  We show that the $\mathbb{Z}/2$-equivariant Morava K-theories with reality
(as defined by Hu) are self-dual with respect to equivariant Anderson duality.
In particular, there is a universal coefficients exact sequence in Morava
K-theory with reality. As a particular example, we recover the self-duality of
the spectrum $KO$. The study of $\mathbb{Z}/2$-equivariant Anderson duality
made in this paper gives a nice interpretation of some symmetries of
$RO(\mathbb{Z}/2)$-graded (i.e. bigraded) equivariant cohomology groups in
terms of Mackey functor duality.
