Totally Nonsensical, therefore worth answering question

Dear people of the internet,

Yesterday I was watching snooker on the television and a thought suddenly occurred to me. Wouldn’t a game of pool be infintely more interesting if each of the players were allowed only one shot, and the amount they potted directly equalled their score?

Naturally the next thought was, given that my pool table was indestructible, ignoring spin and assuming all the balls are the same size, that collisions are completely elastic, the force I exert on the cue ball is infinite, where would I shoot the ball in order to gurantee the win, in the fewest amount of bounces against the side of the table?

No. Most people aren’t going to find a game that lasts a minute and a half and consists of two total plays very interesting.

Just so you know, that was written purely as an introduction to the question. The post seemed more interesting with it.

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?

First, read the question carefully-er, if it is always possible (that is never create a repeating pattern, which also means the game may never end), assume those which hit the projection bounce directly back.

This is the kind of thing that happens when people spend too long watching snooker.

In practise, this can’t be done. The table isn’t perfectly made, if you hit the balls too hard the smallest imperfection will cause all the balls to jump off the table.

The smart move is to slowly jack up one of the table legs by about a foot.