Expected Value

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What is Expected Value?

Back

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

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How do you calculate Expected Value?

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To calculate Expected Value, multiply each possible outcome by its probability and sum all these products: EV = Σ (Outcome × Probability).

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What does it mean if the Expected Value is negative?

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

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What is the Expected Value of a fair six-sided die roll?

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The Expected Value of rolling a fair six-sided die is 3.5, calculated as (1+2+3+4+5+6)/6.

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In the context of gambling, what does a positive Expected Value indicate?

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A positive Expected Value suggests that the game is favorable to the player, meaning they can expect to win money over time.

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What is a probability distribution?

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A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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How does the Expected Value relate to real-life outcomes?

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The Expected Value is a theoretical average; actual outcomes may vary significantly in the short term due to randomness.

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What is the Expected Value of betting $6 on red in roulette?

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The Expected Value of betting $6 on red in roulette is -$0.32, indicating an average loss per bet.

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What is the formula for Expected Value in a discrete probability distribution?

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EV = Σ (x * P(x)), where x is each outcome and P(x) is the probability of that outcome.

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What is the Expected Value of a random variable with outcomes 50, 20, and 5 with probabilities 0.1, 0.3, and 0.6 respectively?

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The Expected Value is 14, calculated as (50*0.1) + (20*0.3) + (5*0.6).