Advanced Finance

Decision Trees and Expected Value

Put a number on a decision nobody can be certain about. Then learn precisely what that number is worth knowing, and when following it would be a mistake.

  • Intermediate
  • 8 min total
  • 12 chapters

What decision this helps you make: Which branch of an uncertain choice to take, whether to pay for information before choosing, and when expected value stops being the right criterion at all.

What this topic is

A decision tree lays out every choice you control and every outcome you do not, assigns a probability and a value to each, and folds the whole thing back to a single comparable number for each option. Expected value is the arithmetic underneath it: each outcome multiplied by its probability, summed.

Why it matters

Most business arguments about uncertainty are arguments about adjectives: "risky," "promising," "too speculative." A tree replaces the adjectives with numbers you can disagree about specifically. It also answers a question intuition never gets right: exactly how much a piece of information, a pilot, or a delay is worth paying for.

Who should learn it

Anyone choosing between staged and committed investment, weighing a lawsuit settlement, deciding whether to run a pilot, or trying to make a committee argue about assumptions rather than about feelings.

What you will understand

  • How to build and fold back a tree correctly, right to left
  • The exact value of perfect information, and why it caps what any test is worth
  • The two ways analysts double-count risk without noticing
  • When expected value is the wrong criterion, and what replaces it

Prerequisites

Common misconception

"The option with the highest expected value is the one to take." Usually, but not always, and the exceptions are the ones that end companies. Expected value is the right criterion when a decision repeats often enough for the average to arrive, and when no single bad outcome removes you from the game. A positive-expected-value bet that has a 10% chance of bankrupting the business is not a good bet; it is a good bet you cannot afford to make. Expected value tells you what a choice is worth on average. It says nothing about whether you survive the bad branch.