  We study Manneville-Pomeau maps on the unit interval and prove that the set
of points whose forward orbits miss an interval with left endpoint 0 is strong
winning for Schmidt's game. Strong winning sets are dense, have full Hausdorff
dimension, and satisfy a countable intersection property. Similar results were
known for certain expanding maps, but these did not address the nonuniformly
expanding case. Our analysis is complicated by the presence of infinite
distortion and unbounded geometry.
