It is totally random now (was changed this past april) that doesnt mean you cant increase your odds by having more accounts / characters, but it Is in fact totally random for each character played.
Which is how it should be. Except for the multiple accounts thing, but hey, it's part of the game. Shut up & deal with it, right?
Personally, I've only ever had one account, and it will remain that way. When I do LS's EM events, I don't go for the drops or rare items (Well, that's not entirely true.
@EM_Falcon has been using various monsters & we're currently facing the old Crimson/Platinum Dragons, and I've been checking religiously for a Crimson Cincture), I go for the combat/fighting in a group, and banter between us & the EM/the characters she's playing.