Expected Value Calculator

Calculate the expected value of an uncertain outcome from a list of values and their probabilities.

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Outcomes (value, probability — one per line)

Result

Enter values to calculate.

Summary

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Detail

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Calculate the expected value of an uncertain outcome from a list of values and their probabilities.

How It Works

How Expected Value Calculator Works

Each possible outcome is multiplied by its probability of occurring, and those products are added together — the result is the long-run average result you'd expect if the same uncertain situation played out many, many times.

Real-World Use Cases

Who Uses Expected Value Calculator and Why

Evaluating whether a bet, game, or wager is favorable on average before deciding whether to play.
Comparing two decisions with uncertain payoffs to see which has the better long-run average outcome.
Teaching or reviewing the basic building block of decision theory and probability-weighted outcomes.

Common Mistakes

Mistakes to Avoid

Expecting any single trial to actually produce the expected value itself — on one try, you'll only ever get one of the listed outcomes; the expected value is a long-run average, not a guaranteed or even necessarily achievable single result.
Entering probabilities that don't sum to 1 — the calculator will still compute a result and flag the issue, but a probability set that doesn't account for every possible outcome will produce a misleading expected value.
Using expected value alone to judge a risky decision — a positive expected value doesn't account for the SIZE of potential losses or your tolerance for that risk; two options can have the same expected value with very different risk profiles.

Pro Tips

Tips for Best Results

Always double-check that your listed probabilities sum to 1 before trusting the result — a missing outcome or a data-entry slip is a common source of an off expected value.
Expected value is most meaningful for situations that repeat many times (or that you can meaningfully compare against other options), rather than as a prediction for a single occurrence.

Troubleshooting

Fixing Common Problems

My probabilities don't add up to 1 and I'm not sure why. — Review your outcome list for a missing possibility (for example, forgetting a "no result" or "tie" case) — every realistic outcome needs to be included and its probabilities need to sum to 1 for the expected value calculation to be meaningful.

Glossary

Terms Explained

Expected value: The long-run average outcome of an uncertain event, computed by multiplying each possible outcome by its probability and summing the results.

Probability distribution: The complete list of possible outcomes for an uncertain event along with each outcome's probability of occurring.

FAQ

Frequently Asked Questions

Does the expected value mean I should expect that exact result?

No — on any single try, you'll only ever get one of the actual listed outcomes, never the expected value itself unless it happens to match one exactly. It's a long-run average, most meaningful when a situation repeats many times.

What if my probabilities don't add up to 1?

The calculator will still compute a result, but it will flag that your probabilities don't sum to 1 — double-check that you've accounted for every possible outcome before trusting the answer.