What to remember
- Separate decision, chance and outcome nodes.
- Make probabilities total 100% at each chance node.
- Fold the tree back from right to left.
- Test EMV against risk, liquidity and reversibility.
Build an unambiguous structure
A decision node contains controllable options. A chance node contains mutually exclusive uncertain events. A leaf holds a payoff in a common unit and horizon.
Assign, date and justify probabilities. A missing branch or a total other than 100% makes the calculation incomplete.
Fold back expected value
For an option, EMV = Σ(probability × payoff). In the illustrative example, A gives 40% × €5m + 60% × −€1m = €1.4m. B gives 40% × €2m + 60% × €0.5m = €1.1m.
A decision node selects the maximum when EMV is the sole objective. This does not automatically represent risk aversion.
| Option | High outcome | Low outcome | EMV |
|---|---|---|---|
| A | 40% × €5m | 60% × −€1m | €1.4m |
| B | 40% × €2m | 60% × €0.5m | €1.1m |
Test assumptions that change the choice
Find the probability or payoff threshold that reverses the preference. Sensitivity turns an average into an evidence question.
Similar EMVs may hide different maximum losses, funding needs, timing and exit options.
Retain the calculation and accountability
The editorial connection is to Plot for the tree and Atlas for the decision file, without proving public runtime or autonomous recommendation.
Retain structure, probabilities, payoffs, sources, sensitivities and the human rationale.
Frequently asked questions
Does EMV predict the outcome?
No. It is a probability-weighted average under assumptions.
Should the highest EMV always be chosen?
No. Liquidity, maximum loss, constraints, utility and reversibility may change the choice.
What if probabilities are uncertain?
Use ranges and calculate the threshold at which the choice changes.
Full sources
- Open University, decision trees and expected valueComplete source available online · Read the complete source
- PMI, analysing a complex decision with a treeComplete source available online · Read the complete source
- Decision under uncertainty and EMV calculationComplete source available online · Read the complete source