Win-Rate Confidence Interval Calculator
How confident can you be in your observed win rate?
Enter your sample size, your win rate in BB/100, and your standard deviation to see the 95% confidence interval — the range your true long-run win rate is likely to fall in.
- Enter the total hands played. The number of hands in your sample. Online cash players track this automatically; live players estimate from sessions × hands-per-hour.
- Enter your observed BB/100. Your measured win rate over the sample, expressed in big blinds per 100 hands.
- Enter your standard deviation. Most online 6-max cash games run between 90 and 110 BB/100. If you don't know your number, leave the default — it's representative of typical online play.
- Read the 95% confidence interval. The true long-run win rate lies inside this range with 95% confidence. The narrower the band, the more reliable your number.
Most players have FAR fewer hands than they think they need. A 50,000-hand sample at 5 BB/100 with 100 stdev gives a 95% CI roughly from -3.8 to +13.8 BB/100 — wider than the win rate itself.
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What is a confidence interval?
A confidence interval is a statistical range built around your observed win rate that's likely to contain your true long-run win rate. A 95% confidence interval means: if you ran 100 identical sample-collection experiments, your true win rate would fall inside the calculated range in 95 of them.
Poker is the textbook case for confidence intervals because variance is brutal. A solid winning player in online mid-stakes cash games might run at 5 BB/100 with a standard deviation around 100 BB/100. After 50,000 hands — which feels like a lot — the 95% CI is roughly -4 to +14 BB/100. That means at this sample size, your observed 5 BB/100 might really be a 14 BB/100 monster, OR a small loser. The sample isn't large enough to tell.
The math (it's simpler than it looks)
The 95% CI for win rate uses the standard error of the mean: SE = σ / √(N/100), where σ is your standard deviation in BB/100 and N is the number of hands. The CI is then your observed win rate ± 1.96 × SE — the 1.96 multiplier comes from the normal distribution and corresponds to the central 95% of probability mass.
The key insight: SE shrinks with the square root of sample size, not linearly. To halve your CI width, you need to quadruple your sample. That's why pros emphasize logging hands — the difference between 50,000 hands and 200,000 hands is the difference between not knowing if you're winning and being sure.
When can you trust your win rate?
The standard threshold is: your CI does not include 0. If the entire interval is positive, you're a statistically significant winner at the standard 95% confidence level. If the entire interval is negative, you're a statistically significant loser. If 0 is inside the interval, the data can't yet distinguish you from a break-even player.
Practical milestones for online 6-max NLHE (stdev around 100): you need roughly 250,000 hands to confidently confirm a 4 BB/100 win rate. Less than that and a small upswing or downswing can flip your observed number by 3 BB/100 either way.
How to estimate your standard deviation
Most modern tracking software calculates standard deviation automatically. Typical ranges by format: online 6-max NLHE: 80-110 BB/100. Online 9-max (full-ring): 65-85 BB/100. Live cash: 50-90 BB/100 (much less variance from fewer hands per hour and tighter ranges). PLO and short-deck: 130+ BB/100. MTTs are best measured by ROI variance instead of BB/100 — the variance is too high for this framework to be useful as-is.
Frequently asked questions
Why is my CI so wide?
Because poker variance is genuinely brutal. Even 100,000 hands at 100 BB/100 standard deviation only narrows your CI to about ±6.2 BB/100 — meaning the difference between a real 0 BB/100 break-even player and a real 12 BB/100 crusher is just barely larger than the CI width. The fix is more hands, not a different calculation.
Should I report my CI or my point estimate?
Both. The point estimate (your observed BB/100) is your best single-number guess of your true win rate. The CI tells you how seriously to take it. A player who reports '5 BB/100 over 30K hands' is doing you a disservice without also reporting the CI — at 30K hands the CI is wider than the win rate itself.
Does this work for tournaments?
Not directly. Tournament variance is much higher and concentrated in rare deep runs, so the normal-distribution assumption breaks down at small sample sizes. For tournaments, ROI confidence intervals work — but require a separate calculation and typically need 500+ tournaments before the CI tightens meaningfully.
Does PokerCharts have other free poker tools?
Yes — try our free pot odds calculator for one-bet equity decisions, SPR calculator for postflop commitment thresholds, ICM calculator for tournament deals, and tournament payout calculator for prize structures.