Summary: We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price \(\pi\) is given by the supremum over the prices of the American option under randomized models. That is, \(\pi =\sup_{(c_i,Q_i)_i}\sum_ic_i\phi^{ Q_i}\), where \(c_i \in \mathbb{R}_+\) and the martingale measure \(Q^i\) are chosen such that \(\sum_ic_i=1\) and \(\sum_ic_iQ_i\) prices the European options correctly, and \(\phi^{Q_i}\) is the price of the American option under the model \(Q_i\). Our result generalizes the example given in [D. Hobson and A. Neuberger, “More on hedging American options under model uncertainty”, Preprint, arXiv:1604.0227] that the highest model-based price can be considered as a randomization over models.