The Monte Carlo method for estimating π works by randomly placing points inside a square and counting how many fall within the inscribed circle.

The Algorithm:

1. Generate random points (x,y) within a 1×1 square
2. Count points that fall inside the inscribed quarter-circle: x² + y² ≤ 1
3. The ratio of points inside the circle to total points approaches π/4
4. Multiply this ratio by 4 to get an estimate of π

The accuracy of this estimate improves with more iterations, demonstrating the law of large numbers in probability theory.