Fair Price of a Squared Roll
You pay an entry fee to play the following game: a fair six-sided die is rolled once, and you receive k² dollars, where k is the face shown. What entry fee makes the game fair, meaning your expected net gain is exactly zero? Give the exact value in dollars as a reduced fraction (a decimal rounded to two places is also accepted).
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Source: Standard expected-value exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.