Mafia (party game)

Mafia, also known as Werewolf, is a social deduction game, created by Dimitry Davidoff in 1986. The game models a conflict between two groups: an informed minority (the mafiosi or the werewolves), and an uninformed majority (the villagers). At the start of the game, each player is secretly assigned a role affiliated with one of these teams. The game has two alternating phases: first, a night role, during which those with night killing powers may covertly kill other players, and second, a day role, in which surviving players debate the identities of players and vote to eliminate a suspect. The game continues until a faction achieves its win condition; for the village, this usually means eliminating the evil minority, while for the minority this usually means reaching numerical parity with the village and eliminating any rival evil groups.
History.
Dimitry Davidoff (, "Dmitry Davydov") is generally acknowledged as the game's creator. He dates the first game of "Mafia" to spring 1987 at the Psychology Department of Moscow State University, from where it spread to the classrooms, dorms, and summer camps of Moscow University. "Wired" attributes the creation to Davidoff but dates the first game to 1987, with 1986 being the year in which Davidoff was starting the work which would produce "Mafia". He developed the game to combine psychology research with his duties teaching high school students. The game became popular in other Soviet colleges and schools, often associated with hugely popular TV series La Piovra, which ran since 1986. In the 1990s it began to be played in other parts of Europe and then the United States. By the mid 1990s a version of the game became a Latvian television series (with a parliamentary setting, and played by Latvian celebrities).
Andrew Plotkin gave the rules a werewolf theme in 1997, arguing that the mafia were not that big a cultural reference, and that the werewolf concept fit the idea of a hidden enemy who looked normal during the daytime. Mafia and a variant called Thing have been played at science fiction writers' workshops since 1998, and have become an integral part of the annual Clarion and Viable Paradise workshops. The Werewolf variant of Mafia became widespread at major tech events, including the Game Developers Conference, ETech, Foo Camps, and South By Southwest. In 1998 the Kaliningrad Higher school of the Internal Affairs Ministry published the methodical textbook "Nonverbal communications. Developing role-playing games 'Mafia' and 'Murderer"' for a course on Visual psychodiagnostics, to teach various methods of reading body language and nonverbal signals. In September 1998 Mafia was introduced to the Graduate College at Princeton University, where a number of variants were developed. The werewolf theme was also incorporated in the French adaption of Mafia, The Werewolves of Millers Hollow.
In August 2000, a user under the alias "mithrandir" of The Grey Labyrinth, a website devoted to puzzles and puzzle solving, ran a game of Mafia adapted for play on a forum board. Both The Grey Labyrinth and sister site MafiaScum claim that this was the first game of Mafia run on a forum board. From there, Mafia has spread to numerous online communities.
In March 2006 Ernest Fedorov was running a Mafia Club in Kyiv, using his own patented variation of the rules. The club organizes games, rates players, and awards prizes (including a Sicily trip for their tournament-series champion).
In June 2006 a Rockingham school inquiry was launched after parents complained of the traumatic effects classroom Mafia was having on their fifth-grade children. Davidoff responded to the reports, saying that as a parent who had studied child psychology for 25 years, he felt that the game could "teach kids to distinguish right from wrong", and that the positive message of being honest could overcome the negative effects of an "evil narrator" moderating the game as if it were a scary story.
Mafia was called one of the 50 most historically and culturally significant games published since 1890 according to about.com.
Gameplay.
In its simplest form, Werewolf is played by two teams: the werewolves and the villagers. Live games require a moderator who does not participate as a player, and identities are assigned by handing out cards. At the start of the game, every werewolf is given the identities of their teammates, whereas the innocents only receive the number of werewolves in the game, and do not know which players are werewolves and which are villagers.
In an open setup, the numbers of each power role (e.g. militia) present in the game is known to the players, while in a closed setup, this information is not revealed, and in a semi-open setup, only limited or tentative information about the power roles is revealed. Thus, in an open or semi-open setup, if it is revealed that no militia are present in the game, it will not be possible for a werewolf to plausibly claim a militia role.
There are two phases: "night" and "day". At night, certain players secretly perform special actions; during day, players discuss and vote to eliminate one player. These phases alternate with each other until all werewolves have been eliminated or they reach numerical parity with the innocents.
Some players may be given roles with special abilities. Common special roles include:
Andrew Plotkin recommends having exactly two mafiosi, whereas the original Davidoff rules suggest a third of the players (rounding to the nearest whole number) be mafiosi. Davidoff's original game does not include roles with special abilities. In his rules for "Werewolf", Plotkin recommends that the first phase be night and that there be an odd number of players (including the moderator). These specifications avoid a tie votes for eliminations and ensure that the game will end dramatically on an elimination rather than anticlimactically with murder as a foregone conclusion.
Night.
All players close their eyes. The moderator then instructs all werewolves to open their eyes and acknowledge their accomplices. The werewolves pick a "victim" by silently gesturing to indicate their target and to show unanimity then close their eyes again.
A similar process occurs for other roles with nightly actions. In the case of the seer, the moderator may indicate the target's innocence or guilt by using gestures such as nodding or head shaking.
Night may be accompanied by players tapping gently to mask sounds made by gesturing.
Day.
