The Game of Chaos

Game of Chaos is a red sorcery in the oldest of all customizable card games: Magic, the Gathering, trademarked by the Wizards of the Coast inc. Successfully casting this spell enables the caster to engage the opponent player in a potentially unbounded series of coin-flip games about life. Initially the ante is one life. The winner decides to stop or to play a next round. However, for every next round the ante in lives is doubled. This will ensure that the game will be terminated as soon as the loser has his total amount of lives reduced to zero or lower, since terminating the game of chaos at this point yields immediate victory of the duel. Given the inherent symmetry of this game the question is whether it offers the caster any strategic advantage to play it. For every possible play which yields a positive outcome there is a corresponding play which yields the same outcome to his opponent. Consequently the utility value of this game should be zero. We invoke elementary game theory in order to illustrate how this theory does confirm this intuition. However, the same theory can also be invoked in different scenarios, like Thorgrim’s last stand where the utility value can be shown to be positive. The illustrations for this note are contained in the powerpoint presentation which is available in pdf format at the website of the first author. See The game of Chaos for 12 pages displaying the sheets presented at the 1999 Dutch Mathematical Conference