  An open question of Gruenhage asks if all strategically selectively separable
spaces are Markov selectively separable, a game-theoretic statement known to
hold for countable spaces. As a corollary of a result by Berner and
Juh$\acute{a}$sz, we note that the strong version of this statement, where the
second player is restricted to selecting single points in the rather than
finite subsets, holds for all $T_3$ spaces without isolated points. Continuing
this investigation, we also consider games related to selective sequential
separability, and demonstrate results analogous to those for selective
separability. In particular, strong selective sequential separability in the
presence of the Ramsey property may be reduced to a weaker condition on a
countable sequentially dense subset. Additionally, $\gamma$- and $\omega$-
covering properties on $X$ are shown to be equivalent to corresponding
sequential properties on $C_p(X)$. A strengthening of the Ramsey property is
also introduced, which is still equivalent to $\alpha_2$ and $\alpha_4$ in the
context of $C_p(X)$.
