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n uniform random values are revealed one at a time and you must guess each one's final rank as it appears. What is the best strategy, and how likely are you to get them all right?

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n iid Uniform(0,1) values x_1, ..., x_n are revealed one at a time. As each x_i is revealed you must immediately guess its final rank r_i among all n values, having seen only x_1..x_i. You win only if every guess is right. What is the optimal strategy and what is the probability of winning?

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