# 100-sided die probability

The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the expected value of the game? There is no limit on number of rolls.

The EV for a 100-sided die roll is 50.5, but the fact that you can pay a dollar for an extra roll complicates things. Not quite sure how to proceed.

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