# Rolling Higher

Roll a fair six-sided die until you roll a number that is less than one of your previous rolls. To three decimal places, what is the expected value of the number of rolls made?

Bonus: Suppose you rolled a fair $$n$$-sided die instead. What is the expected value of the number of rolls made?

Extra Bonus: As $$n \to \infty,$$ what does the expected value of the number of rolls approach?

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