Collaborative robotics represents a modern and efficient framework in which machines can safely interact with humans. Coupled with artificial intelligence (AI) systems, collaborative robots can solve problems that require a certain degree of intelligence not only in industry but also in the entertainment and educational fields. Board games like chess or checkers are a good example. When playing these games, a robotic system has to recognize the board and pieces and estimate their position in the robot reference frame, decide autonomously which is the best move to make (respecting the game rules), and physically execute it. In this paper, an intelligent and collaborative robotic system is presented to play Italian checkers. The system is able to acquire the game state using a camera, select the best move among all the possible ones through a decision-making algorithm, and physically manipulate the game pieces on the board, performing pick-and-place operations. Minimum-time trajectories are optimized online for each pick-and-place operation of the robot so as to make the game more fluent and interactive while meeting the kinematic constraints of the manipulator. The developed system is tested in a real-world setup using a Franka Emika arm with seven degrees of freedom. The experimental results demonstrate the feasibility and performance of the proposed approach.