Wizard of Odds optimal strategy chart

Thirty-six lines, the longest published chart. Everything a pattern matcher can express; the six penalty-card footnotes are the part it cannot. Played through every one of the 2,598,960 possible deals on a full-pay 9/6 machine, this chart returns exactly 99.5429% against 99.5439% for perfect play — a gap of 0.0010 percentage points, or $0.01 an hour at quarters and $0.03 an hour at dollars.

Source

Jacks or Better Optimal Strategy (9/6), Michael Shackleford, Wizard of Odds. Transcribed 2026-09-19. The source quotes 99.54% for this chart; exhaustive enumeration of the list as published gives 99.5429%.

• Footnotes A-F are penalty-card exceptions and are not implemented; they depend on the discards, which a ranked pattern matcher never looks at.
• The chart's 'hands that are never played' -- suited ten and ace, and 4 to an inside straight with fewer than three high cards -- are absent by having no row, not by a special case.

The chart

Read it top down and hold the first line your hand matches. A high card means a jack, queen, king or ace.

Where it differs from perfect play

5,496 deals are played differently from the exact solution — 0.21% of hands, in 6 kinds. They are listed costliest first, with the share of the whole 0.0010-point gap each one carries and the running total. The example is the single worst hand in that class.

The worst hand in each class

"Worth" is the exact expected value of that hold in coins per coin bet, over all the ways the draw can come out of the remaining 47 cards. You can check any of them in the hand analyzer.

On the other standard machines

The chart was written for 9/6 and is applied unchanged to the rest, which is what a player does. Cost per hour assumes 600 hands an hour at five quarters a hand.

Other charts