Expected value multiplies each outcome by its probability and adds the results. Use it only when outcomes and probabilities are defensible, and keep affordability and tail risk outside the average.
Probabilities are percentages and must stay between zero and one hundred.
Enter outcomes to compare the probability-weighted averages.
Expected value is a probability-weighted average across repeated or comparable uncertain outcomes. It is not the outcome you should expect to receive in one attempt.
An option can have the higher expected value and still contain a loss you cannot absorb. Check safety, legality, cash limits, and tail exposure separately.
Use base rates, observed frequencies, or transparent assumptions. Test a range when evidence does not support one precise percentage.
Option A pays 120 in the stronger outcome with a 60 percent chance and loses 20 otherwise. Its expected value is 120 multiplied by 0.60 plus negative 20 multiplied by 0.40, which equals 64. Option B returns 75 in either condition, so its expected value is 75. B leads on the average even though A has the larger upside.
| Check | Option A | Option B |
|---|---|---|
| Probability-weighted value | 64 | 75 |
| Lowest entered outcome | Negative 20 | 75 |
| Question to resolve | Can the loss be absorbed? | Is the fixed result credible? |
This example shows why the calculator reports an average rather than a command. If A's higher-outcome probability rises, recalculate and note the point where the lead changes. Preserve the downside check even after the average flips. Also record whether the choice happens once or repeatedly, because repetition changes how useful the average is for planning.
Record the probability source and the largest tolerable loss beside the result.
Use the two-option comparison engine to preserve constraints, evidence, and missing facts beside this calculation. Read the EITHER.SO comparison methodology before treating any calculated lead as final.
Understand the weighted average, probability assumptions, and why the highest expected value may still be unaffordable.
Expected value is useful when the outcomes share one measurable unit and the probabilities have a defensible basis. It is strongest for repeatable risks or choices where an average result is meaningful. A single irreversible choice also needs a separate downside and affordability check.
Learn how to compare uncertain outcomesNo. An option can have a higher average while containing a loss you cannot absorb. Apply hard limits first, compare tail exposure, and test whether a realistic probability change reverses the result.
Compare downside and upside rangesPrefer observed frequencies from comparable cases, documented base rates, or a transparent forecast. When evidence is weak, calculate a low and high probability rather than presenting one guess as precise.
Use base rates in a decision