We consider the existence of coherent families of finite-to-one functions on countable subsets of an uncountable cardinal $\kappa$. The existence of such families for $\kappa$ implies the existence of a winning 2-tactic for player TWO in the countable-finite game on $\kappa$. We prove that coherent families exist on $\kappa = \omega_n$, where $n \in \omega$, and that they consistently exist for every cardinal $\kappa$. We also prove that iterations of Axiom A forcings with countable supports are Axiom A.