Expected value calculator
Working: 40% × 125 + 60% × 90 = 104.00
Expected value in one line
Multiply each outcome by its probability and add them up. That number is the fair value of the bet or contract: the price at which you would be indifferent between buying and selling if you could repeat it many times.
From fair value to a market
A market maker does not quote fair value. They quote a bid below it and an offer above it, and earn the difference when both sides trade. The calculator shows a market of the width you choose, centred on the expected value. The standard deviation tells you how much a single outcome can differ from fair value, which is the risk you carry while you hold a position.
Updating when news arrives
In a market making game the probabilities change as information comes in. Change a probability above and the fair value and both prices move with it. Being able to do that update in your head, quickly, is most of what the game tests.
Practise it
Frequently Asked Questions
Do the probabilities have to add up to 100%?
Yes. The calculator tells you if they do not, and you can press Normalise to scale them.
Is the expected value the most likely outcome?
No. It is the long-run average. A bet that pays 100 one time in ten has an expected value of 10, although you will never receive exactly 10.
More free tools: Black-Scholes calculator · Kelly criterion calculator · Probability distribution calculator
For education and interview practice only. Not investment advice.