Petals Around the Rose: Fraternity Register

Saw this on a Youtube video and was challenged to solve it myself before the answer was divulged at the end of the video. After a couple rounds of rewatching the video over and over to try and divulge the rolls that were previously shown, I decided to find a generator that would generate rolls for me and give the answer if I couldn't find it myself. With a lot of persistence, I finally figured out the algorithm to this game.