Expected Value

The long-run average result when each outcome is weighted by its probability.

Visual intuition

50%

Many repeats settle around the weighted average

The expected value is the probability-weighted balance point of the possible outcomes.

Formula

sum(outcome * probability)

Example

A 50% to win 10 and a 50% chance to win 0 has expected value 5.

How It Works

Expected value is useful for repeated bets, forecasts, and decisions with known probabilities. It says what happens on , not what will happen in the next single case.

Concepts

Expected Value

The long-run average outcome: each result weighted by how likely it is. It tells you whether a bet is favourable on average, but it ignores how badly a single rare outcome would hurt — which is why people rationally pay to avoid losses they could not absorb.

Lessons

A calm average marker beside a heavy rare-outcome tail.

The Average Isn't the Whole Story

Expected value ignores how badly the rare outcome would hurt.