*in my best Clint Eastwood voice*
Yeah.
Ha ha ha. If you do read through that, you'll see I signed up for and played that mafia game I linked. I wanted to try out this version of what you refer to as the proper way to play. Unsurprisingly, the mafia won. Of course, I thought there were a few other elements that further skewed the game in the mafia's favor but I just don't see how there is an equal chance in that version. Further backing this up is the fact that of the three times they have played Mafia on that forum, the mafia has won all three times.
Still, I've meant to do a write-up on that game for a good 6 months so maybe now is the time.