Expected Value in Games

Probability · Axiom Academy

EXAMPLE Expected Value in Games Calculating expected winnings and determining if a game is fair Roll a fair six-sided die. Your winnings depend on the result: Excellent work! You've completed this expected value example. Here's what we learned: Expected Value Formula: E[X] = Σ x · P(X = x) gives the long-run average value of a random variable. Weighted Average: Expected value weighs each outcome by its probability, showing what you'd expect "on average" over many trials. Fair Game: A game is fair if the expected net winnings equal zero. If E[winnings] > cost, the game favors the player. Interpretation: E[W] = 1/3 means on average, you win about 0.33 per game. Since the cost is 1, you lose 0.67 per game on average. Understanding expected value helps you make informed decisions about games of chance and risk!

This is the written version of the interactive lesson above. See the full Probability course.