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The holder has a 20% chance to move before all Pokemon using an attack of equal or lesser priority. Pokemon activating Quick Claw completely ignore Trick Room.
Quick Claw certainly has an interesting effect, which helps many Pokemon revenge kill faster threats. However, it's outclassed by Choice Scarf as an item that allows you to move faster, mostly because of its unreliability. Even though it lacks the reliable quality of Choice Scarf, some Pokemon are simply too slow to use it, and are still outsped by a large portion of the metagame, making Quick Claw the superior choice. Even then, there are better held items to give to those slow Pokemon, such as Leftovers.