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You are given a die with 100 sides. One side has 1 dot, one has 2 dots and so on up until 100. You are given a chance to roll the die and, however many dots come up, you can choose to (a): take that many dollars, or (b): pay $1 and roll again. You can continue to reroll as many times as you see fit, but you only keep the money of the one roll that you choose to end with. What is the optimal strategy and expected value?
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Assistant Trader

Interviewed at Jane Street

4.4★
Jun 8, 2014

You are given a die with 100 sides. One side has 1 dot, one has 2 dots and so on up until 100. You are given a chance to roll the die and, however many dots come up, you can choose to (a): take that many dollars, or (b): pay $1 and roll again. You can continue to reroll as many times as you see fit, but you only keep the money of the one roll that you choose to end with. What is the optimal strategy and expected value?

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