Poker Variance Calculator
This free variance calculator shows what your win rate actually guarantees — and what it doesn't. Enter your win rate, standard deviation, and sample size, and it computes your expected result, the 70% and 95% ranges your outcome will land in, your chance of finishing the sample a loser, your risk of ruin for a given bankroll, and the bankroll you'd need to cap that risk at 5% or 1%. Everything runs in your browser; nothing is uploaded.
How the math works
Poker results are a random walk with drift. Your win rate supplies the drift; your standard deviation supplies the noise. Over a sample of n units (100-hand blocks for cash, single tournaments for MTTs), the expected result is EV = win rate × n, while the spread of outcomes grows only with the square root: σ(n) = SD × √n. That mismatch — profit linear, noise square-root — is all of poker variance in one line. The 70% and 95% ranges are the normal intervals EV ± 1.0364·σ and EV ± 1.96·σ, and your chance of finishing the sample a net loser is Φ(−EV/σ), the standard normal CDF.
Risk of ruin = e−2 · WR · B / SD², where WR is your win rate (bb/100), B is your bankroll (in big blinds), and SD is your standard deviation (bb/100). The units cancel, so you can feed bb/100 figures straight in — and the same formula works in tournament units (ROI in buy-ins per tournament, SD in buy-ins, bankroll in buy-ins). Invert it and the bankroll needed to hold risk of ruin to r is B = SD² · ln(1/r) / (2 · WR).
This is the classic drift formula popularized by Mason Malmuth and derived in Chen & Ankenman's The Mathematics of Poker — the same equation behind the guidelines in our bankroll management guide. It assumes you keep playing the same stakes at the same win rate forever; in practice, moving down during a downswing makes your true risk lower than the formula's.
A worked example
Take a solid live winner: 5 bb/100 win rate, 90 bb/100 standard deviation, over a 10,000-hand sample (about 350–400 hours of live play), with a 2,000 bb bankroll. The calculator returns:
- Expected result: +500 bb (5 × 100 units).
- 70% of outcomes: −433 to +1,433 bb.
- 95% of outcomes: −1,264 to +2,264 bb — yes, a clear winner can be down 12+ buy-ins after 10,000 hands and be running normally.
- Chance of losing overall: 28.9%.
- Risk of ruin with 2,000 bb: 8.5%.
- Bankroll for 5% risk of ruin: 2,427 bb. For 1%: 3,731 bb.
Those last two numbers are why "how many buy-ins do I need?" has no single answer — the bankroll you need is the price of the risk tolerance you choose.
What standard deviation should you use?
Ideally, yours, measured from tracked sessions — it's the input everything else hinges on. If you haven't measured it yet, the figure used in Primedope's published risk-of-ruin example is 85 bb/100 for no-limit cash, and per-tournament standard deviations are commonly cited at roughly 5–10× a comparable cash session, driven by top-heavy payout structures. The sources and the full context are in our bankroll management guide.
Want your real numbers instead of estimates? The free TableLab app tracks every session and computes the exact win rate and standard deviation this calculator needs — and range-vs-range equity lives in the free TableLab app too, alongside the hand recorder and AI coaching. Open the web app or get it on Google Play.
FAQ
What standard deviation should I enter?
Measure it from your own tracked sessions if you can — it is the input the whole calculation hinges on. If you haven't measured yours yet, Primedope's published risk-of-ruin example uses 85 bb/100 for no-limit cash, and per-tournament standard deviations are commonly cited at roughly 5 to 10 times a comparable cash session. See our bankroll management guide for the sourced figures.
What is risk of ruin in poker?
The probability that you eventually lose your entire bankroll despite being a winning player, estimated with the classic drift formula RoR = e−2·WR·B/SD². It assumes you keep playing the same game at the same win rate and never move down in stakes — moving down when losing makes your real risk lower than the formula says.
Why is my chance of losing so high even with a good win rate?
Because your expected profit grows linearly with volume while the spread of outcomes grows with the square root of volume. Over 10,000 hands, a solid 5 bb/100 winner with a 90 bb/100 standard deviation still finishes the sample as a net loser about 29% of the time. The edge wins eventually — but "eventually" is measured in tens of thousands of hands.
Does this calculator work for tournaments?
Yes — switch to Tournament mode and enter your ROI, your standard deviation in buy-ins, and the number of tournaments. One caveat: everything here is a normal approximation, and tournament results are heavily right-skewed, so at small sample sizes the tournament figures understate tail risk. Treat them as estimates.
Is this poker variance calculator free, and where does my data go?
Completely free, and nothing leaves your device — the math runs in your browser with plain JavaScript. There is no signup, no upload, and no tracking of the numbers you enter.
All outputs are normal-approximation estimates of a random walk with drift — useful for sizing risk, not guarantees. Tournament distributions are right-skewed, so tournament tail risk is understated at small samples. Also try the ICM deal calculator.