If it was a
game of point sources, then it would be easier. The
exit point of the
half-ray on the target ball is difficult to identify when the angles are small.
The
invisible ball way to
compensate for the full width of 1 ball is a very
ingenious technique. After too many years and beers, this is the best explaination I have heard.
This is a great way to adjust to the different playing surfaces and equipment dimensions. On the same night, you might play a game on a pay pool table - that actually has a cue ball slightly larger than the others - and then move to an hourly-rated
snooker table - with larger surface, tighter pockets, and smaller balls.
Everyone needs time and a technique to
warm-up.
Bravo.