So suppose we stand on a position(x0, y0) of a map. We can only move on the horizontal plane(no jump and stuff) but we can move forward, left, or right (in a discrete math way, i.e. integer movement).
As soon as we move to the next position(x1, y1), everything around us is generated randomly by a program. We could be surrounded by one of mountain, lake, and road. We can only move on the road. The road is always 2D as the map itself.
My question is, are we able to play this game endlessly? "End" means that we come across a dead end and the only way out is to go backward.