What is expected value in simple terms?

It’s the long-run average payoff of a decision: each possible outcome multiplied by its probability, then added up. It tells you whether a bet is worth taking over many repetitions, regardless of any single result.

How do you calculate expected value?

Multiply each possible outcome by its probability and sum the results. A 50% chance of +$100 and 50% of −$40 has expected value (0.5×100) + (0.5×−40) = $30.

Can a positive expected value bet still be a bad idea?

Yes — if it risks ruin on a single try. Expected value assumes many repetitions; a wager that wipes you out on one bad outcome can be positive on paper but reckless in practice.

Expected value

Also called expected-value thinking · Probability & decision theory

Expected value is the average outcome of a decision if you could repeat it many times — each possible result weighted by its probability. It tells you which choice pays off in the long run, even when any single outcome is uncertain.

How it works

For each option, multiply every possible outcome by its probability and sum them. Compare options by their expected value, not by their best or worst case — and remember a positive-expected-value bet can still lose on any single try.

How to use it

Deciding whether a risky bet, investment, or project is worth taking over many repetitions.
Resisting both fear (avoiding good bets after one loss) and greed (chasing bad bets after one win).
Comparing options with different odds and payoffs on a single common scale.

Worked example

A lottery ticket costs $2; the prize is $1,000,000 at 1-in-10-million odds. Expected value = $1,000,000 × 0.0000001 = $0.10 — far below the $2 price. Positive-feeling, negative-value: on average you lose 90 cents on the dollar.

Where it fails

It assumes you can survive to repeat the bet. A positive-expected-value wager that risks ruin on a single try can be correct on paper and catastrophic in life, where you don’t get infinite repetitions.

The deeper point

The trap isn’t miscalculating expected value — it’s forgetting it assumes infinite tries. In a one-shot life, avoiding ruin can matter more than maximising the average, which is why expected value and the margin of safety must be read together.

Frequently asked

What is expected value in simple terms?: It’s the long-run average payoff of a decision: each possible outcome multiplied by its probability, then added up. It tells you whether a bet is worth taking over many repetitions, regardless of any single result.
How do you calculate expected value?: Multiply each possible outcome by its probability and sum the results. A 50% chance of +$100 and 50% of −$40 has expected value (0.5×100) + (0.5×−40) = $30.
Can a positive expected value bet still be a bad idea?: Yes — if it risks ruin on a single try. Expected value assumes many repetitions; a wager that wipes you out on one bad outcome can be positive on paper but reckless in practice.

Bayesian thinking Margin of safety Regression to the mean Gambler's fallacy

Editorial synthesis © ReadGlobe 2026, drawing on the mental-models tradition (Charlie Munger, Farnam Street) and the primary sources for each model. · Last reviewed 2026-05-29.