You have a Race deck in front of you. You are going to draw cards from the deck until you have all abilities.

What is the expected number of cards to draw to get all abilities? Can you compute this efficiently and exactly if you are sampling without replacement? How does this number change as you start your hand with various home worlds? What would you estimate this number at before running the code?

I think this number will give a pretty good ranking of the likelihood of drawing the all abilities goal. I'd expect Old Earth and Separatist Colony to be favorites.

This Race stats spreadsheet (or converted to CSV, your laziness, or converted to a readable text file, with frequency counts and abilities listed, and an encoding of the ability subset for your maximal laziness) might be useful.