  The task of state discrimination for a set of mutually orthogonal pure states
is trivial if one has access to the corresponding sharp (projection-valued)
measurement, but what if we are restricted to an unsharp measurement? Given
that any realistic measurement device will be subject to some noise, such a
problem is worth considering. In this paper we consider minimum error state
discrimination for mutually orthogonal states with a noisy measurement. We show
that by considering repetitions of commutative L\"uders measurements on the
same system we are able to increase the probability of successfully
distinguishing states. In the case of binary L\"uders measurements we provide a
full characterisation of the success probabilities for any number of
repetitions. This leads us to identify a 'rule of three', where no change in
probability is obtained from a second measurement but there is noticeable
improvement after a third. We also provide partial results for $N$-valued
commutative measurements where the rule of three remains, but the general
pattern present in binary measurements is no longer satisfied.
