Comment by tsimionescu

This is a complete tangent, but I would note that we don't have physical models nearly good enough to actually compute the way billiards balls (or even worse, snooker balls) interact with each other and the fabric on the table. It's all guesswork and experience, mostly. The interactions between the balls and the fabric are critical for the vast majority of the movements, and they are far too complex for any physical first-principles based model to capture.