Abstract This paper deals with the issue of strategic argumentation in the setting of Dung-style abstract argumentation theory. Such reasoning takes place through the use of opponent models—recursive representations of an agent’s knowledge and beliefs regarding the opponent’s knowledge. Using such models, we present three approaches to reasoning. The first directly utilises the opponent model to identify the best move to advance in a dialogue. The second extends our basic approach through the use of quantitative uncertainty over the opponent’s model. The final extension introduces virtual arguments into the opponent’s reasoning process. Such arguments are unknown to the agent, but presumed to exist and interact with known arguments. They are therefore used to add a primitive notion of risk to the agent’s reasoning. We have implemented our models and we have performed an empirical analysis that shows that this added expressivity improves the performance of an agent in a dialogue.