In the cultural controversy surrounding "violent video games," the manufacturers and players of games often insist that computer games are a form of harmless entertainment that is unlikely to influence the real-world activities of players. Yet games and military simulations are used by military organizations across the world to teach the modern arts of war, from how to shoot a gun to teamwork, leadership skills, military values, and cultural sensitivity. We survey a number of ways of reconciling these apparently contradictory claims and argue that none of them are ultimately successful. Thus, either military organizations are wrong to think that games and simulations have a useful role to play in training anything other than the most narrowly circumscribed physical skills or some recreational digital games do, in fact, have the power to influence the real-world behavior and dispositions of players in morally significant ways.