Estimate π by randomly throwing darts at a square containing a quarter circle. The ratio of points inside the circle to total points converges to π/4.
Why it works: A quarter circle of radius r inside a square of side r has area (πr²)/4. The square has area r². The ratio of inside/total converges to π/4.
Convergence: Error decreases as 1/√n, so you need 100× more darts to get 10× more accuracy.