The video poker mistake nobody notices costs 52× the one everyone argues about.
This is the one casino game where skill genuinely moves the number. So we solved it, and then measured what specific errors actually cost. The famous hard decision is worth almost nothing.
The short version, in dollars
A quarter machine at five coins is $1.25 a hand, and a steady player puts through about 600 hands an hour — roughly $750 of action. Here is what each thing on this page is worth at that pace.
- $47.55 an hour
- keeping a high card alongside your pair. About $190 across a four-hour session, and almost nobody knows they are doing it.
- $36.75 an hour
- sitting at a “6/5” machine instead of a “9/6” one. Those two numbers are all that differ: what a full house and a flush pay. Same game, same buttons, same correct strategy — different price.
- 92 cents an hour
- never tearing up a made flush to chase a royal — the decision players argue about all night. It is real, it is correct, and it is worth under a dollar.
- the order to learn
- read the glass, drop the kicker, then worry about the flush. Most advice has that exactly backwards.
Words we could not avoid
- a pat hand
- Five cards that already pay something on their own — a straight or better — before you draw anything.
- a kicker
- An extra card kept alongside your pair because it looks useful. It is the expensive habit in this piece.
- a paytable
- The list printed on the machine showing what each hand pays. Two machines can run the same game with different paytables.
- action
- The total amount you bet over a session, counting every hand. A dollar bet 600 times is $600 of action, not $1.
- percentage point
- A flat difference between two percentages. Losing 6.34 percentage points of return means 6.34% more of everything you bet stays with the house.
- paired difference
- Comparing two options on the exact same hands, rather than measuring each separately. Far more precise, because whatever luck they share cancels out.
What this was computed on
Jacks or Better, five coins, single-deck 52-card draw. Discarded cards do not return to the deck, so every draw is enumerated from the remaining 47.
The game
- Five cards dealt, hold any subset, draw to replace the rest
- 32 possible holds per deal — all of them priced, every time
- Draws enumerated exhaustively from the 47 unseen cards, never sampled
Reading the glass
- A paytable is named “full house / flush” — 9/6 pays 9 and 6, 8/5 pays 8 and 5
- Royal 800, straight flush 50, quads 25, straight 4, trips 3, two pair 2, jacks+ 1 — the same on all of them
- Five priced here: 9/6, 8/6, 8/5, 7/5 and 6/5 Jacks or Better
- The machines are otherwise indistinguishable, which is the entire point
What is exact
- The hand evaluator, checked on 12 known-answer hands and against a second independent implementation on 60,000 random hands
- Every one of the 2,598,960 possible deals, for the frequency questions
- All 32 hold values for each deal examined
What is sampled
- Which deals get examined — 2,000 of them
- A full 32-hold solve of all 2,598,960 deals is 148 hours on this machine
- So absolute returns are estimated; every comparison is paired on identical deals
We do not publish an absolute return figure, because we cannot measure one. Sampled across 2,000 deals it carries a standard error worse than ±2.5 percentage points, and the distribution is right-skewed so even that understates it. Published figures put 9/6 Jacks or Better at 99.54%; we neither confirm nor dispute that here.
The paytable gaps below are not five independent confirmations. All of them are measured against the same 9/6 baseline on the same deals, so a sample slightly rich in full houses inflates every one of them together. Treat it as one correlated agreement.
Everything here is Jacks or Better. Deuces Wild and Double Bonus have different optimal play and different error costs, and none of these figures transfer.
Finding one
This is the one game where the skill is real and the answer is exact.#
- possible deals
- 2,598,960
- holds per deal
- 32
- decisions in the game
- 83,166,720
- guesswork required
- none
Roulette has no skill to exercise: every bet carries the same edge and no decision changes it. Baccarat has no decisions at all. Video poker is the opposite — you are handed five cards and choose which to keep, there are 32 ways to choose, and exactly one of them is correct. That correctness is computable rather than arguable.
So we built the solver. For any deal it enumerates every possible draw from the 47 remaining cards and prices all 32 holds exactly. The evaluator was checked against twelve hands whose category is not in dispute — including a wheel straight, a pair of tens that must not pay, and a pair of jacks that must — then rewritten for speed and verified against the original on 60,000 random hands. Identical, every hand.
