Why is it called Ba Zi and not Liu Zi?

Note: In the modern era, there are some so called 'masters' out there who claim to be able to read a person's Ba Zi with only three pillars. If so, why didn't the Chinese call it Liu Zi (6 Characters) instead.

If you come across any 'monsters' using Liu Zi to read your life destiny, make very sure you ask for a 25% discount! And if you intend to learn Liu Zi from the same 'monsters', you'll get 25% off pronto!

Dare you sit on a Liu Zi (3 Pillars) chair? Sit your butt down!
Dare you get your destiny read with Liu Zi? Get your life drowned!