These are games that are based somewhat on Mafia but are so different that they no longer really are Mafia. Good examples would be ConfrontationMafia, ConspiracyMafia, and GayMafia. There is no administrative classification for such games on MafiaScum; some are considered to be Theme Games, while others are sent to The Whole Sort Of General Mish Mash with non-Mafia games.
What defines a mafia mutation as not being mafia is not the degree of change but the kind. cuban smoker's LogicMafia is not a mutation, as the group dynamic is essentially the same. InnerCircle?, on the other hand, is a mutation, since the "town" and "mafia" no longer really exists, and players choose their own motives. The best way to describe it is to say that the primary question of the game changes. In Mafia the question is "Who are the good guys", whereas in Gay Mafia (or its simpler and less well-known version SpyHuntingStandDown) the question is "How can we get people from the other side killed?" and in InnerCircle?, the question is "Which alliances will leave me alive at the end?".
The distinction is a fuzzy one, and not well defined as yet.
The term "Mafia Mutation" was first coined on mafiascum by Foolster41 when describing his CCG Mafia, Though games that could be defined as mafia mutations existed before he gave it a name.
Norinel: Let me give it a shot. I think the distinction between an Experimental Game and a Mafia Mutation is how tweaked the core concept is. I think that if anything were to be The Core Rule Of Mafia, it would be "A minority of the players are evil, and know who else is evil. Everyone else has to figure out who's evil." (Note that I did not specify the manner of figuring out who's evil; lynching and the concepts of day, night, and even perhaps death are, IMO, not at the absolute heart of the game. But some might say that The Core Rules are the rules of Roleless Mafia, and anything that greatly changes those is a Mafia Mutation.) Having a game based on Improbable Roles or changing the structure of the nights doesn't change that, it just adds on extra rules to make the figuring out who's evil part more interesting. However, once the alignments become any different from informed minority vs. uninformed majority (As described by Dimitry Davidoff), you've entered the territory of Mafia Mutation. There are some border cases though, especially if you think about things that change the days & nights and stuff without touching the alignments. Is a game only composed of lynches, with no pro-town roles or nights at all, a Mafia Mutation? Is Italian Stand-Down, identical to SpyHuntingStandDown except that the alignments are town and mafia, a MafiaMutation?
On a side note, my opinion is that all major Mafia Mutations shouldn't be in the Mafia forums in the first place. Have there been any games classified officially as Theme Games that you'd consider a Mafia Mutation?
PolarBoy: Nothing comes to mind. There was GayMafia, which was run in the NewYork forum as a Normal Game. Various scummers suggested that the game should've been run as a Theme Game though.