Throwing up numbers would just be pointless guessing for the sake of pointless guessing
If you do it systematically, picking odds and tracking them can help with your calilbration. Doing it in public helps because it puts a little bit of status on the line, which makes one care about getting it right.
You see, I've seen the word "rationalism" used to mean all five of these things at different times:
Edited to reinstate that proposed solution, since this discussion is presumably finished.