Quanta on ‘the mysteries of polygonal billiards‘:
Is it always possible to hit a ball so that it returns to its starting point traveling in the same direction, creating a so-called periodic orbit? Nobody knows. For other, more complicated shapes, it’s unknown whether it’s possible to hit the ball from any point on the table to any other point on the table.
Some very deep maths involved here and I can only assume Ronnie O’Sullivan would be a pro at this kind of game as well.