Poker Variance Calculator
Enter your win rate, standard deviation and a sample size to see the real range of results it can produce — a confidence interval, the odds of being down, risk of ruin, and a live simulation graph.
How to use the variance calculator
Enter your win rate. In big blinds per 100 hands — your true edge, or a target.
Set the standard deviation. Around 100 bb/100 for 6-max NLHE; use your own if you track it.
Read the spread. Expected profit, confidence range, downswing odds and risk of ruin.
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.
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.