One of the suggestions submitted by Miguel Balauag from Stanford:

At the start of the game, the moderator selects an extra card to mark the Accident Victim. This leaves one card left over. The Accident Victim is actually that role, but because of an accident before the first day, he/she has amnesia and does not "remember" what he/she is until the 3rd nightfall. At the start of the 3rd nightfall, the moderator wakes the Accident Victim and shows him/her the remaining card, and starting that night, that player assumes that role (and can exercise any special powers that night).

This can greatly favor one side depending on what role the Accident Victim really is, since this can start the Mafia one member short, or the civilians without a doctor/archangel or detective/angel, etc.

We tried this variant twice, and both times the Accident Victim died in the first night from the hands of Mafia. It has thus not been a great success yet! We call that the Accident Victim's Curse ;-)