To try and analyze the algorithms, I made three separate accounts and sorted myself. Twice I've gotten Hufflepuff, once Ravenclaw. Every time my Ilvermorny house is Horned Serpent, and my wand is always 10 3/4", slightly springy, Cypress with Phoenix core. I've gotten a robin, a dun stallion, and a mongrel hound as patronuses. Of the different quizzes, Hogwarts' sorting has a close variance between Hufflepuff and Ravenclaw (I think the only differentiators are 'wisdom' questions and other such moral ilk), the Ilvermorny and Wand quizzes are more or less consistent with little room for variance, and the new Patronus quiz is literally randomized depending on the questions selected for you.