You are a third party role. You have a hat on your head, that is either black or white, but you don't know which one.
There are other Logicians in the game: xxx, yyy... whose hats are colored xxx, yyy... Not all hats are colored white.
At any point during a Day Phase, you can guess your hat's color; if you're wrong, you die; if you're right, you win, the other Logicians lose, and you all leave the game.
I just thought it was a funny idea to have a completely unrelated game running in the same thread as Mafia