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While researchers have looked at many aspects of argumentation, an area often neglected is that of argumentation strategies. That is, given multiple possible arguments that an agent can put forth, which should be selected in what circumstances. In this paper, we propose a heuristic that implements one such strategy. The heuristic assigns a utility cost to revealing information, as well as a utility to winning, drawing and losing an argument. An agent participating in a dialogue then attempts to maximise its utility. We present a formal argumentation framework in which this heuristic may operate, and show how it functions within the framework. Finally, we discuss how this heuristic may be extended in future work, and its relevance to argumentation theory in general.