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Expected Value Calculator

Math Calculators

E(X), variance, standard deviation

Quick Answer

Expected Value Calculator: E(X), variance, standard deviation. Expected Value Calculator uses standard math formulas to compute accurate results instantly.

E[X] = Σ xᵢ·pᵢ
25
Favorable game (positive EV)
E[X²]6250
Variance Var(X)5625
Std dev σ75
Σp1

Calculation steps

  1. 1E[X] = 100×0.5 + -50×0.5
  2. 2E[X] = 25
  3. 3E[X²] = Σ xᵢ²·pᵢ = 6250
  4. 4Var(X) = E[X²] − (E[X])² = 6250 − 625 = 5625

Classic expected values

GameE[X]Verdict
Fair coin ±10Fair
Dice roll3.5—
Roulette single number ($1)−$0.053House edge 5.3%
Typical lottery≈ −50% of ticket
Insurance premiumNegative for buyer (by design)
💡 Expected value is a LONG-RUN average, not a prediction for a single play. A −$0.05 EV roulette bet means losing ~5 cents per dollar ON AVERAGE over thousands of spins — any single night you might win big. But the law of large numbers makes the casino's profit a mathematical certainty.

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How to Use

  1. Enter values or expressions: type directly into the Expected Value Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Expected Value Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: E(X), variance, standard deviation.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Expected Value Calculator formula

Expected Value Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Expected Value Calculator?
Open the page and fill in the input fields — results update automatically. E(X), variance, standard deviation.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Expected Value Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/expected-value

Results provided by this tool are for reference only and do not constitute professional advice.