Wizard of Odds intermediate strategy (2005 edition)
The 24-row version the Wizard published until 2007, before 'AKQJ unsuited' was inserted. The return still quoted on the live page was computed for this list. Played through every one of the 2,598,960 possible deals on a full-pay 9/6 machine, this chart returns exactly 99.5372% against 99.5439% for perfect play — a gap of 0.0067 percentage points, or $0.05 an hour at quarters and $0.20 an hour at dollars.
Source
Jacks or Better Intermediate Strategy, captured 2005-07-17, Michael Shackleford, Wizard of Odds (Internet Archive). Transcribed 2026-09-19. The source quotes 99.52% for this chart; exhaustive enumeration of the list as published gives 99.5372%.
- Written in the pre-2007 notation, 'high cards - gaps', which the site later renamed to type 1/2/3. The renaming was not purely cosmetic: the type 2 definition picked up an 'ace low' and a '2-3-4' clause that the arithmetic never had, so this list is implemented with the arithmetic and the current one with the types.
The chart
Read it top down and hold the first line your hand matches. A high card means a jack, queen, king or ace.
| # | Hold |
|---|---|
| 1 | Four of a kind, straight flush, royal flush |
| 2 | 4 to a royal flush |
| 3 | Three of a kind, straight, flush, full house |
| 4 | 4 to a straight flush |
| 5 | Two pair |
| 6 | High pair |
| 7 | 3 to a royal flush |
| 8 | 4 to a flush |
| 9 | Low pair |
| 10 | 4 to an outside straight |
| 11 | 3 to a straight flush (high cards - gaps >= 0) |
| 12 | 2 suited high cards |
| 13 | 4 to an inside straight w/ 3-4 high cards |
| 14 | 3 to a straight flush (high cards - gaps = -1) |
| 15 | J/Q/K unsuited |
| 16 | J/Q unsuited |
| 17 | 10/J suited |
| 18 | J/K, Q/K unsuited |
| 19 | 10/Q suited |
| 20 | J/A, Q/A, K/A unsuited |
| 21 | 10/K suited |
| 22 | One high card |
| 23 | 3 to a straight flush (high cards - gaps = -2) |
| 24 | Discard everything |
Where it differs from perfect play
10,560 deals are played differently from the exact solution — 0.41% of hands, in 9 kinds. They are listed costliest first, with the share of the whole 0.0067-point gap each one carries and the running total. The example is the single worst hand in that class.
| Chart holds | Perfect play holds | Row that fires | Deals | Cost | Share | Running |
|---|---|---|---|---|---|---|
| 2 suited high cards | 4 to an inside straight | 2 suited high cards | 4,860 | 0.00468 pp | 69.5% | 69.5% |
| low pair | 4 to an outside straight | Low pair | 252 | 0.00047 pp | 7.0% | 76.5% |
| 3 to a straight flush | 2 suited high cards | 3 to a straight flush (high cards - gaps >= 0) | 180 | 0.00047 pp | 7.0% | 83.5% |
| 2 to a royal flush | 2 unsuited high cards | 10/Q suited | 1,512 | 0.00036 pp | 5.3% | 88.8% |
| 4 to an inside straight | 4 to an inside straight | 4 to an inside straight w/ 3-4 high cards | 96 | 0.00024 pp | 3.5% | 92.3% |
| 2 to a royal flush | 2 unsuited high cards | 10/J suited | 1,260 | 0.00024 pp | 3.5% | 95.8% |
| 3 to a royal flush | 4 to a flush | 3 to a royal flush | 864 | 0.00017 pp | 2.6% | 98.4% |
| 2 to a royal flush | 1 high card | 10/K suited | 1,440 | 0.00009 pp | 1.3% | 99.7% |
| 4 to an inside straight | 3 to a straight flush | 4 to an inside straight w/ 3-4 high cards | 96 | 0.00002 pp | 0.3% | 100.0% |
The worst hand in each class
| Dealt | Chart holds | Worth | Perfect play holds | Worth |
|---|---|---|---|---|
2♥ J♥ Q♣ K♦ A♥ | J♥ A♥ | 0.5512 | J♥ Q♣ K♦ A♥ | 0.5957 |
T♣ T♠ J♣ Q♦ K♥ | T♣ T♠ | 0.8237 | T♣ J♣ Q♦ K♥ | 0.8723 |
2♦ 3♦ 4♦ J♥ Q♥ | 2♦ 3♦ 4♦ | 0.5338 | J♥ Q♥ | 0.6245 |
2♦ 9♣ T♦ Q♦ A♥ | T♦ Q♦ | 0.4619 | Q♦ A♥ | 0.4743 |
9♠ J♠ Q♣ K♦ A♥ | 9♠ J♠ Q♣ K♦ | 0.5319 | J♠ Q♣ K♦ A♥ | 0.5957 |
2♦ 8♣ T♦ J♦ K♥ | T♦ J♦ | 0.4762 | J♦ K♥ | 0.4862 |
2♥ T♥ J♥ Q♦ A♥ | T♥ J♥ A♥ | 1.2692 | 2♥ T♥ J♥ A♥ | 1.2766 |
2♥ 3♣ 9♦ T♥ K♥ | T♥ K♥ | 0.4582 | K♥ | 0.4598 |
7♣ 9♣ J♣ Q♦ K♥ | 9♣ J♣ Q♦ K♥ | 0.5319 | 7♣ 9♣ J♣ | 0.5375 |
"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
| Machine | This chart | Perfect play | Gap | Cost/hour, quarters |
|---|---|---|---|---|
| 9/6 (800-50-25-9-6-4-3-2-1) | 99.5372% | 99.5439% | 0.0067 pp | $0.05 |
| 9/5 (800-50-25-9-5-4-3-2-1) | 98.4381% | 98.4498% | 0.0117 pp | $0.09 |
| 8/6 (800-50-25-8-6-4-3-2-1) | 98.3857% | 98.3927% | 0.0070 pp | $0.05 |
| 8/5 (800-50-25-8-5-4-3-2-1) | 97.2866% | 97.2984% | 0.0118 pp | $0.09 |
| 7/5 (800-50-25-7-5-4-3-2-1) | 96.1351% | 96.1472% | 0.0121 pp | $0.09 |
| 6/5 (800-50-25-6-5-4-3-2-1) | 94.9836% | 94.9961% | 0.0125 pp | $0.09 |
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.