Expected Value

The long-run average

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

• Expected value $E = \sum p_i x_i$: the long-run average.
• A fair game has zero expected profit; casinos build in a small house edge.
• For big one-off decisions, expected money isn’t the whole story.

Steps

1. Weighing outcomes
2. A dice game
3. Price a fair game
4. Roulette
5. A lottery ticket
6. Always maximise EV?