52! = 8.06e+67 (roughly)
We have 10e+9 * 1e+9 * 200e+9 * 500e+9 = 1e+42 people on the job
Each checks a million a second, so we're going through 1e+48 combos/second
It ought to take about 8.06e+19 seconds
There are about pi * 1e+7 seconds in a year, so about 2.56e+12 years
The universe is about 13.8 billion years old, so we'd be about 0.5% done.
I started this out thinking I might show you were wrong. Obviously, we're _way_ behind on the job... time to start populating the universe, building lots of playing card factories, and practicing our shuffling skills.
Biting the hand that feeds IT
