In Monster auf der Flucht, five monsters are escaping from their exploding home planet to find a new home, and each player will secretly be assigned one of these monsters to watch over and care for. At the end of the round, the monster farthest away from its home planet scores 0 points – it went a tad too far, mind you – while the second farthest monster scores 3 points, and the other monsters in order score 2, 1 and -1 points.