Video Poker Variance Calculator
Pick your game, your bet and how many hands you will play. The calculator works out exactly how that session can end: the average result, the typical swing, the chance of finishing ahead or hitting a royal, and the worst and best 1 in 20 sessions.
$1,250.00 bet over 1,000 hands
−$5.70 over the whole session, on averageThe game keeps 0.46% of every dollar bet.
One standard deviation
±$174.62 around the averageThe swing is 31 times the average loss.
65% of 1,000-hand sessions end behind.
At $1.25 a hand, 1,000 hands put $1,250.00 through the game, about 1 hour of online play. The average result is −$5.70, but two sessions in three end between −$102.50 and +$50.00, and one in twenty ends at −$150.00 or worse. The royal accounts for 81% of the game’s variance, and 2.45% of sessions this long have at least one.
Where sessions end
Where sessions of 1,000 hands end, from the worst to the best. Each row is a cut-off: the worst 1 in 20 sessions end at or below their row’s result, the best 1 in 20 at or above theirs.
| Sessions | Result |
|---|---|
| Worst 1 in 100 | −$193.75 |
| Worst 1 in 20 | −$150.00 |
| Worst 1 in 6 | −$102.50 |
| Worst 1 in 4 | −$81.25 |
| The middle session | −$31.25 |
| Best 1 in 4 | +$23.75 |
| Best 1 in 6 | +$50.00 |
| Best 1 in 20 | +$125.00 |
| Best 1 in 100 | +$985.00 |
How is this worked out?
Every hand ends on one of a few payouts, each with its chance when the hand is played its best way (from the full solve of the game). A session is the sum of its hands. The calculator works out that sum exactly: it counts the royals on their own, since they carry so much of the swing (81% of the variance in 9/6 Jacks or Better), and adds up the other hands through their Fourier transform. Nothing is simulated, so the same choices always give the same figures.
The swing is one standard deviation of the session’s result. A royal is rare and large, so sessions are lopsided: the middle session ends below the average, and the best few end far above it. That is why the table gives cut-offs rather than a range around the average.
Every figure assumes the pay table shown and every hand played its best way. Mistakes lower the average and change the swing; progressive jackpots and the double-up are not modelled. Playing several hands at once swings harder: multi-hand video poker. Why a game that returns nearly everything still swings this far: video poker variance.
Why the average says so little about one session
Played perfectly at $1.25 a hand, 9/6 Jacks or Better keeps 0.46% of everything you bet. Over 1,000 hands, about an hour online, that is an average result of −$5.70. Yet 65% of those sessions end behind, the middle one at −$31.25, and the worst 1 in 20 end at −$150.00 or worse. The royal holds the average up: at that bet it pays $1,000, it comes in 2.45% of 1,000-hand sessions, and it accounts for 81% of the game’s variance. It is worth 1.98% of the return: a hand that does not end in a royal returns 97.57% on average.
That gap is what the calculator measures. The average result is what the game keeps over many sessions; the swing is how far a single session strays from it. Over 1,000 hands of 9/6 Jacks or Better the swing is ±$174.62, 31 times the average loss, so one session says almost nothing about whether the game is a good one. Play longer and the average grows with the number of hands, while the swing grows only with its square root: over 100,000 hands the average loss is $570.12 and the swing ±$1,746.19, about three times the loss. Our variance and bankroll guide explains where the swing comes from and how much to bring.
Reading the answer
The dark panel is the average result for the whole session: the amount bet times what the game keeps, for the pay table selected and every hand played its best way. The light panel is the typical swing, one standard deviation of the result. Under them are the chance of ending ahead, the chance of at least one royal, and the cut-offs for the worst and best 1 in 20 sessions. Open “Where sessions end” for the whole spread, from the worst 1 in 100 sessions to the best.
Sessions are lopsided, which is why the calculator gives cut-offs rather than the average plus or minus the swing. No royal comes in 97.55% of 1,000-hand sessions of 9/6 Jacks or Better, and those sessions lose 2.43% of what they bet on average; the 2.45% with a royal end well ahead. So the middle session ends below the average, and the best 1 in 100 end far above it: +$985.00, against −$193.75 for the worst 1 in 100.
Which games swing hardest
The pay table moves the swing far more than it moves the average. Over 1,000 hands at $1.25, 9/6 Jacks or Better swings ±$174.62 and full-pay Deuces Wild ±$200.91. Triple Double Bonus, which pays 800 per credit for four aces with a 2, 3 or 4, swings ±$391.87, more than twice as far as Jacks or Better. Its big four-of-a-kind awards are paid for by the small hands (two pair pays only your bet back), so more of its sessions end behind, 69.14% against 64.87%, and the best 1 in 20 end at +$837.50 or better, against +$125.00.
A return over 100% does not make a short session safe. Full-pay Deuces Wild returns 100.76%, but only 35.84% of 1,000-hand sessions end ahead. The edge needs time: 48.58% of 10,000-hand sessions end ahead, and 66.76% of 100,000-hand sessions.
Fewer credits: a smaller swing and a bigger loss
Betting fewer than five credits shrinks the swing, because the royal then pays 250 per credit instead of 800. For the same $1.25 a hand on 9/6 Jacks or Better, the swing over 1,000 hands halves, from ±$174.62 to ±$87.74, but the average loss rises from $5.70 to $20.33, because the game returns 98.37% instead of 99.54%. Pick “9/6, under five credits” in the calculator to compare the two.
What it does not cover
Progressive jackpots, which raise the royal and with it both the return and the swing. The double-up offered after a win, which adds a swing of its own. Mistakes: every figure assumes each hand is played its best way, and a mistake lowers the average and changes the swing (the strategy calculator finds the best hold for any hand). And playing several hands at once: a round of 10 hands swings 1.38 times as far as 10 hands played one at a time, as multi-hand video poker explains.
Every figure here is where a session finishes. On the way there, the balance dips lower before a win brings it back, so money set aside to cover the worst 1 in 20 results runs out in more than 1 in 20 sessions. Bring more than the result you are planning for, and decide before you start where you will stop.