Leagues magic relic idea: rolls all RNG effects twice and picks the "better roll". (similar to OSRS Osmumten's Fang rolling accuracy twice). Examples of "RNG Effects": Critical Strikes. Temporal Anomaly and Roar/Ode cooldown resets. God book activation chances. Darkness dodge chance. Even niche stuff like Amulet of Souls chance to increase Soul Split healing would roll twice.
Note that this would not affect drop chances, just combat RNG effects.