  The Hilbert space of three-qubit pure states may be identified with a
Freudenthal triple system. Every state has an unique \emph{Freudenthal rank}
ranging from 1 to 4, which is determined by a set of automorphism group
covariants. It is shown here that the optimal success rates for winning a
three-player non-local game, varying over all local strategies, are strictly
ordered by the Freudenthal rank of the shared three-qubit resource.
