## What a Confidence Interval Tells You
A 95% confidence interval for your ROI gives the range within which your true ROI almost certainly falls, given your observed results. It quantifies how uncertain your performance estimate is.
## The Formula
For n bets, observed ROI r, and standard error SE:
SE = σ / √n
95% CI = r ± 1.96 × SE
Where σ is the standard deviation of your per-bet returns.
## A Worked Example
After 300 bets: observed ROI = +3.5%, σ = 1.0 unit per bet (typical even-money betting)
SE = 1.0 / √300 = 0.0577 units = 5.77% (per unit staked)
95% CI = 3.5% ± 1.96 × 5.77% = 3.5% ± 11.3% = [−7.8%, +14.8%]
Interpretation: "My true ROI is between −7.8% and +14.8% with 95% confidence." The confidence interval includes zero — so at 300 bets, you cannot rule out zero edge.
## Using Confidence Intervals Operationally
Run a confidence interval calculation at every 100-bet milestone. Track how the interval narrows as the sample grows. Only begin scaling stakes when the 95% CI lower bound is above 0% (the entire interval is positive).
This is the statistical test that distinguishes validated edge from lucky variance.
## The Upper Bound Information
The upper bound of the CI is also informative: "My true ROI is probably not higher than X%." This constrains the maximum expected return and prevents overconfident scaling based on hot streaks.
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