Alivia and Bavid are playing a game.
###### Image Credit: Flickr Lo8i.

Alivia rolls two fair

*n*-sided dice. She chooses the greater of the two numbers shown on the dice and adds 5.Bavid rolls three fair

*n*-sided dice. He chooses the greatest of the three numbers shown on the dice.

What is the least positive integer *n* such that the expected value of Bavid's number is **greater** than the expected value of Alivia's number?

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