To develop and sustain rich social interactions between humans and robots, previous research has mostly looked at task-oriented performance metrics or the ability for a robot to adequately express messages, emotions, or intents. In contrast, our research starts from the premise that movement, as a nonverbal modality of social interaction, can cover other essential aspects of social interaction that do not have to do with the expression of messages, inner states, or drives but that nonetheless contribute to improving the quality of interaction. These aspects have to do with interaction dynamics and highly depend on appropriate action choice. Drawing inspiration from rule-based improvisation, this paper seeks to show that there exists implicit expert knowledge that can be used to inform these movement action choices, contributing to rich, playful, and non goal-oriented interactions between humans and robots. We present an experimental study conducted at a performing arts festival, in which participants interacted with a robot in three simple rule-based movement games, in two conditions: one where the robot was fully controlled by an improvisation expert (Improv Timing/Improv Action) and one where the timing of the actions was controlled by the expert but the robot's action choices were drawn randomly (Improv Timing/Random Action). This was done in order to focus on action choice, beyond the timing of a response. Our results show that the Improv Timing/Improv Action condition not only performs better in terms of anthropomorphism and animacy, but also increases the interest of people in interacting with the robot for longer periods of time. These results serve as preliminary evidence of how improvisational knowledge in this context contributes to improving the quality of an interaction, and point at the value of further work in this field.