Expected Value

The long-run average

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Expected value = sum of (value × probability): the long-run average.
• Casino games and lotteries have negative expected value for players.
• Expected value ignores risk, which matters too (that’s why insurance makes sense).

Steps

1. Average roll
2. Expected value
3. A fair game?
4. Play all night?
5. Lottery
6. Beyond the average
7. A fair price
8. Waiting for a six