Decision tree

A decision tree is a branching diagram mapping decisions and uncertain outcomes, evaluated by rolling expected values back from the end branches to find the best choice.

ByHoang TruongUpdated July 11, 2026

What it is

See it move

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A firm weighs launching a product against doing nothing. Launching has a 60% chance of €200,000 profit and a 40% chance of a €50,000 loss: 0.6 × €200,000 + 0.4 × (−€50,000) = €120,000 − €20,000 = €100,000 expected value. Doing nothing is worth €0, so the decision tree recommends launching.

The formula

LaTeX

EV = \sum_{i} p_i \times X_i

Variables

$E V$: Expected value (€)
$p_{i}$: Probability of outcome i (probability (0–1))
$X_{i}$: Payoff of outcome i (€)

Combines every chance outcome at a node into the single expected value used to compare branches.

Check yourself

PracticeCORE

A firm is choosing between investing in new equipment and not investing. Investing has a 70% chance of a €150,000 profit and a 30% chance of a €30,000 loss. Not investing has a certain profit of €0. Based on expected value, which option should the firm choose, and what is its expected value?

Select an answer to check your understanding.