Here’s a sample of what we worked on at a spring Math Teachers’ Circle meeting with Justin Lanier.  If the green pool ball is sent off in the 45 degree angle shown, then it will bounce off the opposite wall, one unit below point B.

If it continues to bounce around the table, will it eventually go into one of the pockets marked A, B, or C, and if so, which one will it reach first?

For a neat Geogebra applet that shows off this and other pool bouncing arrangements please check out:  https://tube.geogebra.org/student/m93224