  We give a new proof of the theorem of Boesch-Tindell and
Farzad-Mahdian-Mahmoodian-Saberi-Sadri that a directed graph extends to a
strongly connected digraph on the same vertex set if and only if it has no
complete directed cut. Our proof bounds the number of edges needed for such an
extension; we give examples to demonstrate sharpness. We apply the
characterization to a problem on non-transitive dice.
