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 proposed journey associates Plot with the tree and Atlas with the decision file. Probabilities and payoffs remain sourced, discussed and validated; expected monetary value does not choose on the decision-maker’s behalf.
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.