  This paper investigates the parity concept in knotoids in $S^2$ and in
$\mathbb{R}^2$ in relation with virtual knots. We show that the virtual closure
map is not surjective and give specific examples of virtual knots that are not
in the image. We introduce a planar version of the parity bracket polynomial
for knotoids in $\mathbb{R}^2$. By using the Nikonov/Manturov theorem on
minimal diagrams of virtual knots we prove a conjecture of Turaev showing that
minimal diagrams of knot-type knotoids have zero height.
