How is the casting time implemented in the game?
As the manual says: the casting time is the same as the speed factor for weapons, meaning that the number indicates tenths of 6 seconds (one round).
Example:
Chain Lightning: casting time = 5
This would mean that once the round starts it takes 5/10 of a round to cast the spell, so after 3 seconds the spell will be cast.
Both the robe of Vecna and Amulet of Power will let you cast spells faster. Indeed, the description can be confusing. There were probably several "item-description-writers" who interpreted the rules differently (but with the same result).


