  Often, a given selection game studied in the literature has a known dual
game. In dual games, a winning strategy for a player in either game may be used
to create a winning strategy for the opponent in the dual. For example, the
Rothberger selection game involving open covers is dual to the point-open game.
This extends to a general theorem: if $\{\operatorname{ran}{f}:f\in\mathbf
C(\mathcal R)\}$ is coinitial in $\mathcal A$ with respect to $\subseteq$,
where $\mathbf C(\mathcal R)=\{f\in(\bigcup\mathcal R)^{\mathcal
R}:R\in\mathcal R\Rightarrow f(R)\in R\}$ collects the choice functions on the
set $\mathcal R$, then $G_1(\mathcal A,\mathcal B)$ and $G_1(\mathcal
R,\neg\mathcal B)$ are dual selection games.
