  In this paper we study connections between topological games such as
Rothberger, Menger and compact-open, and relate these games to properties
involving covers by G_{\delta} subsets. The results include: (1) If Two has a
winning strategy in the Menger game on a regular space X, then X is an Alster
space. (2) If Two has a winning strategy in the Rothberger game on a
topological space X, then the G_\delta-topology on X is Lindelof. (3) The
Menger game and the compact-open game are (consistently) not dual.
