This is a list of various mafia game formats that differ from the standard one. These formats don't specify which roles are included, but rather they pertain to how the game runs or how the game is broadly designed.
In an Anonymous Game all players are given a new anonymous account to post on. This feature is supported by the Modbot, allowing the Game Host to simply enter which names they'd like for the anonymous accounts to have. Upon initiating the game, each player will be automatically contacted by the Mafia Host account with an account name and a password.
The purpose behind these games is to eliminate the element of meta, i.e. knowledge about each other's "tells" (the belief that specific players have alignment indicative behavioral patterns etc.). It allows the players to play freely without having to worry about living up to other players' pre-conceived expectations. As such, it is usually frowned upon and disallowed for the players to either reveal their own true identity or openly discuss/refer to other players' identities.
In a Bastard Game players are often subjected to high variance, chaos, moderator deception and/or unbalanced setups. The term "bastard" is most often used in a derogatory fashion. If a game is openly marketed as a bastard setup, you should only sign up for it if you think the mayhem might be fun and are willing to accept that you can/should trust nothing told to you by the Game Host.
Examples of bastard roles include Death Millers (same as a regular Miller, except the player is revealed as Mafia-aligned upon death) or False roles where a player is misled about their true role. These are viewed as bastard because they involve the moderator lying to the players.
An example of a bastard mechanic would be Cult conversions (the Cult is a third-party team that recruits players into itself), which is viewed as potentially violating the spirit of the game, since players change alignment and are forced to play for a new team. Additionally, it creates a nearly impossible situation for the town to solve, especially if the presence of a Cult is unknown to the players.
Some also consider the Jester role to be bastard due to its nature of being potentially very disruptive to games and often having an unforseen negative impact on the game. In other words, some people believe that it is against the spirit of the game for the town to be punished for lynching a player acting "scummy", given that that is what they are taught and motivated to do in regular games of mafia.
In a Bring Your Own Role (BYOR) Game players submit a character name and/or a role to the Game Host pre-game. After having received all players' submissions, the Game Host then tries to make a balanced setup, inspired by the ideas that they have received.
For example, if it's a character-only BYOR, someone might submit that they want to be Batman. The Game Host might then reply back and tell that person that they are Batman, a Town Vigilante. In special cases where players may even submit a preferred role, the Game Host will usually take these role ideas into account, but ultimately it is up to their discretion whether they want to completely rework or replace the role with something else in order to make it fit with what else is in the game.
As for the alignment of the submitted characters/roles, the Game Host will usually randomize this in accordance with standard town/mafia ratios. This means even if someone submitted a character that is known to be aligned with forces of good, this has no impact on whether the player will end up being town or mafia.
In a Hydra Game players are paired up to share one role slot. I.e. a 13-man hydra game would feature 26 players paired up, meaning that each pair shares one of the 13 roles in the game. When a hydra is lynched or killed, both players are thus eliminated from the game.
Usually, the hydra pair must post on one shared account, a hydra account. They are both allowed to be logged on and post in the game thread whenever, even at the same time. It's also common for a hydra pair to be allowed to discuss the game with each other outside of the game thread (the host usually provides them with a private thread).
In a Mentor Game the participants are usually inexperienced players that have played only a few or no mafia games at all. These players are assigned a mentor that will often follow the game thread and offer advice from the sidelines via private communication channels.
Usually the rule is that the mentor shouldn't be playing the game for the mentee. They should merely answer mechanical and strategical questions as well as provide various clarifications where needed. Unless allowed by the Game Host, the mentor should, for example, not be giving specific reads on posts or advise the mentee on who to lynch/kill.
Sometimes these mentor games are hybrid mentor/hydra games where the experienced player is paired up with the newbie on a shared hydra account and thus also allowed to post.
In a Mish-Mash Game the roleset is closed and nowadays the game typically has a single well-known theme used for flavor, such as Harry Potter or Lord of the Rings. However, as the name suggests, these games were originally a mish-mash of many different themes all mixed together, meaning that a game could feature characters from many different universes.
Mish-Mashes usually have daily events, which are various mini-games in which players can compete in order to win game-related prizes and boosts. Mish-Mash games furthermore tend to feature In-Thread Attack windows, i.e. periods in which the players are allowed to shoot at each other during Day Phases. These In-Thread Attack windows commonly last 30 minutes, occur twice per day phase, and each player's shot usually has a 15% chance of hitting the other player.
Besides this, these games often feature completely original roles and/or mechanics that have never been seen before, using the source material (theme) as creative inspiration. Examples of previously used themes with special mechanics include "Choose Your Own Adventure" where the players could vote on which direction to take the "story" (game) or "Saw" where the players not only had to play mafia, but also had to escape their own death traps.
While not technically a defining feature of a Mish-Mash game, they do tend to feature very large player lists, often between 40-100 players. Small Mish-Mashes are sometimes referred to as Mini-Mashes.
In a Multiball Game there are more than just the two regular factions of Town and Mafia. For example, there might be a Town faction and then 3 different Mafia factions (these will often have different faction names such as Mafia, Werewolves and Vampires). Note that the term Multiball isn't used for regular games only featuring independents such as Serial Killers besides the Town and Mafia factions.
The different mafia factions in a Multiball are all intended to be equal in strength, though they do not necessarily have the exact same roles or even the same number of faction members.
Due to the nature of Multiball games, they can sometimes end in draws or result in Kingmaker scenarios where a player who is incapable of winning can still influence which other faction wins.
In a Nightless Game there are no Night Phases, i.e. no nightkills. Instead, the game simply continues from one Day Phase to the next. Since these games take away the mafia team's ability to kill townies, they are usually compensated in some way, either via larger numbers or abilities to be used during day (such as day kills).
In an Outside Communication (OC) Game the players are allowed to not only post in the game thread, but may also communicate with each other outside of the game thread. Usually there are no restrictions to this communication, though some Game Hosts may prefer that it only occurs in specific channels and/or that the Game Host can monitor all these communications.
These games are notoriously difficult to balance, given that outside communication allows for plays not possible in regular games, such as information power roles privately sharing their findings with those that they have investigated and/or other clear players in the game, creating a network of confirmed/confirmable players that the mafia will have a difficult time infiltrating, unless certain mechanics and roles exist to counteract this.
In a Post Restricted (PoR) Game the Game Host has set a maximum posting restriction. I.e. if the maximum posting restriction is 50 posts, this means that no one in the game is allowed to make more than 50 posts per game day.
This maximum posting restriction is often enforced via a setting in the Modbot, which makes it impossible for players to keep posting after they've hit the maximum.
However, sometimes the Game Host may have a rule that the posting restriction is lifted 1 hour before End of Day (EOD), in which case the restriction is usually enforced manually in combination with a rule that for each illegal post that a player makes, one vote is manually added to their tally. I.e. say that the maximum is 20 posts and a player has 22 posts with 1 hour before End of Day, then they will have 2 votes added to their final vote tally.
This thread contains an overview of the popular Modbot-supported mafia setups that have previously been run on Mafia Universe as well as descriptions of the various game formats that you may find here.