[symmetricsaurus]

The resulting balls always travel at a 45 degree angle from the direction of the shot. So shooting diagonally should keep all resulting balls travelling up-down or left-right. This would keep all balls in a rough cross shape on the playing field.

Stay out of this area and you will be able to live forever and easily beat the game.

In practice this is really hard to achieve since only a small deviation will cause some of the ever increasing number of balls to hit you anyways.

[sleepysort]

Nice job picking up on the nuances of the game :) and as you said, much easier said than done.