Expected Value Calculator
Probability-weighted average outcome
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Expected Value Calculator is built for probability-weighted average outcome — fast, free, and private. Just enter Outcomes (comma separated) and Probabilities (comma separated); Expected Value updates the result as you type. Every Expected Value answer can be reproduced by hand. Expected Value shines when speed matters. Nothing typed into Expected Value leaves your device or the tab. Expected Value sits in the Math section next to related tools and expected value calculator probability weighted average outcomes ev. The labels in Expected Value match the terms in its result. Expected Value is free, instant and local.
What does the Expected Value Calculator do?
Expected Value Calculator works out the expected value from the Outcomes and Probabilities, using Math conventions. With the defaults, expected value calculator gives an expected value of 23.0000.
- Inputs: Outcomes and Probabilities.
- Output: the expected value, plus the intermediate steps behind it.
- Method: the Math formula for the expected value, with each substitution shown.
Quick answer
expected value calculator returns an expected value of 23.0000 with the default inputs (outcomes of 10,20,30, probabilities of 0.2,0.3,0.5).
How does the Expected Value Calculator work?
Expected Value Calculator computes the expected value directly from your inputs — the Outcomes and Probabilities feed the formula. No server sees the inputs, so the expected value is computed on the device and keeps working offline.
How the Expected Value Calculator works
Short of doing the Math arithmetic yourself, Expected Value Calculator is the shortest path to a figure you can defend, because every term stays visible.
How to use it
- Outcomes — the field the rest of the expected value case hangs on; revisit it to move the figure.
- Probabilities — the value feeding the expected value formula directly — match it to your scenario first.
- Start at the result on Expected Value Calculator and work down through the intermediate lines; the first figure that disagrees with your expectation is the one to investigate.
- Rerun Expected Value Calculator with the Outcomes and Probabilities rounded up, then rounded down — the spread is what a single output hides.
The formula behind the result
The calculation in Expected Value Calculator applies the standard Math method, keeping full precision internally and rounding only the final display.
Worked example: with outcomes of 10,20,30, probabilities of 0.2,0.3,0.5, this expected value calculation returns Expected Value: 23.0000. The same run reports Each outcome × its probability, summed | Positive EV favours repeating the bet; negative EV does not.
The steps it follows:
- Formula: EV = Σ outcomeᵢ × probabilityᵢ
- Products: 10×0.2=2.0000, 20×0.3=6.0000, 30×0.5=15.0000
- Sum = 23.0000
- Long-run average per trial — individual outcomes still vary around it
Understanding the result
The expected value answers "what follows from these inputs", and the intermediate lines under it answer "how" — Expected Value Calculator keeps the two side by side on purpose.
Where it helps
Where Expected Value Calculator earns its keep: revisiting a decision with new figures, checking the same case a different way, and spot-checking a quoted figure, and the smaller questions that sit around them.
Common mistakes
Rounding intermediate values by hand introduces error Expected Value Calculator does not have; it keeps full precision internally, so trust the displayed figure over mental arithmetic.
Tip: The expected value page keeps your last inputs in the URL, so a reload restores the result instead of an empty form.
Assumptions and limitations
Expected Value Calculator answers the arithmetic and stops there — it cannot tell whether the Outcomes and Probabilities you supplied describe a realistic case.
Why use this calculator
Because a wrong answer is easy to catch: the steps on the expected value page show where a mistyped value entered the result, which a bare result never reveals.
Frequently Asked Questions
What does expected value calculator compute?
Expected Value Calculator answers one question well — given the values you provide, what is the output? Enter the Outcomes and Probabilities, and the result panel returns the value with the full working underneath. Because the Math conventions are stated rather than assumed, Expected Value Calculator removes the guesswork about which method produced the result.
Where does the expected value come from?
The first steps are formula: ev = σ outcomeᵢ × probabilityᵢ, then products: 10×0.2=2.0000, 20×0.3=6.0000, 30×0.5=15.0000. Expected Value Calculator treats the formula as a sequence rather than a black box — every operator is printed with the values it consumed on the way to the expected value.
Does Expected Value Calculator need anything besides its fields?
Only Outcomes and Probabilities — with the expected value following at once.
What does the result from the Expected Value Calculator mean?
The main number the expected value calculator returns is the expected value for your exact inputs. Zero is treated as a real value throughout Expected Value Calculator, so a field left at zero changes the output rather than being skipped.
In which situations does the page help?
The expected value page comes up most for revisiting a decision with new figures, checking the same case a different way, and spot-checking a quoted figure — the recurring cases where a rough mental estimate tends to be off by enough to matter. Keep one tab on Expected Value Calculator while you compare quotes — switching inputs is faster than rebuilding the same calculation elsewhere.
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