Comparing independent (geometric) trials vs Bayesian learning across repeated attempts. Adjust parameters to see how the models diverge.
Each trial is identical. P(fail all n) = (1−p)ⁿ. Requires log(1−τ)/log(1−p) trials to hit threshold τ. Assumes no learning — every attempt starts from zero.
Each failure raises p_t toward p_max at rate α. P(fail through n) = ∏(1−p_t). You need fewer trials because you're getting better — but only if α > 0 and learning is real.