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As Vervolka rightly noted, this type of game is not designed for a large number of players (I think a maximum of up to seventeen, but usually fewer), which is one of the reasons for the need for parallel games. Many players may not have time to sign up and will have to wait for the next one, but they still want to play. Moreover, someone might not like this type of game, and the player will be forced to wait for the standard HeroesWorld mafia.
One
example of psychological mafia that I played (and
here are the rules for it).