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Difficulty: Hard
Category: Conditional Expected Value
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Topics: probability, expected-value, mental-math, conditional-probability
You are given a fair six-sided die. You roll it once. You have the option to pay $1 to reroll the die. You can reroll as many times as you want. What is the optimal strategy to maximize your expected value, and what is the expected value of this game? - You must decide on a stopping rule (e.g., stop if the roll is greater than or equal to X). - Assume the expected value of a fair six-sided die is $3.5$. - The cost of each reroll is $1.
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