a matching jack, queen, or king elsewhere — the royal draw pulls ahead. We verified this across all 3,456 possible overlap hands by exact enumeration: the rule holds with two exceptions the chart states (never ace-high royal draws, never when a 4-flush is present). On 9/6 Jacks or Better the same hand correctly keeps the pair — the play is game-specific.
See this hand solved on 10/7 Double Bonus →What else the solver found — and what it refused
The second addition: Q-J-10 unsuited earns a line, and machine search over every line-position move showed it belongs above J-10 suited — an ordering no published chart has. Just as important is what failed: every “intuitive” improvement we tested measured worse. Blanket royal-over-pair promotion loses 0.091% (ace and ten overlaps favor the pair). Ablation shows no line of the 34 is removable. The only clean merge (J/Q/K-10 suited) costs 0.003% and was rejected. Exactness cuts both ways — that’s the point.
Learn it, then drill it
The full 36-line chart with per-line tooltips is on the strategy page — free, like everything here. The methodology mirrors our Jacks or Better simple-strategy study, and the classic dilemmas are answered one by one in exact-answer questions.