How Long Until…?

First-step analysis

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

• First-step analysis: E = 1 + the average of the E-values where you land.
• Waiting for an event of probability p takes 1/p tries on average.
• One equation per state gives exact expected times to absorption.

Steps

1. First-step analysis
2. Waiting for a six
3. A board game
4. Place the ladder
5. Two hits
6. Back to the start