Calculator
Expected value calculator
Enter each outcome with its payoff and its chance. The expected value is the probability-weighted average. Add a cost to see the net value, then turn it into a full decision tree to compare it with other options.
OutcomePayoffChance %
Probabilities sum to 100%
Expected value
92,000
Net of the cost: 42,000. Worth taking on average.
40% × 200,000 + 60% × 20,000 = 92,000
Turn this into a decision tree
Opens the editor with this gamble versus walking away, so you can add more options and see the switch points.
Expected value, briefly
Expected value answers one question: what is this gamble worth on average? It is the sum of each outcome times its probability. It does not tell you how likely you are to lose, or how bad the worst case is. That is what the risk profile in the decision tree analysis calculator adds, and why a decision with several options is better handled as a tree.
Questions
- How do you calculate expected value?
- Multiply each outcome by its probability and add the results. With a 40% chance of 200,000 and a 60% chance of 20,000, the expected value is 0.4 × 200,000 + 0.6 × 20,000 = 92,000.
- What if there is a cost to play?
- Subtract it from the expected value. If the gamble above costs 50,000 to enter, its net expected value is 42,000, so it is worth taking on average.
- Does expected value tell me what to do?
- It tells you what is best on average over many repeats. For a one-off decision, also look at the risk profile: the chance of a loss and the worst case. The decision tree editor shows both.
- Why must the probabilities add to 100%?
- Because the outcomes are meant to cover every possibility exactly once. If they add to less, something is missing; if more, two outcomes overlap.