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Fifty ranked players play winner-stays-on at one table, and the higher number always wins. What is the probability that player 49 is still in after the first 10 rounds?

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Fifty players numbered 1-50 share one table; the higher number always wins. Two players are chosen at random to start, the loser is eliminated, and the winner stays on to face a randomly chosen new opponent, and so on. What is the probability that player 49 is still in the tournament after the first 10 rounds?

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