As a follow up to my all abilities coder challenge post, here are some results. From Daniel Cristofani's C implementation with GMP. My implementation confirms his results.

Doomed World           19.2441
Separatist Colony      19.2441
Old Earth              20.9860
Epsilon Eridani        21.8792
Earth's Lost Colony    21.8998
Alpha Centauri         21.9158
New Sparta             21.9158
Damaged Alien Factory  21.9377
Ancient Race           21.9715

At first, 20 cards seems quite high compared to experience playing Race, since I'd estimate, the all abilities goal tends to be won at before the 10th card is dropped. But these numbers make sense if you realize how rare the development bonus is, with only 7 cards providing one from the whole deck. If you just draw randomly until you find a development bonus, you are likely to be waiting for ~14 cards. Also, I hope that people are playing better than dropping cards on their tableau at random.

Thanks to Larry and David desJardins for algorithmic insights into the problem. Also, see the thread on board game geek.

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.