Ian Hargreaves.
Rigour for strategic decisions
Instrument № 03.5 · Branch
№ 03.5
Decision-tree instrument

Branch

Decision Tree Calculator

The choice · one square, then the gambles
The tree, averaged from the right (folded back)Start at the payoffs on the right. At each circle, replace its branches with their probability-weighted average; at the square, keep the best branch. The number above every node is that running average, in EUR k (the technical name is folding back the tree, or backward induction). · EUR k
The verdict · ranked by expected valueThe probability-weighted average of an option’s payoffs: each payoff times the chance of reaching it, summed. Necessary but not sufficient. Two options can share an average and carry very different risk, so read the number beside the downside in the tree. · EUR k
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Method. Exact arithmetic, no simulation: each option’s expected value is its two payoffs weighted by their probabilities, then summed; the square keeps the highest. Payoffs are in thousands of euros and may be negative. Probabilities are clamped to 0–1; the second outcome takes the complement automatically. No data leaves your browser.
Method

Draw it,
then price it

Draw the choice before you price it: the options you actually have, then the odds and payoffs of each. Once that shape is on paper the arithmetic is the easy part. Each option is a small gamble; its expected value is its payoffs weighted by how likely they are, and the square keeps the best of them.
i

The options come first

Most of a tree’s value is produced while drawing it: naming the options you genuinely have, and being honest about the odds and the payoffs of each. A wrong probability is easy to repair later; a missing option is invisible. Price the tree only once the people in the room agree it is the decision they face.

ii

Each option is a gamble

The expected value of an option is each payoff times its chance, added up. It ranks the options, but it is the average of a bet you place once. Read it beside the downside: with the defaults above, Launch now averages well yet loses money about half the time, while Pilot first earns a touch more on average for far less risk.

iii

Keep the best, knowing its risk

The square keeps the option with the highest expected value. That is necessary, not sufficient: two options can share an average and carry very different risk. The tree shows you both at once, the number and the spread behind it, so the ranking comes with the reason.

Read next
ElicitWhere the probabilities and payoffs come from when you have judgement, not data: three numbers turned into a calibrated range. SimulateWhen a payoff is itself a chain of uncertain numbers, simulate it instead of entering a single figure. From sensitivity to simulationWhen the chain of uncertainties grows too long to fold back by hand.