The Drunkard’s Walk

How far do you get?

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

• A symmetric random walk averages 0, but typically strays √n from the start.
• Variance of the position after n steps: n.
• Ten times the distance takes a hundred times the steps.

Steps

1. Eight walkers
2. The square-root law
3. Back to zero
4. A walk in the plane
5. Checking the law
6. An hour of wandering