1. An apparatus for playing pool, comprising; a) a robot having a robotic arm with an end effector, the robot mounted on a gantry for movement above a pool table, a pool cue attached to the end-effector, the pool cue having a longitudinal axis; b) a first image capturing means mounted above the pool table for acquiring an image of the pool table and positioned such that its image plane is substantially parallel to both a playing surface of the pool table and said longitudinal axis of said pool cue; c) a second image capturing means mounted on the robotic end-effector so that its image plane is substantially perpendicular to the longitudinal axis of the pool cue for capturing an image of a pool table using a camera, the position of said camera being fixed with respect to the longitudinal axis of the pool cue; d) a computer processing means connected to the first image capturing means for analysis of the images transmitted thereto from the image capturing means, the computer processing means including means for determining a position and identity of each pool ball on the pool table within this image within a frame of reference of the image capturing means, said computer processing means including means for planning a shot of a cue ball by the pool cue by calculating a desired position of the cue with respect to the cue ball; and e) a robotic controller connected to said computer processing means for instructing the robot to place pool shots with the cue.