Hello, I just reread the passage about Bloody Mary and I have a theory about her relationship with Falcon. It is said (not only in this wiki) that Mary would have had a history because they are very on edge between them. But I think that actually, when she arrives in Japan, Mary is the only one who is still a real professional (Ryo no longer kills these opponents and only takes bodyguard contracts and Falcon spends most of his time as a cafe waiter). She therefore applies the "law of the underworld" and imagines a time when Ryo and Falcon were also part of it. At the time, Falcon would have avenged the injury Ryo inflicted on him and Ryo would have killed him to prevent this from happening. So I think Mary being on Ryo's side and enforcing the law of the middle takes Falcon for an enemy.
What do you think about this ?