Poker Variance Calculator
Model the expected swings in your poker results over a large sample of hands. Use it to set realistic bankroll goals and mentally prepare for inevitable downswings.
About this calculator
Even a winning poker player experiences large short-term swings due to variance. Your results over N hands follow an approximately normal distribution centred on your expected profit, with a spread determined by your standard deviation. The upper confidence bound formula used here is: Upper Bound = (winRate × handsPlayed / 100) + (z × standardDev × √handsPlayed), where z = 1 for 68% confidence, 2 for 95%, and 3 for 99.7%. Win rate and standard deviation are both expressed in big blinds per 100 hands (bb/100). A typical standard deviation for No-Limit Hold'em is around 80–100 bb/100. By computing both the upside and downside bounds you can see the realistic range of outcomes, helping you determine the bankroll needed to withstand downswings without going broke.
How to use
Suppose you have a win rate of 5 bb/100, a standard deviation of 100 bb/100, and you want to know your 95% confidence range after 10,000 hands. Expected profit = 5 × 10,000 / 100 = 500 bb. The z-value for 95% is 2. Swing = 2 × 100 × √10,000 = 2 × 100 × 100 = 20,000 bb. So your upper bound is 500 + 20,000 = 20,500 bb and your lower bound is 500 − 20,000 = −19,500 bb. This wide range illustrates why 10,000 hands is still a small sample — you need hundreds of thousands of hands before results closely reflect your true win rate.
Frequently asked questions
How many hands do I need to play before my poker results are statistically significant?
Most poker researchers consider 100,000 hands the minimum sample for a reliable win-rate estimate at a single stake level, and 300,000+ hands for high confidence. Variance is so large in No-Limit Hold'em — with standard deviations of 80–120 bb/100 — that even 50,000-hand samples can look misleading. Until you have a large sample, use a variance calculator to understand the possible range of outcomes rather than treating your current results as proof of your true skill level.
What is a typical standard deviation for No-Limit Hold'em cash games?
For full-ring (9-player) No-Limit Hold'em cash games, a typical standard deviation is roughly 80–100 bb/100 hands. 6-max games tend to have higher variance, often 100–120 bb/100, because there are more aggressive postflop spots and a higher proportion of contested pots. Tournament play has dramatically higher variance still. Knowing your personal standard deviation — trackable in poker tracking software like PokerTracker or Hold'em Manager — lets you model your specific swings accurately.
Why do I keep losing despite having a positive win rate in poker?
A positive win rate guarantees profit only over a very large sample; in the short run, chance dominates. Because each hand's result is one draw from a high-variance distribution, extended downswings of tens of thousands of hands are statistically normal even for winning players. The variance calculator quantifies this by showing that a 5 bb/100 winner can realistically be down 10,000 bb over 10,000 hands within a 95% confidence interval. This is not bad luck — it is an expected feature of the game's variance.