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Poker variance calculator Win rate, standard deviation and sample size in, the range of results out
Poker results swing far more than most players expect. Enter a win rate and a standard deviation in big blinds per 100 hands and see what can happen over a sample: the expected result, the range most results fall in, the chance of being down, how big the downswings get, and what bankroll keeps the risk of going broke low.
How the numbers are worked out
Over n hands the expected result is the win rate times n/100, and the standard deviation of the result is the standard deviation per 100 hands times √(n/100). Results are close to normally distributed, so about 70% of them fall within 1.04 standard deviations of the expected result and 95% within 1.96.
expected = WR × n/100 · spread = SD × √(n/100) · P(down) = Φ(−expected / spread)
The number of hands a winner needs to show a profit 95% of the time is (1.645 × SD / WR)² × 100. At 5 bb/100 and a standard deviation of 90 that is close to 88,000 hands, which is why short samples say little about how good a player is.
A bankroll measured in buy-ins is 100 big blinds per buy-in. The bankroll for a target risk of ruin r is −SD² × ln(r) / (2 × WR).
Questions
What standard deviation should I use?
Take it from your tracking software over as many hands as you have. Without one, these are common ballparks in bb/100: No-Limit Hold'em 6-max cash around 80–110, full ring around 60–90, heads-up around 100–150, Pot-Limit Omaha much higher at roughly 120–200. Looser, more aggressive play and deeper stacks mean a higher number.
What does risk of ruin mean here?
The chance that a bankroll is ever lost completely if you keep playing forever at this win rate and standard deviation, without moving down or adding money. It uses the standard formula for a random walk with drift: e−2 × win rate × bankroll / SD², with win rate and SD per 100 hands and the bankroll in big blinds.
Why is my real result so far from the expected one?
Because the spread grows with the square root of the hands while the expected result grows with the hands themselves. Over a few thousand hands the spread is much larger than the win rate, so the luck you had dominates. Over hundreds of thousands of hands the win rate starts to show.
How are the downswings worked out?
By simulation: 2,000 players with exactly your win rate and standard deviation each play the number of hands you entered, and the page counts how often their largest drop from a peak reached each size. Results change a little from run to run.
Want to see where a win rate comes from? The free preflop ranges and the free web viewer show solved strategies hand by hand, and GTO vs exploitative play explains where the edge is.
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