  A game in which one player makes unitary transformations of a simple system,
and another seeks to confound the resulting state by a randomly chosen action
is analyzed carefully. It is shown that the second player can reduce any system
to a completely random one by rotation through an angle of 120 degrees, about
an axis chosen at random. If, on the other hand, the second player is forced to
behave ``classically'' by reducing the wave function, then the first play
retains an advantage, which the second player may eliminate by repeated
measurement using randomly selected bases.
