Risk
Decision Tree & Expected Value Calculator
Two options, three ways the world could go. The tool weights every branch by its probability, nets off what each option costs to take, and shows not just which one wins on expected value but what you would lose by picking the other one — and how bad each choice looks if the world goes against you.
Inputs
- Probability — strong demand
- Probability — expected demand
- Probability — weak demand
- Option A payoff — strong
- Option A payoff — expected
- Option A payoff — weak
- Option A upfront cost
- Option B payoff — strong
- Option B payoff — expected
- Option B payoff — weak
- Option B upfront cost
How to use this calculator
- Describe the world in three states (a strong case, an expected case, and a weak case) and give each one a probability. They should add to 100; if they do not, the tool rescales them and tells you in the first row.
- Enter what each option pays off in each state. Use the same measure for both options (profit over the same period, or cash over the life of the decision) and enter losses as negative numbers.
- Enter what each option costs to take upfront. The tool nets this off every branch, so the expected values you compare are already after cost.
- Read the two expected values and the difference. Then read the two worst cases. A higher expected value with a ruinous downside is not automatically the better choice.
- Use the regret rows to size the mistake. Expected regret is what picking that option costs you on average once you know how the world turned out. The smaller of the two is what perfect foresight would be worth buying.
What each term means
- Expected value
- Each outcome multiplied by its probability, added up: the average result if this same decision were repeated many times.
- State of the world
- One way things could turn out (demand strong, as expected, or weak). The three states are treated as covering every possibility.
- Net payoff
- The payoff in a state minus what the option cost to take: what actually lands in your hands on that branch.
- Worst case
- The lowest net payoff an option produces across the three states, regardless of how likely that state is.
- Expected regret
- How much better off you would have been with the other option, weighted by probability. Also called expected opportunity loss.
- Value of perfect information
- The expected regret of the option you would actually pick: the most it could be worth to know in advance which state occurs.
Educational disclaimer: Outputs are simplified educational estimates built from the numbers you enter — they are not financial, legal, tax, or investment advice, and real decisions deserve verified figures and qualified professionals.