The Game of Chaos
Peter van Emde
Boas
ILLC-WINS-Univ.
of Amsterdam
Plantage Muidergracht
24
1018 TV Amsterdam
the Netherlands
peter@wins.uva.nl
http://www.wins.uva.nl/~peter
Evert van Emde
Boas
Lord Trevor
Productions
Franz Lisztlaan
5
2102 CJ Heemstede
the Netherlands
Abstract
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).
THOSE WERE THE DAYS
Dvi-file
PS-File
PDF-File
Bibtex
Entry
