What a Simplified Video Poker Strategy Actually Costs
Nobody plays perfectly. People play off a card — a short list of hands in order, hold the first one that matches. Every one of those cards is a deliberate trade: fewer rules to remember, in exchange for some return. This page measures the exchange rate. Not by simulation: by playing every published card through all 2,598,960 possible deals and pricing every draw exactly.
The answer, on a full-pay 9/6 machine
| Strategy | Rows | Exact return | Gap | Cost/hour, quarters | Publisher claims |
|---|---|---|---|---|---|
| Perfect play | — | 99.5439% | — | — | 99.54% |
| Wizard of Odds optimal strategy chart | 36 | 99.5429% | 0.0010 pp | $0.01 | 99.54% |
| Wizard of Odds intermediate strategy | 25 | 99.5424% | 0.0015 pp | $0.01 | 99.52% |
| American Casino Guide simple strategy table | 36 | 99.5376% | 0.0063 pp | $0.05 | — |
| Wizard of Odds intermediate strategy (2005 edition) | 24 | 99.5372% | 0.0067 pp | $0.05 | 99.52% |
| Wizard of Odds simple strategy | 16 | 99.4590% | 0.0849 pp | $0.64 | 99.46% |
Cost per hour is the gap multiplied by a $1.25 bet — five quarters, which is what you must bet to be paid 800 for a royal — at 600 hands an hour. On dollars it is four times that. The whole spread between the best and the worst card on this page is 0.0839 percentage points. Walking past a 9/6 machine and sitting at an 8/5 one costs 2.2455 points — 27 times as much. Which machine you choose matters far more than which card you carry.
Four rules are 81% of what the simple strategy costs
This is the part worth memorising. The simple chart misplays 58,944 of the 2,598,960 deals — 2.27% of hands, about one in 44 — but those mistakes are nothing like equal. They fall into 12 kinds, and the four below are 81% of the money.
| The card says hold | Perfect play holds | Deals | Cost | Share of the gap |
|---|---|---|---|---|
| 2 unsuited high cards | 4 to an inside straight | 11,976 | 0.02495 pp | 29.4% |
| 3 to a straight flush | 1 high card | 12,432 | 0.02025 pp | 23.9% |
| 2 suited high cards | 3 to a straight flush | 6,456 | 0.01741 pp | 20.5% |
| 2 unsuited high cards | 3 unsuited high cards | 8,040 | 0.00653 pp | 7.7% |
- 2 unsuited high cards over 4 to an inside straight. Dealt
9♠ J♠ Q♣ K♦ A♥, the card holdsJ♠ Q♣, worth 0.4788 per coin. HoldingJ♠ Q♣ K♦ A♥is worth 0.5957. - 3 to a straight flush over 1 high card. Dealt
2♦ 3♦ 4♣ 6♦ J♥, the card holds2♦ 3♦ 6♦, worth 0.4255 per coin. HoldingJ♥is worth 0.4899. - 2 suited high cards over 3 to a straight flush. Dealt
2♣ 9♦ J♦ Q♦ A♥, the card holdsJ♦ Q♦, worth 0.5845 per coin. Holding9♦ J♦ Q♦is worth 0.7364. - 2 unsuited high cards over 3 unsuited high cards. Dealt
2♠ 8♠ J♣ Q♦ K♥, the card holdsJ♣ Q♦, worth 0.4913 per coin. HoldingJ♣ Q♦ K♥is worth 0.5153.
Learn those four and you keep most of the difference without learning a thirty-six row chart. The remaining 8 kinds of mistake are together worth 0.0157 percentage points, or $0.12 an hour.
On the machine you are actually sitting at
Every card here was written for 9/6. Short-pay machines change the return but barely change the right play, so the gap a card costs is nearly the same everywhere — what changes, and changes a great deal, is the number it is a gap from.
| Machine | Perfect play | Optimal chart | Intermediate | American Casino Guide | Intermediate (2005) | Simple |
|---|---|---|---|---|---|---|
| 9/6 | 99.5439% | 99.5429% | 99.5424% | 99.5376% | 99.5372% | 99.4590% |
| 9/5 | 98.4498% | 98.4457% | 98.4456% | 98.4447% | 98.4381% | 98.3504% |
| 8/6 | 98.3927% | 98.3917% | 98.3912% | 98.3865% | 98.3857% | 98.3073% |
| 8/5 | 97.2984% | 97.2945% | 97.2944% | 97.2936% | 97.2866% | 97.1986% |
| 7/5 | 96.1472% | 96.1433% | 96.1431% | 96.1424% | 96.1351% | 96.0469% |
| 6/5 | 94.9961% | 94.9921% | 94.9918% | 94.9913% | 94.9836% | 94.8951% |
Two things we found that the sources do not say
The Wizard of Odds' optimal chart is not optimal, by exactly its own footnotes. Implemented as a pure list of hand patterns it returns 99.5429%, not 99.5439%. The difference is 0.00099 percentage points and it decomposes into precisely six classes of hand — one for each of the six "rare exceptions" the page footnotes, which depend on what you are throwing away and so cannot be written as a row in a list at all. Those six footnotes are worth about a cent an hour between them.
The intermediate chart's published return belongs to a list it stopped printing in 2007. The page has quoted 99.52% since at least 2005, and its comparison table is byte-identical to the Internet Archive's 2005 capture — but the ranked list beside it grew from 24 rows to 25 in 2007. We implemented both. The 25-row list returns 99.5424% and the 24-row one returns 99.5372%. Neither is 99.52%, and the 2007 edit made the chart better, not worse.
How this is computed
Every hold of every deal is priced over the whole remaining deck, in integer arithmetic, and weighted by how often the deal comes up. No sampling, so no error bar: the returns above are exact rational numbers rounded for display. The full enumeration is 2,598,960 draws per deal, which is 6.8 trillion five-card evaluations done naively; it is restructured into a few million integer additions instead, and the 2,598,960 deals collapse to 134,459 distinct problems once you notice that no payout can tell hearts from spades.
The check that it is right: the same engine reproduces the published return of all thirty paytables we carry — including 99.5439% for 9/6 — and agrees, hand for hand, with the precomputed tables behind our hand analyzer. It also reproduces the Wizard of Odds' own 99.459% for his simple strategy to five decimal places, which is the strongest evidence that our reading of his chart is his.
Bob Dancer and Liam W. Daily's Winner's Guide orderings are the other charts people ask about. They are sold as a book and a strategy card and are not published anywhere we can cite, so they are not here. We would rather leave a gap than print a list under somebody's name that they did not write.