The Mad Hatter gives 30 turns of Oleaginous Soles (+40% init) for a hat with at least 30 characters; currently the only one is the semi-recently-added brainwave-controlled unicorn horn. Mafia's dropdown list in the relay browser (rabbithole.php) says "brainwave-controlled unicorn horn: unknown (31 characters)". Still a thing in r12223.
(Wild guess: it's already in the code, but it looks for hats with exactly 30 characters instead of 30 or more.)
(Wild guess: it's already in the code, but it looks for hats with exactly 30 characters instead of 30 or more.)