Jeffery and Bad Dice

Define a bad dice to be a fair dice with 13 sides numbered 1 through 13, inclusive. (That is, each of the 13 sides lands with equal probability). When Jeffery rolls a bad dice 37 times, compute the expected value of the maximum value of these 37 rolls.

Note: You may use a calculator, and round your answer to at least 3 decimal places.

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