In that case, everybody's luck would be averaged. Luck was the most unpredictable factor. It might not seem very important, but the shortage of a tiny bit of luck could mean the difference between life and death.
Let's assume someone's luck was 80 points, again someone's luck was 100, and another's was 30. If the one whose luck was 80 points averaged everybody else's luck, then everybody would have less luck than he did, which could give him an edge.
Alonzo never thought of using the tool in such a way. It was meant to attack an enemy. Who would use it on themselves?
Alonzo was the one who made the Voodoo Doll. He was also the one who knew the Voodoo Doll the best. After hearing what Lin Yun said, he realized what he could do and how he could do it. All he needed was the Bloody Lich's full real name.
