Let D1 and D2 be two dice with k and l integer faces, respectively, where k and l are two positive integers. The game Gn consists of tossing each die n times and summing the resulting faces. The die with the higher total wins the game. We examine the question of which die wins game Gn more often, for large values of n. We also give an example of a set of three dice which is non-transitive in game Gn for infinitely many values of n.