Mimicry plays an important role in social interaction. In human communication, it is used to establish rapport and bonding both with other humans, as well as robots and virtual characters. However, little is known about the underlying factors that elicit mimicry in humans when interacting with a robot. In this work, we study the influence of embodiment on participants' ability to mimic a social character. Participants were asked to intentionally mimic the laughing behavior of the Furhat mixed embodied robotic head and a 2D virtual version of the same character. To explore the effect of embodiment, we present two novel approaches to automatically assess people's ability to mimic based solely on videos of their facial expressions. In contrast to participants' self-assessment, the analysis of video recordings suggests a better ability to mimic when people interact with the 2D embodiment.