Dice games, part 1Discrete Mathematics Level 5
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?