Geometry and pool: Playing a game of loop

Maths writer Alex Bellos recently spent a lot of money on a pool table - an unusual one with only one hole, and no straight sides.

The pool table is in the shape of an ellipse, a shape with two focus points and Alex invented a game for it, called Loop.

Unlike pool you only have four balls- the cue ball, one black and two colours, one for each player. The idea is the same - if you pot your colour, and then the black, you've won.