Poker Variance Calculator

What is variance in poker?

Variance is the statistical spread between what you expect to win and what you actually win over any finite sample. Your win rate is an average that only emerges over hundreds of thousands of hands; over any single session, week, or even year, the cards you're dealt and the way all-ins resolve dominate the result. Two players with identical skill and an identical 5 bb/100 edge can finish the same 50,000 hands 40 buy-ins apart — not because one played better, but because variance is that wide.

Mathematically, poker results over N hands are well-approximated by a normal distribution with mean WR × N/100 and standard deviation σ × √(N/100), where WR is your win rate and σ your per-100-hands standard deviation. The mean grows linearly with hands while the spread grows with the square root — which is why skill always wins eventually, but takes far longer than intuition suggests.

How to read the confidence cone

The shaded cone on the chart is the 95% confidence band: at every point along the x-axis, 95% of all possible outcomes for a player with your exact win rate fall inside it. The bold center line is expectation — the result you'd average across infinitely many attempts. Early in the sample the cone is enormous relative to expectation; it only separates from zero once the linear EV growth outpaces the square-root growth of the spread.

The practical reading: if the bottom of the cone is still below zero at the end of your simulated sample, then a genuinely winning player can finish that entire stretch as a loser purely through bad luck — and the calculator shows you the exact probability. That single number explains most poker tilt: losing streaks that feel impossible are usually well inside the cone.

Why winners still hit 20+ buy-in downswings

A downswing isn't measured from zero — it's measured from your peak. Even in a simulation that ends up 30 buy-ins ahead, the path there almost never rises smoothly; it makes a high, gives a chunk back, makes a new high, and so on. The Monte Carlo results above measure the largest peak-to-trough fall in each simulated run. For a solid 5 bb/100 winner with 100 bb/100 standard deviation, downswings of 20+ buy-ins are not a rare disaster — over a long enough sample they're close to inevitable.

This is the single most misunderstood fact in bankroll management. Players ascribe a 15 buy-in downswing to being 'off their game' or the site being rigged, when the math says a winning player should expect one. The right responses are boring: keep a bankroll sized for the swings (which is what the risk-of-ruin figure quantifies), review hands for real leaks, and never move up stakes to chase losses.

Standard deviation: live vs online

Standard deviation depends on format and playing style far more than on skill. Online 6-max NLHE typically runs 90–110 bb/100 — aggressive, many all-ins, wide ranges. Online full-ring is calmer at 65–85 bb/100. Live full-ring cash usually measures 80–120 bb/100 per 100 hands: looser, multiway pots push it above online full-ring even though the hourly pace is slower. PLO commonly exceeds 130 bb/100. If you track your sessions, use your own measured number — it's the input this calculator is most sensitive to, since risk scales with σ².

Frequently asked questions