Minimax Box

Hard

Probability

You have 2 boxes and 100 distinct cards numbered 1−1001-100. At each turn, you deal a card from the top of the deck and place the card in a box uniformly at random. What is the expected value of the smallest numbered card in the box that has card 100100 in it? The answer is in the form a(1−a−b)a(1-a^{-b}) for integers aa and bb. Find abab.

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Expected Value

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Minimax Box

Hard

Probability

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