Let's assume there are two players in a dice game; zombie and hero.
The Zombie rolls z fair 6-sided dice.
The Hero rolles h fair 6-sided dice.
If the heroes greatest dice roll is larger than the zombie's greatest dice roll, the hero wins. Otherwise, the zombie wins.
How can I calculate the probability of the hero winning as a function of z and h (without just enumerating the answers).
Example 1: z = 1, h = 2
Zombie rolls (4), hero rolls (1,5). Hero has a higher dice roll and wins.
Example 2: z = 2, h = 2
Zombie rolls (4,4), hero rolls (1,4). Hero does not have a higher dice roll and loses.