In this article, we investigate the effects of the physical influence of a virtual human (VH) in the context of face-to-face interaction in a mixed reality environment. In Experiment 1, participants played a tabletop game with a VH, in which each player takes a turn and moves their own token along the designated spots on the shared table. We compared two conditions as follows: the VH in the virtual condition moves a virtual token that can only be seen through augmented reality (AR) glasses, while the VH in the physical condition moves a physical token as the participants do; therefore the VH's token can be seen even in the periphery of the AR glasses. For the physical condition, we designed an actuator system underneath the table. The actuator moves a magnet under the table which then moves the VH's physical token over the surface of the table. Our results indicate that participants felt higher co-presence with the VH in the physical condition, and participants assessed the VH as a more physical entity compared to the VH in the virtual condition. We further observed transference effects when participants attributed the VH's ability to move physical objects to other elements in the real world. Also, the VH's physical influence improved participants' overall experience with the VH. In Experiment 2, we further looked into the question how the physical-virtual latency in movements affected the perceived plausibility of the VH's interaction with the real world. Our results indicate that a slight temporal difference between the physical token reacting to the virtual hand's movement increased the perceived realism and causality of the mixed reality interaction. We discuss potential explanations for the findings and implications for future shared mixed reality tabletop setups.