Expected Value Calculator
List each possible outcome with its probability and payoff to get the expected value, the long-run average result. The tool also totals your probabilities so you can check they add up to 1.
How to calculate expected value
- Enter the probability of each outcome as a decimal between 0 and 1.
- Enter the value or payoff for each outcome.
- Read the expected value and confirm the probabilities total 1.
Examples
A simple bet
50% to win 10, 50% to lose 5
Expected value 2.5
Rolling a fair die
Each face 1 to 6 with probability 1/6
Expected value 3.5
Frequently asked questions
What is expected value?
Expected value is the probability-weighted average of every possible outcome. You multiply each outcome's value by its probability and add the results. It tells you the average payoff if the situation were repeated many times, even if no single trial ever lands on that exact figure.
How do I calculate expected value?
Use the formula EV = sum of probability times value for each outcome. For a bet with a 50 percent chance to win 10 and a 50 percent chance to lose 5, the expected value is 0.5 times 10 plus 0.5 times minus 5, which equals 2.5.
Should my probabilities add up to 1?
For a complete distribution, yes, every possible outcome should be listed and the probabilities should total 1. This tool shows the running total so you can spot a gap. If the total is not 1 the expected value is still computed, but it is only meaningful once the outcomes are exhaustive.
Can outcomes have negative values?
Yes. Losses are entered as negative values, such as minus 5 for a 5 unit loss. This is common in gambling and finance, where the expected value combines potential gains and losses into a single average figure.
What does a positive or negative expected value mean?
A positive expected value means the average outcome favors you over many repetitions, while a negative expected value means it works against you. An expected value of zero is a fair game with no long-run edge either way.
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