  We show a geometric formulation for minimum-error discrimination of qubit
states, that can be applied to arbitrary sets of qubit states given with
arbitrary a priori probabilities. In particular, when qubit states are given
with equal \emph{a priori} probabilities, we provide a systematic way of
finding optimal discrimination and the complete solution in a closed form. This
generally gives a bound to cases when prior probabilities are unequal. Then, it
is shown that the guessing probability does not depend on detailed relations
among given states, such as angles between them, but on a property that can be
assigned by the set of given states itself. This also shows how a set of
quantum states can be modified such that the guessing probability remains the
same. Optimal measurements are also characterized accordingly, and a general
method of finding them is provided.
