The Luck Plane consists of 2 dimensions unknown to mere humans, but which SubGenii are quite familiar, as we surf the Luck Plane using Time Control and Sales Magic. It basically connects many parallel universes and time periods, and consists of 1 dimension of Time and one dimension of Slack.
By surfing the Luck Plane, a SubGenius is able to do many things, such as make a million dollars every time they make a mistake, have intercourse with a beautiful nude girl, or run a successful used car dealership or advertising agency. It also allows the SubGenius to always win in games of chance, which is why you always see SubGenii winning the lottery. The master of surfing the Luck Plane is, of course, "Bob", which is why he is the luckiest man alive, even though he's legally dead (which means that he doesn't have to pay any taxes and can't be convicted of any crime... like I said, quite a lucky guy). This video about "Bob" tells a little about surfing the Luck Plane: