🔍 /

Expected Value (EV) Calculator

Calculate the weighted average of probabilistic outcomes. Essential for risk management, poker strategy, and investment analysis. Includes Variance and Standard Deviation.

User Rating 0.0 ★★★★★
Total Usage 6 times
Category Statistics & Probability
Outcome Value (x)Probability (P)
Is this tool helpful?

Your feedback helps us improve.

★ ★ ★ ★ ★

About

Expected Value (EV) is a fundamental concept in statistics used to determine the long-term average value of a random variable. It is widely used in finance to assess the profitability of investments and in game theory (such as Poker) to make mathematically sound decisions.

A positive EV (+EV) implies that a decision is profitable in the long run, while a negative EV (-EV) suggests a loss. This tool calculates the mean, but also the Variance and Standard Deviation, providing insight into the volatility or "risk" associated with the scenario.

expected value probability statistics risk management EV calculator

Formulas

For a discrete random variable X having outcomes x1, x2, ... with probabilities p1, p2, ... :

E[X] = p1x1 + p2x2 + ... + pnxn

Constraint:

∑ pi = 1 (or 100%)

Reference Data

MetricSymbolFormula
Expected Valuex (μ)∑ [P(x) × x]
Varianceσ2∑ [P(x) × (x − μ)2]
Standard Deviationσ√Variance

Frequently Asked Questions

Yes. The tool accepts decimals (0.5) or percentages (50). It automatically normalizes them.
Variance measures how spread out the possible outcomes are. A high variance means the actual result often deviates significantly from the Expected Value (high risk), while low variance means outcomes are predictable.
For a complete probability model, the sum of all possible outcomes must equal 100%. If it is less, there are unaccounted scenarios. If more, the model is invalid.