Interactive programs allow users to engage in input and output throughout execution. The ubiquity of such programs motivates the development of models for reasoning about their information-flow security, yet no such models seem to exist for imperative programming languages. Further, existing language-based security conditions founded on non-interactive models permit insecure information flows in interactive imperative programs. This paper formulates new strategy-based information-flow security conditions for a simple imperative programming language that includes input and output operators. The semantics of the language enables a fine-grained approach to the resolution of nondeterministic choices.