What is expected value?

Expected value is the average result you would get if a decision were repeated many times. You multiply each possible outcome by its probability and add them up. It reduces a risky choice to one number, which makes options comparable.

How it works

For outcomes x with probabilities p, the expected value is the sum of p times x. It is a good guide when you can repeat the choice many times, or when losses are small compared with total resources. It can mislead when a single loss would be ruinous, since an option with a good average may still have a chance of bankruptcy. It also says nothing about spread, so it is usually reported together with variance. Two options with the same expected value can have very different risk.

Expected value is also useful for ranking options when they differ in both probability and payoff. Computing it forces you to write down your probabilities, which are often the most debatable and most valuable part of the decision.

Example

Say a company can launch a product with a 30 percent chance of earning 1,000,000 and a 70 percent chance of losing 200,000. The expected value is 0.3 times 1,000,000 plus 0.7 times minus 200,000, which is 300,000 minus 140,000, or 160,000. The launch is worth doing on average, but 70 percent of the time it loses money, so the company must be able to absorb that loss. This is an illustration with round numbers.

How to model it in Machinations

Use a Gate with the probability of success to route resources into a gain Pool or a loss Pool, and sum the result in a Register. Play many times at once and compare the average of the results to the expected value. Change the probability or payoff Levers to see how the decision shifts.