You are trying to make an impossible game where there are $100$ balls numbered from $1$ to $100$ and ordered in the worst case and put next to each other. The player is supposed to order the balls from $1$ to $100$ with the simple rule you are going to assign:
The player can switch two balls location if there is at least $x$ amount of balls between these two balls.
What should be the least $x$ value to make the player not able to win this game in the worst ordered form possible? So the player may think it is a fair game.