  In this paper we review the combinatorics of the twisted sectors of
$\mathcal{M}_{g,n}$, and we exhibit a formula for the age of each of them in
terms of the combinatorial data. Then we show that orbifold cohomology of
$\mathcal{M}_{g,n}$ when $g \to \infty$ reduces to its ordinary cohomology. We
do this by showing that the twisted sector with minimal age is always the
hyperelliptic twisted sector with all markings in the Weierstrass points; the
age of the latter moduli space is just half its codimension in
$\mathcal{M}_{g,n}$.
