Here's one: Group 3 billiard balls together and send a cue ball moving into the first ball in the group. Model where the balls go as a function of the angle and velocity of the cue ball hitting the first ball in the rack. That should keep you busy for a while.
Group them like this:
O
OO
I did this with a 9-ball break as a computational project during my undergrad. My goal was to figure out the angle and velocity of hitting the first ball that would cause the 9-ball to go into a pocket thus winning the game. I had to simplify a lot of elements like no follow on the cue ball and a tight rack. I played around with the model to show what would happen with a loose rack.. Needless to say it became obvious why I made a lot more money gambling on pool after this project. Even with a fairly solid model, things don't always work out as simulations will show and a project like this will only open your eyes to how complex the real world really is.
When I got to grad school some of the professors here asked about my academic projects from undergrad and I told them about this one.. they're still wondering why I'm not doing statistical mechanics for my research, lol.