1. What is Expected Value?

The Expected Value (EV) is a concept in probability that calculates the average outcome when an experiment is repeated multiple times. It helps in decision-making by quantifying the potential value of different options.

2. How Does the Calculator Work?

The calculator uses the Expected Value formula:

Where:

• \( Probability \) — The chance of the outcome occurring (0 to 1)
• \( Outcome \) — The value gained if the event occurs
• \( Cost \) — The investment or expense required

Explanation: The formula multiplies the probability of an event by its potential outcome, then subtracts the cost to determine the net expected value.

3. Importance of EV Calculation

Details: Expected Value is crucial for risk assessment, investment decisions, game theory, and any scenario requiring quantitative comparison of probabilistic outcomes.

4. Using the Calculator

Tips: Enter probability as a decimal between 0 and 1, outcome and cost in consistent units. All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What does a negative EV mean?
A: A negative EV suggests the proposition is unfavorable on average - the expected costs outweigh the expected benefits.

Q2: How is EV different from actual value?
A: EV represents the long-term average if the scenario is repeated many times, while actual value is the result of a single trial.

Q3: When should I use EV calculations?
A: Use EV when comparing different options with uncertain outcomes, such as investments, business decisions, or game strategies.

Q4: What are the limitations of EV?
A: EV doesn't account for risk tolerance or the variability of outcomes. Two options with the same EV might have very different risk profiles.

Q5: Can EV be used for multiple outcomes?
A: Yes, for multiple outcomes you would sum the EVs of each possible outcome (probability × value for each outcome).