It also reproduces the textbook advanced play, which is the check that matters most. Dealt a made flush that happens to contain four cards to a royal, standing pat is worth 6.00 coins and breaking the flush is worth 19.55. The solver finds that without being told.
Finding two
The paytable on the glass matters more than anything you will do at it.#
- 9/6 to 8/6
- -1.222% ± 0.097
- 9/6 to 8/5
- -2.456% ± 0.187
- 9/6 to 6/5
- -4.900% ± 0.327
- cross-check
- matches hand frequencies
Two machines can be the same game with the same optimal strategy and differ only in what a full house and a flush pay. That difference is worth more than any decision you make while sitting there.
The gaps above are measured as paired differences: the same deal is priced under both paytables, so what changes is only the payout, and the royal flush cancels out of the subtraction entirely. They cross-check independently against hand frequencies — the 9/6 to 8/6 change touches only the full house, by one coin, so the gap should be roughly how often a full house occurs. It is.
This is also where sampling earns its keep. The same 2,000 deals give these gaps to a tenth of a percentage point and give the absolute return to worse than two and a half percentage points — useless. A difference measured on identical inputs is a fundamentally cheaper thing to measure than either side of it.
Finding three
The decision players agonise over is worth 0.12 points.#
- break a pat hand for a royal draw
- worth +13.55 coins
- how often it arises
- 1 in 11,013 deals
- cost of never doing it
- 0.123 points of return
- dealt a pat hand at all
- 0.7586% of deals
Tearing up a made flush to chase a royal is the play that gets argued about, and it is unambiguously correct when it appears: 6.00 coins for standing pat against 19.55 for the draw. On a made straight containing four to a royal it is even starker — 4.00 against 19.60.
It just almost never appears. We enumerated all 2,598,960 deals: exactly 236 of them are both pat and holding four to a royal. One in eleven thousand. Refusing the play every single time it comes up costs about 0.123 percentage points of return.
Our first pass reported this cost as zero and we nearly published that. In 3,500 sampled deals the situation never once arose, and a zero can mean either “this is never right” or “we never saw it” — two completely different findings that a frequency count cannot distinguish. The fix was to construct the hand deliberately and then count its frequency across every possible deal, rather than infer anything from an absence.
Finding four
The habit nobody questions costs 6.34 points.#
- hold a kicker with your pair
- -6.34% of return
- how often it applies
- 41.9% of deals
- cost each time
- 15.1% of a bet
- versus the famous mistake
- 52x worse
Dealt a pair of jacks and a king, the instinct is to keep the king too — it is a high card, it feels like a live one. Holding just the pair is worth 1.53654 coins. Holding the pair plus the king is worth 1.41628. The kicker costs 12% of a bet, and it costs it because you have thrown away a card you could have drawn.
That situation is not rare. It applies on 41.9% of all deals, at an average cost of 15.1% of a bet, which comes to 6.34 percentage points of return. That single habit takes a 99.5% game down to roughly 93% — worse than most slot machines, on the game with the best odds in the building.
It is 52 times more expensive than the pat-hand decision people actually debate. The reason is entirely structural: one situation is rare and dramatic, the other is constant and invisible. Nobody feels a twelve percent leak. Everybody remembers tearing up a flush.
Finding five
Cost per hand is not enough. You need frequency and severity together.#
- pair plus a kicker
- 42% of hands, -15% each
- pair over any draw
- 0.9% of hands, -58% each
- break a pat hand
- 0.009%, -1355% each
- stand pat always
- 99% of hands, -67% each
Every error above has a per-hand cost, and per-hand cost alone is misleading in both directions. Taking the pair over any draw looks trivial at 0.49 points — but when it fires it costs 58% of a bet. It is a rare disaster wearing the numbers of a small leak. The kicker habit is the reverse: modest each time, ruinous in aggregate.
Three genuinely different shapes, needing three different responses. A frequent small leak is fixed by drilling until it is automatic. A rare catastrophe is fixed by learning to recognise one specific board. A vanishingly rare huge play is worth knowing and worth almost nothing.
Which is the practical answer to “what should I learn first”, and it is not what the strategy guides lead with. Learn to drop the kicker. It is worth fifty times the play you will spend an evening arguing about.
