 It is easy to travel either way between Amsterdam and the German town of Saarbruecken. Now, let a malevolent Demon start canceling connections in the network. At every stage, let the Demon take out one link, while the Traveler can afterwards follow one of the remaining links. This turns a one-agent planning problem into a two-player sabotage game. Zermelo-style reasoning shows that, from Saarbruecken, a German Traveler still has a winning strategy, while in Amsterdam, the Demon has the winning strategy against the Dutch Traveler, by first cutting a link close to Saarbruecken. The symmetry of the original search problem is broken.