Dice games, part 1

Alivia and Bavid are playing a game.

  • 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?

Image Credit: Flickr Lo8i.

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