I wasn't aware of the 12 draws, with my city it feels like it actually got flat 30% chance to get a new citizen per day, but maybe I am just unlucky.
Speaking of unlucky, I had the whole Sim City review done and recorded but then a dog came along and ate the whole thing... ^^*. I will get back to it, back then I completed the tutorial but havent made a real run yet. It is coming soon TM