Future robots may need lighthearted physical interaction capabilities to connect with people in meaningful ways. To begin exploring how users perceive playful human–robot hand-to-hand interaction, we conducted a study with 20 participants. Each user played simple hand-clapping games with the Rethink Robotics Baxter Research Robot during a 1-h-long session involving 24 randomly ordered conditions that varied in facial reactivity, physical reactivity, arm stiffness, and clapping tempo. Survey data and experiment recordings demonstrate that this interaction is viable: all users successfully completed the experiment and mentioned enjoying at least one game without prompting. Hand-clapping tempo was highly salient to users, and human-like robot errors were more widely accepted than mechanical errors. Furthermore, perceptions of Baxter varied in the following statistically significant ways: facial reactivity increased the robot’s perceived pleasantness and energeticness; physical reactivity decreased pleasantness, energeticness, and dominance; higher arm stiffness increased safety and decreased dominance; and faster tempo increased energeticness and increased dominance. These findings can motivate and guide roboticists who want to design social–physical human–robot interactions.