Video Poker Bankroll Calculator

99.54% is the return on 9/6 Jacks or Better over an infinite number of hands. It tells you almost nothing about an evening. This page answers the question the return figure hides — how far down does it go, and does the bankroll survive — by dealing and playing up to half a million real hands in your browser under exact optimal strategy, and showing you what happened.

Where the variance comes from

On 9/6 Jacks or Better the royal flush pays 800 for one coin and turns up about once in 40,391 hands under optimal play. Multiply those together and the royal alone accounts for 1.98 percentage points of the game's 99.54% return. Take it away and everything else returns 97.56%.

That is the whole story of video poker bankrolls in one line. Until the royal arrives you are playing a game that pays about 98 cents on the dollar, and at six hundred hands an hour the average wait for one is over sixty hours of play. A bankroll sized for a 99.54% game is not sized for the game you are actually sitting at, and the simulation above is the cheapest way to see the difference.

Reading the result

• Return this run — coins out over coins in for these hands only. Expect it to miss the theoretical figure by a lot; that is the finding, not an error.
• Deepest fall from a high — the largest peak-to-trough drop, in credits and in bets. This is the number that decides whether a session is playable, and it is usually far larger than people expect.
• Standard deviation — per hand, and for the run as a whole. It grows with the square root of the number of hands while the expected loss grows linearly, which is why short sessions are dominated by luck and long ones are not.
• Hand frequencies — what the run actually made against the exact optimal-play frequency. The common hands converge quickly; the royal does not converge at all at these sample sizes.

How to check this

We publish as Voitto Virta LLC and there is no expert's name on this page, so nothing here asks you to take our word for it. Everything the tool does rests on numbers you can verify against any other source, and the ones worth checking first are these.

• 9/6 Jacks or Better returns 99.5439% at optimal play, from the payout string 800-50-25-9-6-4-3-2-1. Every published analysis of this machine rounds to 99.54%. If ours did not, the rest of the page would not be worth reading.
• A royal flush arrives once in 40,391 hands under that strategy, and contributes 1.98 percentage points of the machine's whole return.
• The hand frequencies a run produces are printed beside the exact ones, so the simulation is checkable against theory on every run rather than only in principle. The common hands converge within a few thousand hands; the royal does not converge at all.
• Two independent implementations have to agree before this ships. The optimal hold comes from a precomputed solve of all 134,459 distinct hands per paytable; the cost of your own hold is computed a completely different way, by enumerating every one of the 1,533,939 possible draws behind it. Our build runs both over thousands of random hands on several of the 30 paytables and fails if they disagree by more than the precision the tables are stored at. A simulator that disagreed with our own solver would be worse than no simulator.

Practise at home, not at a machine

A strategy card printed on paper is sold in casino gift shops. Consulting a phone at a machine is a different thing. Nevada NRS 465.075 makes it unlawful to use, or possess with intent to use, any electronic device designed or programmed to obtain an advantage at a game in a licensed establishment — and it names, among the things such a device might do, analysing the probability of an event in the game and analysing the strategy for playing it. That is a plain description of this page. Other jurisdictions have their own rules and their own enforcement.

We are not lawyers and this is not legal advice. It is simply what this tool is for: practice at home, so that at the machine you are reading your own memory rather than a screen.

What this is not

It is not advice, and there is nothing to buy. No video poker paytable we publish has a positive expected value on its own — the best of the 30 here returns 100.000% — so the honest summary of every run on this page is that playing longer loses more. We do not link to anywhere you could bet, and there is no account, no deposit and no stored result.

Frequently asked questions

How big a bankroll do I need for video poker?

There is no single answer, which is why this page simulates instead of quoting a number. The honest version is: the bankroll you need depends on how long you intend to play, how much of a chance of going broke you will accept, and above all the variance of the game — and 9/6 Jacks or Better has enormous variance for a 99.54% game because 2.0% of its return arrives once in 40,391 hands. Set your bet and your bankroll above, run a few hundred thousand hands, and watch how often it survives.

Why does a 99.5% game still lose my whole bankroll?

Because the return is an average over an unimaginable number of hands and your session is not. Strip the royal flush out of 9/6 Jacks or Better and the remaining hands return only 97.56% — so until you hit one, you are playing a game that pays about 97.6 cents on the dollar. The royal is what closes the gap, and most bankrolls do not last long enough to see one.

Is this a formula or an actual simulation?

An actual simulation. Every hand is dealt from a shuffled deck, the optimal hold is looked up from a complete solve of the paytable, the discards are replaced from the remaining 47 cards and the result is paid from the paytable. No distribution is being sampled and no normal approximation is used — a normal approximation cannot represent a payout that arrives once in forty thousand hands, which is exactly the thing this page exists to show.

What is risk of ruin?

The chance that your bankroll reaches zero before you stop playing. A single run here either survives or it does not; run it several times, or with a larger number of hands, to get a feel for how often. Ruin is recorded the moment the bankroll can no longer cover the next bet, and the run continues past it so you can see what would have happened.

Why can I set a seed?

So a run is repeatable and can be argued about. With a seed the same settings always produce the same hands, which is what you want when comparing two bets or two paytables; leave it blank and the cards come from your browser’s cryptographic random source instead.

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