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Open containers, i.e., containers without covers, are an important and ubiquitous class of objects in human life. In this letter, we propose a novel method for robots to "imagine" the open containability affordance of a previously unseen object via physical simulations. We implement our imagination method on a UR5 manipulator. The robot autonomously scans the object with an RGB-D camera. The scanned 3D model is used for open containability imagination which quantifies the open containability affordance by physically simulating dropping particles onto the object and counting how many particles are retained in it. This quantification is used for open-container vs. non-open-container binary classification (hereafter referred to as open container classification). If the object is classified as an open container, the robot further imagines pouring into the object, again using physical simulations, to obtain the pouring position and orientation for real robot autonomous pouring. We evaluate our method on open container classification and autonomous pouring of granular material on a dataset containing 130 previously unseen objects with 57 object categories. Although our proposed method uses only 11 objects for simulation calibration (training), its open container classification aligns well with human judgements. In addition, our method endows the robot with the capability to autonomously pour into the 55 containers in the dataset with a very high success rate. We also compare to a deep learning method. Results show that our method achieves the same performance as the deep learning method on open container classification and outperforms it on autonomous pouring. Moreover, our method is fully explainable.