  We prove that the set of bounded geodesics in Teichmuller space are a winning
set for Schmidt's game. This is a notion of largeness in a metric space that
can apply to measure 0 and meager sets. We prove analogous closely related
results on any Riemann surface, in any stratum of quadratic differentials, on
any Teichmuller disc and for intervals exchanges with any fixed irreducible
permutation.
