A Combination of Both: If the GM can vary the randomness on a case-by-case basis, then they can fit not only their preference, but realism also.

I think this was the point where the idea of describing other players success and failure really clicked with everybody.
Both Chio and Yoko found clues that led them to believe that our homeroom teacher was somehow connected with the Demon and the disappearance of the swim team. The crowd is stunned at this blatant display of psychic powers, as are our Students, who had no idea their friend was a psychic.