"King of the Hill"

What does "can" mean? Are you playing hide-and-seek? Or maybe you won't get a chance at all, or you'll get one after 9 months and won't play 5 times in a row.
You'll like it when you get a chance, become the chip leader in terms of wins, and watch with wide eyes as another player gets a chance to win the tournament just because they had 5 times more access to King of the Hill games than you? Everyone should have the same number of chances, and how they use them should determine the winner.

You could offer all participants n number of chances (the number is the same, for example, 5). Then, if a player receives 5 chances, they go into a waiting group. The tournament continues randomly until everyone has used their chances. The player who has used their chances and surpassed the others in the number of wins becomes the King of the Hill.

This is just one of the ways to avoid the random selection of a winner. :)