The Game of Chaos

Peter van Emde Boas

ILLC-WINS-Univ. of Amsterdam
Plantage Muidergracht 24
1018 TV Amsterdam
the Netherlands

Evert van Emde Boas

Lord Trevor Productions
Franz Lisztlaan 5
2102 CJ Heemstede
the Netherlands


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.

Further Information

Suggested topic for a future class of Johan on Games and the illogical ...
Evidence of the relevance of game theory for contemporary computer science is illustrated on sheet STACS'99 (TRIER).


Bibtex Entry