Also depends how much friction, if we are going into pure physics bodies. If the balls just keep going until they eventually sink - then …wait for it… they’ll keep going until the eventually sink. If the force you exert on the cueball is infinite, you just whack it and tada, game over. Too fast to see.
basically, lay out a checkerboard of repeating playing surfaces. Like a mirror image of light ray paths, the balls’ reflected path will travel what looks like continuing in a straight line into the “mirror” pool table. Extend that line until it eventually hits a pocket.
(a) the flaw here is that some balls will bounce off the projection of a pocket opening corner, not the flat side. This alters their path significantly.
(b) The question is can you set up a reflective pattern (45-degree bounces) to create a diamond-shaped path that will never hit a pocket? Otherwise, every ball will bounce in a sort-of-diamond pattern, reflection points creeping along the edges until one hits a pocket. Actually, since the pool table is not square, you are looking for a repeating pattern more like a lissajious (??) figure or a figure 8, as used to be created on oscilloscopes when you have horizontal and vertical frequency that are co-harmonics. Are the edges of a pool table an whole number ratio to each other?