- Background: Effective human-robot interactions in rehabilitation necessitates an understanding of how these should be tailored to the needs of the human. We report on a robotic system developed as a partner on a 3-D everyday task, using a gamified approach. Objectives: To: (1) design and test a prototype system, to be ultimately used for upper-limb rehabilitation; (2) evaluate how age affects the response to such a robotic system; and (3) identify whether the robot's physical embodiment is an important aspect in motivating users to complete a set of repetitive tasks. Methods: 62 healthy participants, young (<30 yo) and old (>60 yo), played a 3D tic-tac-toe game against an embodied (a robotic arm) and a non-embodied (a computer-controlled lighting system) partner. To win, participants had to place three cups in sequence on a physical 3D grid. Cup picking-and-placing was chosen as a functional task that is often practiced in post-stroke rehabilitation. Movement of the participants was recorded using a Kinect camera. Results: The timing of the participants' movement was primed by the response time of the system: participants moved slower when playing with the slower embodied system (p = 0.006). The majority of participants preferred the robot over the computer-controlled system. Slower response time of the robot compared to the computer-controlled one only affected the young group's motivation to continue playing. Conclusion: We demonstrated the feasibility of the system to encourage the performance of repetitive 3D functional movements, and track these movements. Young and old participants preferred to interact with the robot, compared with the non-embodied system. We contribute to the growing knowledge concerning personalized human-robot interactions by (1) demonstrating the priming of the human movement by the robotic movement - an important design feature, and (2) identifying response-speed as a design variable, the importance of which depends on the age of the user.