Law of Large Numbers Visualizer
Simulate N coin flips with a set edge and watch the observed win rate converge. See why a 10-trade backtest means nothing.
Feb 23, 2026, Eric
The Core Idea
A trader with a genuine 53% win rate will look like a 90% genius on trade #3 and a 40% loser on trade #8 — purely by chance. The law of large numbers says the observed win rate will eventually converge to the true edge, but "eventually" can mean hundreds of trades. A 10-trade backtest is not evidence of skill; it is evidence of sample size.
The confidence band below shows the ±1 standard deviation envelope: the zone where your observed rate is statistically expected to land. Watch how wide it is at N=10 and how it collapses as N grows. If your backtest lives entirely inside that band, the result is noise.
Controls
The real probability of winning each trade.
How many trades to simulate in the main chart.
Observed Win Rate vs. Number of Trades
Shaded band = true edge ± 1 standard deviation. Dashed line = true edge.
Streaks at N=10 — 500 Mini-Simulations
Each bar shows how often a 53.0% edge produced that win count over exactly 10 trades. Green = looks like a genius. Red = looks like a loser. Neither means anything.
True Edge
53.0%
Observed at N=500
53.8%
Convergence Point (±2%)
#290
Trades for 95% CI ±2%
2,393
What This Means
After 500 trades, the observed rate of 53.8% is within 1% of the true edge — the law of large numbers has done its work.
Converged late at trade #290. Early in this run, the observed rate strayed far from the true edge — exactly the danger zone for short backtests.
Statistical requirement: To be 95% confident your observed win rate is within ±2% of the true edge, you need approximately 2,393 trades. This is calculated as n = (1.96² × p×(1−p)) / 0.02². For a 53.0% edge, that's well beyond what most discretionary traders ever log.