What the paytable costs you, per hand
A machine is named for two numbers: what a full house pays, then what a flush pays. Everything else — royal 800, straight flush 50, four of a kind 25, straight 4, three of a kind 3, two pair 2, jacks or better 1 — is identical across all five. Those two lines are the dial because a full house and a flush each come up about 1% of hands, often enough to matter and quietly enough that nobody notices. Figures below are paired differences from 9/6 under optimal play, on identical deals.
| 9/6 Jacks or Better — the benchmark | 0.000% |
| 8/6 Jacks or Better | 1.222% |
| 8/5 Jacks or Better | 2.456% |
| 7/5 Jacks or Better | 3.678% |
| 6/5 Jacks or Better | 4.900% |
What to hold
Eleven hands you will actually be dealt, each solved exactly. The bright cards are the ones to keep. Ordered by how often the situation turns up — not by what the mistake costs, because the expensive-looking rows at the bottom are the ones you can safely learn last.
research/video-poker/playbook.py · 9/6 Jacks or Better · every row a full 32-hold enumeration over all C(47,k) draws, at $1.25 a hand
Every session
These come up constantly. Learn these and you have taken most of what is available.
A high pair, and a bigger card beside it
Most people — Keep the ace with the jacks. It is the best card left.
Correct — Hold the two jacks. Throw the ace away.
The most expensive habit in the game, and it applies to four hands in ten.
Three of a kind, and a bigger card beside it
Most people — Hold the ace too. It might pair up.
Correct — Hold the three eights and draw two.
The same habit as the row above, costing nearly four times as much.
Two pair, one of them small
Most people — Play the jacks with an ace rather than a pair of fours.
Correct — Hold both pairs.
Two pair already pays. Trading it for one pair throws a made hand away.
Nothing at all, with one high card
Most people — Junk. Throw all five and start again.
Correct — Hold the jack.
The junk hand is not a free swing. One high card is worth keeping.
Most sessions
A pair in your hand and a draw on the screen. The answer depends on which pair.
A high pair, and four to a flush
Most people — Four to a flush is one card away. Take the draw.
Correct — Hold the kings.
The paying pair beats the pretty draw.
A low pair, and four to a flush
Most people — Never break a pair.
Correct — Hold the four hearts. Break the pair.
Same shape as the row above with the opposite answer — which is the whole rule: the pair has to be a paying one.
A low pair, and four to an open straight
Most people — Two ways to fill the straight. Take it.
Correct — Hold the pair of sixes.
A low pair loses to a flush draw and beats a straight draw. That is the order to remember.
A low pair, and three to a royal
Most people — A pair in the hand beats three cards of a dream.
Correct — Hold the queen, jack and ten. Break the pair.
Three to a royal is worth more than any pair that does not pay.
Rarely — and then it is large
You will wait a long time for these. They are worth almost nothing a year, and everyone argues about them anyway.
A paying pair, and four to a royal
Most people — Keep the kings. That is money already in the hand.
Correct — Break the pair. Hold the four hearts.
The largest single correct play on this page.
A made flush, and four to a royal
Most people — It is a made flush. You do not tear up a made hand.
Correct — Break it. Hold the four royal cards.
The argument players have all night. Correct, and worth 92 cents an hour.
A made straight, and four to a royal
Most people — A straight is a straight. Take the payout.
Correct — Break it. Hold the four hearts.
Same decision as the flush, and easier: a straight pays less to give up.
Read the glass before you sit down. The gap between a 9/6 and a 6/5 machine is 4.9 points — larger than any playing error on this page except standing pat.
Drop the kicker. One habit, 42% of hands, 6.34 points of return. It is the cheapest improvement available in any casino game.
The famous flush-breaking decision is real and correct and worth 0.12 points. Learn it last.
Video poker is the only game in these studies where effort is repaid. Roulette gives every bet the same edge, so there is nothing to learn. Baccarat offers an edge that needs conditions almost no table provides. Here the strategy is exactly solvable, the paytable is printed on the machine, and the difference between careless and correct play is several percentage points of return — which is why it is the one game where a trainer is worth building rather than a warning.