Each trial draws n = 1…400 i.i.d. samples and records the running sample mean. Top: the running mean of the latest trial stays inside the band μ ± ε more and more. Bottom: the empirical tail probability P(|X̄ − μ| ≥ ε), estimated over all trials, falls under the Chebyshev bound σ²/(nε²) and the (much sharper, for large deviations) Hoeffding bound exp(−2nε²/(b−a)²).