Jane Street–styleTrader InternQuant Trader InternQuestion #305

You are playing a game in which you roll a fair 6-sided die. If you roll n, you get n dollars. How much would you pay for this game? Suppose you may reroll if you're not satisfied with the first roll, but must accept the result of the second roll. Now, how much would you pay for the game? What if you can reroll up to two times? How much would you pay?

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