Positive Expected Value Calculator

Expected Value Formula:

\[ EV = \sum (Probability \times Outcome) \]

Expected Value (EV):

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1. What is Expected Value?

Expected Value (EV) is a fundamental concept in probability theory that represents the average outcome of a random variable when the experiment is repeated many times. It calculates the long-term average of possible outcomes weighted by their probabilities.

2. How Does the Calculator Work?

The calculator uses the Expected Value formula:

\[ EV = \sum (Probability \times Outcome) \]

Where:

\( Probability \) — The likelihood of an event occurring (0 to 1)
\( Outcome \) — The value or result if the event occurs
\( \sum \) — Summation of all probability-outcome pairs

Explanation: For positive expected value calculations, this formula helps determine whether a decision or bet is favorable in the long run.

3. Importance of EV Calculation

Details: Calculating expected value is crucial for decision-making under uncertainty, risk assessment, investment analysis, gambling strategies, and business planning. A positive EV indicates a favorable long-term outcome.

4. Using the Calculator

Tips: Enter probability as a decimal between 0 and 1, and outcome in your preferred units. The calculator will compute the expected value, which represents the average outcome per trial over many repetitions.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive expected value mean?
A: A positive EV indicates that over many trials, you can expect to gain value on average. It suggests a favorable decision or investment.

Q2: How is EV used in real-world applications?
A: EV is used in finance for investment decisions, in insurance for premium calculations, in gambling for strategy development, and in business for risk assessment and decision-making.

Q3: Can EV be negative?
A: Yes, negative EV indicates an unfavorable outcome on average. It means you would expect to lose value over many repetitions.

Q4: What's the difference between EV and actual outcome?
A: EV is the theoretical average over infinite trials, while actual outcome is the result of a single trial. Short-term results may vary from the expected value.

Q5: How accurate is EV calculation for decision-making?
A: EV provides a mathematical framework for rational decision-making under uncertainty, but it assumes probabilities are accurate and doesn't account for risk tolerance or utility preferences.