  We consider a quantum version of a well-known statistical decision problem,
whose solution is, at first sight, counter-intuitive to many. In the quantum
version a continuum of possible choices (rather than a finite set) has to be
considered. It can be phrased as a two person game between a player P and a
quiz master Q. Then P always has a strategy at least as good as in the
classical case, while Q's best strategy results in a game having the same value
as the classical game. We investigate the consequences of Q storing his
information in classical or quantum ways. It turns out that Q's optimal
strategy is to use a completely entangled quantum notepad, on which to encode
his prior information.
