You have a State Lotto machine into which N ping pong balls have been placed.
Each ball is numbered with one of the first N primes. Each time you press the button, one more randomly chosen ball appears in the output tray.
Your score is the mean of the numbers displayed on the balls chosen so far.
Your goal is to maximize your score by choosing when to stop pressing the button.

What is the optimal strategy?
For your strategy, what is the ratio of the expected value of your score to the average of the first N primes?

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