  For a given ensemble of $N$ independent and identically prepared particles,
we calculate the binary decision costs of different strategies for measurement
of polarised spin 1/2 particles. The result proves that, for any given values
of the prior probabilities and any number of constituent particles, the cost
for a combined measurement is always less than or equal to that for any
combination of separate measurements upon sub-ensembles. The Bayes cost, which
is that associated with the optimal strategy (i.e., a combined measurement) is
obtained in a simple closed form.
