Expected value
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.
✦ Widely referenced — cross-referenced 15× across this reference (9 related ideas · 4 hubs · 1 book) · The State of Thinking 2026 →
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.
Expected value assumes infinite tries — but in a one-shot life, avoiding ruin can matter more.
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 inputs are usually guesses — for one-off, novel decisions the probabilities are invented, and multiplying invented numbers yields precise-looking fiction.
- It treats all value as linear, but a dollar means more to the broke than the rich; ignoring diminishing utility makes EV endorse bets real people rightly refuse.
- It optimizes the average across repetitions you may never get — for unrepeatable life decisions, the distribution of outcomes matters more than its mean.
The counter-model: Ergodicity — Expected value averages across parallel imaginary trials; ergodicity asks what happens to one person moving through time — when the two diverge, as with ruin risks, the time-average is the one you actually live.
How to apply it, step by step
- List the plausible outcomes of the decision and a rough probability for each.
- Assign each outcome a value, being honest about downside sizes.
- Multiply and sum to get the expected value of each option.
- Check the worst case separately: if it is ruinous, reject the bet regardless of the average.
- Choose the highest-EV survivable option, and note your estimates to score later.
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.
Related
Keep reading
Plato
Almost every later debate about reality, justice, or beauty begins as a footnote to him.
See this alongside the other thinking tools of investing, building a startup, product management and hiring.
Go deeper
The book behind this idea: Thinking in Bets by Annie Duke. Hear the whole thing free — start an Audible trial and your first audiobook is on the house.
Read the full summary of Thinking in Bets →
More canonical picks:
- Thinking, Fast and Slow — Daniel Kahneman
- The Art of Thinking Clearly — Rolf Dobelli
- The Great Mental Models, Volume 1 — Shane Parrish
- Poor Charlie’s Almanack — Charlie Munger
- Super Thinking — Gabriel Weinberg & Lauren McCann
- Seeking Wisdom — Peter Bevelin
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Cite this page
ReadGlobe. (2026). Expected value. https://readglobe.com/model/expected-value/
"Expected value." ReadGlobe, 29 May 2026, readglobe.com/model/expected-value/.
Primary source: Wikipedia
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.