When attempting to persuade an agent to believe (or disbelieve) an argument, it can be advantageous for the persuader to have a model of the persuadee. Models have been proposed for taking account of what arguments the persuadee believes and these can be used in a strategy for persuasion. However, there can be uncertainty as to the accuracy of such models. To address this issue, this paper introduces a two-dimensional model that accounts for the uncertainty of belief by a persuadee and for the confidence in that uncertainty evaluation. This gives a better modeling for using lotteries so that the outcomes involve statements about what the user believes/disbelieves, and the confidence value is the degree to which the user does indeed hold those outcomes (and this is a more refined and more natural modeling than found in [19]). This framework is also extended with a modelling of the risk of disengagement by the persuadee.