Expected value is the probability-weighted average of all possible outcomes. The Expected Value Calculator computes it from outcomes and their probabilities, then reports the single average result you can use for decision-making.
Use it for games, risk analysis, pricing, and any situation where you know (or can estimate) how likely each outcome is. This article explains the formula, the meaning of each variable, and how to apply it correctly.
What “Expected Value” Means
Expected value (EV) summarizes the average result of a random process if you repeat it many times. It does not predict what will happen next. Instead, it tells you the long-run average outcome.
Mathematically, EV is a weighted mean: each outcome is multiplied by its probability, and all those products are added.
Expected Value Formula (Core Concept)
For a discrete set of outcomes, expected value is:
EV = Σ (xᵢ · pᵢ)
- xᵢ = outcome value (what you get)
- pᵢ = probability of that outcome
- Σ = “sum across all outcomes”
Probabilities must be non-negative and should sum to 1. If you enter percentages, the calculator converts them to probabilities.
Units and Interpretation
The expected value has the same unit as the outcomes. For example:
- Outcomes in dollars → EV in dollars
- Outcomes in points → EV in points
- Outcomes in minutes → EV in minutes
That is why you should enter outcomes with clear units. The calculator helps keep your results consistent.
How to Use the Expected Value Calculator
The calculator computes EV from a list of outcomes and their probabilities. You can enter probabilities either as decimals (like 0.25) or percentages (like 25%).
- Enter each outcome value.
- Enter the corresponding probability for that outcome.
- Choose the probability format: decimal or percent.
- Click Calculate to get the expected value.
If your probabilities do not sum to 1 (or 100%), the calculator will alert you so you can correct the inputs.
Common Pitfalls (And How to Avoid Them)
- Forgetting to normalize probabilities: If your probabilities don’t add to 1 (or 100%), the EV will be wrong.
- Mixing units: Outcome values must be in the same unit. Convert before you calculate.
- Using probabilities that don’t match outcomes: Each probability must correspond to the outcome on the same row.
- Assuming EV is guaranteed: EV is an average over many repeats, not a prediction of the next result.
Practical Examples
Example 1: Expected Profit in a Simple Game
Suppose a game pays either $10, $0, or -$5. The probabilities are 40%, 30%, and 30% respectively. The expected value is:
EV = 10·0.40 + 0·0.30 + (-5)·0.30 = 4 + 0 – 1.5 = $2.50
So, over many plays, you’d average a profit of $2.50 per game.
Example 2: Choosing Between Two Options
A decision-maker compares two offers:
- Option A: $100 with probability 0.2, otherwise $0
- Option B: $30 with probability 1 (guaranteed)
EV(A) = 100·0.2 + 0·0.8 = $20. EV(B) = 30·1 = $30. Even though Option A has a chance of a bigger payout, Option B has the higher expected value.
Expected Value vs. Other Averages
Expected value is not the same as a simple average unless all probabilities are equal. For example, if one outcome is much more likely, EV will be pulled toward it.
- Simple average: treats each outcome equally.
- Expected value: weights outcomes by how likely they are.
That probability weighting is the key difference.
Frequently Asked Questions
What is an expected value calculator used for?
An Expected Value Calculator computes the probability-weighted average of outcomes for a random process. It helps you combine multiple possible results into one number, which supports decisions, pricing, and risk comparisons when outcomes have different likelihoods.
Do probabilities have to add up to 1?
Yes. For expected value, probabilities must be non-negative and sum to 1 (or 100% if you enter percentages). If they do not, the weighted average is not properly normalized, and the expected value result will be misleading.
Is expected value the same as the most likely outcome?
No. The expected value is the long-run average across many repeats. The most likely outcome is the single result with the highest probability, which may differ from EV when probabilities and outcome magnitudes vary.
How do I interpret a negative expected value?
A negative expected value means the average outcome is a loss over many repeats. Even if some outcomes are positive, the negative outcomes (or their higher probabilities) outweigh them in the long-run weighted average.
Can expected value be used for real-life decisions?
Yes. Expected value is widely used for comparing choices under uncertainty, such as expected profit, expected cost, insurance pricing logic, and inventory or scheduling trade-offs. It works best when you can estimate probabilities for outcomes.
Bottom Line
The Expected Value Calculator gives you one clear number: the long-run average outcome. Enter outcomes and their probabilities, ensure the probabilities are consistent, and use the result to compare options or quantify average gain or loss.