Expected Value and Fair Games

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What is Expected Value?

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Expected Value (EV) is a calculated average of all possible outcomes of a random event, weighted by their probabilities. It represents the long-term average if the event were repeated many times.

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How is Expected Value calculated?

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Expected Value is calculated by multiplying each possible outcome by its probability and summing all these products.

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What does a positive Expected Value indicate?

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A positive Expected Value indicates that, on average, a player can expect to win money over time.

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What does a negative Expected Value indicate?

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A negative Expected Value indicates that, on average, a player can expect to lose money over time.

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What is the Expected Value of a fair game?

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In a fair game, the Expected Value is zero, meaning players neither gain nor lose money in the long run.

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What is the Expected Value in a lottery game?

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The Expected Value in a lottery game is the average amount of money a player can expect to win or lose from a single ticket.

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What is a fair game?

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A fair game is one where the Expected Value is zero, meaning the average outcome is neither a win nor a loss.

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How does probability affect Expected Value?

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Probability directly influences Expected Value; higher probabilities of winning increase the Expected Value.

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What is the formula for Expected Value?

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The formula for Expected Value is EV = Σ (Outcome × Probability) for all possible outcomes.

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What is an example of calculating Expected Value?

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If a game has outcomes of $10 (with a probability of 0.1) and $0 (with a probability of 0.9), the EV = (10 * 0.1) + (0 * 0.9) = $1.