Bumpers

Bumpers is a combination strategy/arcade game. Basically, you are given a maze, but you can't see the walls until you (or your opponent) touch them. You start out in the upper left corner, and your opponent starts in the lower right corner. You have reach his start point before he reaches yours to win the game. The mazes are randomly generated each time, so you can't memorize a trail to win.

It is also worth noting that the game actually prompts you for the size of the maze... if you create small mazes, the game is not hard at all, but with high X/Y size counts (say, 15x15) it becomes quite difficult.