Darts and π

The Monte Carlo method

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• For a uniformly random point, probability = area.
• Darts in a quarter circle: $\pi \approx 4 \times$ fraction inside.
• Monte Carlo error shrinks like $1/\sqrt n$.

Steps

1. Probability as area
2. Throw darts
3. Your estimate
4. The price of accuracy
5. Any shape at all
6. A biased throw