Expectations

A game costs $150 to play. In this game, you roll a fair six-sided die until all six numbers have been rolled at least once. You are then paid 10 times the number of rolls you made.

For example, if the rolls were 3, 5, 4, 3, 2, 5, 1, 4, 1, 3, 6, then you would get \((10)(11) = 110\) dollars.

Including the price to play, what is your expected value in this game?

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