MEPX
Chapter 9 of 11All chapters
  1. 1What probability means
  2. 2Counting outcomes
  3. 3Independent events
  4. 4Dependent events
  5. 5Complements and at least one
  6. 6Adding probabilities
  7. 7Permutations and combinations
  8. 8Conditional probability
  9. 9Expected value
  10. 10Distributions in outline
  11. 11Fallacies and traps

Chapter 9 of 11

Expected value

The long run average of a gamble.

How to compute it

Multiply each outcome by its probability and add them up. A fair die has an expected value of 3.5, which is not a value it can ever land on.

  • A bet with negative expected value loses money over time however lucky you get.
  • Expected value says nothing about the spread, which is why variance matters too.

Where it is used

Insurance, pricing, game design and any decision under uncertainty. When outcomes repeat many times, the average is what you actually experience.