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Problem of the Day #170: A Card Game September 5, 2011

Posted by Alex in : potd , trackback

Sreenath is playing a card game by himself. He randomly shuffles the standard $52$-card deck and then picks $4$ at random to be in his hand. Every second, Sreenath will add a random card from the deck into his hand and then discard cards until he only has $4$ cards left. Assuming Sreenath discards optimally to minimize game time, what is the expected time Sreenath will be playing the game?

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