Waiting for Patterns

HH, HT and Penney’s game

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

• Average waits: HT takes 4 tosses, HH 6, HHH 14.
• How a pattern overlaps itself decides how long it takes to appear.
• Penney’s game is non-transitive: every pattern can be beaten.

Steps

1. Which comes first on average?
2. Waiting for HT
3. Waiting for HH
4. Penney’s game
5. Rock, paper, scissors
6. Against HHT