What does the Sorceress's Hat do?
The Sorceress Hat enhances the effects of your spells and potions. The only effect I have seen so far is to double the amount healed by the health potion, although I am currently experimenting to determine the effects on other potions/spells.
Effects discovered:
Healing potion: Increases amount healed from 100 -> 200
Black Demons: Increases damage from 750 -> 1200
Anti-gravity potion: Increases flight time by a factor of ~1.5