40% chance: You will automatically tranfer to the White House Comment Line
30% chance: You'll get a person, but sometime during the first or second sentence (of yours or theirs), you'll be instantly transferred to the Comment Line mid-sentence
30% chance: You'll get a person and actually have a chance to tell them what you're calling about. Then:
1 out of 3 times (10% of total): They'll transfer you to the Comment Line regardless of whether it's appropriate.
2 out of 3 times (20% of total): They'll transfer you somewhere other than the Comment Line.
This is based on about 35 minutes of calling, until I finally reached the appropriate department. So I may be biasing these numbers in favor of "transfer somewhere other than the Comment Line", since my termination condition for the experiment fit in that set. The odds may actually be below 20%.
However! 202-456-1111 is the White House Comment Line. If you call it...
~3% chance: Someone will take your comment
~97% chance: Busy signal
So the Switchboard number is actually a great way to bypass the busy signal and get through to the comment line. And usually, you won't even have to ask - you'll just get to the comment line.