Poker Variance Calculator

How to use the variance calculator

Type your win rate, standard deviation and how many hands you want to project, then Calculate. The tool returns your expected profit, a 95% confidence interval, the probability you're still down after the sample, and — with a bankroll entered — your risk of ruin. The graph runs a live Monte-Carlo simulation so you can see the spread of possible runs around the average.

Why variance matters

Over any normal sample, the standard deviation dwarfs the win rate — which is why genuine winners endure long losing stretches. The result over a sample is roughly your win rate times the hands, give or take a standard deviation that grows with the square root of the hands. Understanding that spread is what keeps you from quitting a beatable game or moving up under-rolled.

How risk of ruin works

Risk of ruin is the probability your bankroll hits zero before it grows, assuming a fixed win rate. The tool uses the standard estimate e^(−2 × winrate × bankroll ÷ std²). The takeaways are stark: a bigger edge or a bigger bankroll cuts risk sharply, while higher variance raises it. It's the math behind bankroll-management rules like keeping 20–40 buy-ins for cash. See bankroll management and poker math.

A worked example

A 5 bb/100 winner over 100,000 hands with a 100 bb/100 standard deviation expects +5,000 bb. But the standard deviation of that result is 100 × √(100,000 ÷ 100) ≈ 3,160 bb, so a two-sigma swing spans roughly −1,320 to +11,320 bb. Even a clear winner can finish a six-figure sample in the red — normal variance, not bad play.

Why a small sample tells you nothing

The trap is judging a win rate over too few hands. Because the standard deviation of your result grows with the square root of the sample while your expected profit grows in a straight line, over short runs the noise simply overwhelms the signal. Take the same 5 bb/100 player over just 10,000 hands: the expected result is +500 bb, but the standard deviation is 100 × √(10,000 ÷ 100) = 1,000 bb — twice the size of the edge itself. A 95% range there runs from about −1,460 to +2,460 bb, so a real winner losing money over 10k hands is completely ordinary, and a break-even player running hot looks like a star.

This is why you can't read anything into a good week or a bad one. Meaningful confidence in a win rate takes hundreds of thousands of hands, not thousands. Change the Hands field in the calculator and watch the 95% range tighten relative to the expected profit — that shrinking ratio is the whole reason samples eventually become trustworthy. Until then, judge your play by decisions, not by the graph.

How to reduce variance

You can't remove variance from poker, but you can shrink your swings and survive them. The two levers that matter most are your standard deviation and your bankroll — the same inputs the calculator uses for risk of ruin.

• Widen your edge. A higher win rate cuts risk of ruin faster than anything else, because it sits in the exponent of the formula. Better game selection and stronger play do more than any staking trick.
• Play a lower-variance style and format. Full-ring games and tighter, more disciplined lines run at a lower standard deviation than loose, three-bet-heavy 6-max or PLO, so the same edge produces smaller swings.
• Keep a deep enough bankroll. The usual 20–40 buy-ins for cash exists precisely so a normal 20-buy-in downswing never ends your session. See bankroll management.
• Move down when the roll shrinks. Dropping a stake during a downswing lowers the money at risk without changing your bb/100 edge — the cleanest way to cut real-money variance.

None of this makes downswings disappear; it makes them affordable. The point of the math is to size your game so variance is an inconvenience, never a threat. For more on how long the rough stretches run, see how long downswings last and the underlying poker math.

Frequently asked questions

What does a poker variance calculator do?

It projects the range of results a given win rate can produce over a sample of hands. You enter your win rate, your standard deviation and how many hands you plan to play; it returns your expected profit, a confidence interval around it, the chance of still being down, and — if you enter a bankroll — your risk of ruin. It shows why a winning player can lose over tens of thousands of hands.

What standard deviation should I use?

Standard deviation is measured in big blinds per 100 hands. For 6-max no-limit hold'em it is typically around 80–100 bb/100; full-ring is lower (roughly 60–80) and loose games or PLO are higher (100–150+). If your tracking software reports your own figure, use that; otherwise 100 is a reasonable NLHE default.

How is risk of ruin calculated?

With the standard formula for a positive-expectation random walk: risk of ruin ≈ e^(−2 × winrate × bankroll ÷ standard deviation²), with win rate and standard deviation in bb/100 and bankroll in big blinds. It assumes a fixed win rate and an infinite horizon, so treat it as a well-grounded estimate, not a guarantee.

Why can a winning player lose over 100,000 hands?

Because the standard deviation dwarfs the win rate over normal samples. A 5 bb/100 winner over 100k hands expects +5,000 bb, but the standard deviation of that result is about 3,160 bb — so a swing of two standard deviations puts a genuine winner anywhere from roughly −1,300 to +11,300 bb. Downswings are math, not bad play.

Is this a simulation or a formula?

Both. The profit range, probability of loss and risk of ruin come from exact normal-distribution formulas; the graph runs a live Monte-Carlo simulation of sample trajectories so you can see the spread of possible runs, not just the average.

Is anything saved or uploaded?

No. Everything runs in your browser and nothing you enter is stored or sent anywhere.