  Player ONE chooses a meager set and player TWO, a nowhere dense set per
inning. They play $\omega$ many innings. ONE's consecutive choices must form a
(weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense
sets covers the union of the chosen meager sets. A strategy for TWO which
depends on knowing only the uncovered part of the most recently chosen meager
set is said to be a remainder strategy. Theorem (among others): TWO has a
winning remainder strategy for this game played on the real line with its usual
topology.
