From The Null Set

Trianglia is a jacked-up island where no road has a dead end, and all the crossroads are "Y" shaped. The young prince of Trianglia mounts his horse, and is about to go on a quest to explore the land of Trianglia. He gets to the road by his palace, when the mother queen comes out and shouts: "But Charles, how will you find your way back?". "Don't worry Elizabeth", the prince replies, "I will turn right in every second crossroad to which I arrive, and left otherwise. Thus I shall surely return to the palace sooner or later." Is the prince right?