The moderator instructs players to open their eyes and announces who "died" the previous night. Discussion ensues among the living players. At any point, a player may accuse someone of being a werewolf and prompt others to vote to eliminate them. If over half of the players do so, the accused person is eliminated and night begins. Otherwise, the phase continues until an elimination occurs.
According to some rules, the role of dead players are revealed; according to others, it is not. In both cases, dead players are not permitted to attempt to influence the remainder of the game.
Because players have more freedom to deliberate, days tend to be longer than nights.
Game theory.
Mathematical study.
Mafia is a complicated game to model, so most analyses of optimal play have assumed both (a) that there are only townsfolk and Mafiosi and (b) that the townsfolk never have a probability of identifying the Mafia that is better than chance. Early treatment of the game concentrated on simulation, while more recent studies have tried to derive closed-form equilibrium solutions for perfect play.
In 2006, the computer scientists Braverman, Etesami and Mossel proved that without detectives and with perfect players the randomized strategy is optimal for both citizens and mafia. When there is a large enough number of players to give both groups similar probability of winning, they showed that the initial number of mafiosi "m" needs to be proportional to the square root of the total number of players "P", that is formula_1. With a simulation, they confirmed that 50 mafiosi would have almost a 50% chance to win among 10,000. The Mafia's chance of victory is
which is a good approximation when the right hand side is below 40%. If any detectives are added to the game, Braverman et al. proved that the number of Mafiosi must remain at a fixed proportion of the total number of players for their chance of winning to remain constant.
In 2008, Erlin Yao derived specific analytical bounds for the mafia's win probability when there are no detectives.
In a paper from 2010, the exact formula for the probability that the mafia wins was found. Moreover, it was shown that the parity of the initial number of players plays an important role. In particular, when the number of mafiosi is fixed and an odd player is added to the game (and ties are resolved by coin flips), the mafia-winning chance do not drop but rise by a factor of approx. formula_2 (equality in the limit of the infinite number of players).
Results in live play.
In live (or videoconference) real-time play, the innocents typically win more often than game theory suggests. Several reasons for this have been advanced:
But, the Mafia "can" win in live play; their best chance of winning occurs when mafioso bond with their innocent neighbours and convince those neighbours to value that bond over dispassionate analysis. The game designers Salen and Zimmerman have written that the deep emergent social game play in Mafia (combined with the fear of elimination) create ideal conditions for this.
Optional roles.
These additional roles are named differently in the many versions of Mafia, for thematic flavor, or historical reasons. Also, the same role-name can have differing functions across different versions of the game. What follows is a general list of role "types" found in Mafia variants; since the specific names vary by milieu it must be non-exhaustive.
Investigative roles.
Players with these roles use their own night-phase to discover something about other players. Though the standard game now includes the basic Detective, these roles are optional, and games can exclude them entirely (such as the stool pigeon variant, or Davidoff's original rules).
Election roles.
Public roles.
In "Town of Salem", a version of Mafia, the Sheriff is a role which can interrogate people at night, and get to know their role. The Godfather and the Arsonist are immune to the detection of a Sheriff, and the Framer can frame a player to make them appear as a mafioso.
Complicated roles.
Additional variations exist, sometimes with even more specialized or complicated abilities. There are many special roles, and many moderators design novel roles for each game. Some commercial variants ship with blank cards to allow this customization. For example, neutral factions such as the serial killer could exist (the serial killer would have to kill everyone, innocent or mafia, to win).
Variations.
The naming of various roles, factions, and other elements of play is theme-dependent and has limitless variation. Common alternative themes restyle the mafia as werewolves, cultists, assassins, or witches, with other roles being renamed appropriately.
Over the years, players have created Mafia variants that include additional rules. Some of these are listed here.
Variations on the win conditions.
If there are as many mafiosi as innocents in the day-phase then a mafia victory is declared immediately, under the original Mafia rules. Other variants suspend this rule, and only declare the game after every member of one faction has been eliminated: this makes the game easier to explain, and to run.
Election variants.
Nominees for elimination may be allowed to make a speech in their own defense. Usually, each player must vote, can only vote once and cannot vote for themselves. But some variants have a more complicated process of selecting players to be executed. Davidoff's original 'Mafia' allowed multiple day-time executions (per day), each needing only a plurality to action.
Voting variants abound, but any elimination usually requires an absolute majority of the electorate, or votes cast. So the voting is usually not by secret ballot for multiple candidates with the highest vote count eliminated; it is more usual for the voting to be openly resolved either by:
Tied votes.
Deadlocked elections can be resolved by lot or by killing the player with the scapegoat special role.
The special case of one mafioso and one innocent remaining can be decided randomly or be ruled a Mafia win—this is more usual in live play.
Optional elimination variant.
The Innocents can choose not to kill anybody during the day. Although commonly unsure of Mafia identities, the Innocents are more likely to randomly kill a mafioso than are the Mafia (at night). Therefore, not eliminating anyone (even at random) will typically favor the Mafia.
However, when the number of survivors is even, No Kill may help the Innocents; for example, when three Innocents and one mafioso remain – voting for No elimination gives a 1/3 chance of killing the mafioso the next day, rather than a 1/4 chance today (assuming random elimination).
Mafia killing methods.
Some variants require all Mafia members to choose the same victim independently for a kill to succeed. This can be achieved in the following ways:
In some online versions of the game, a particular player (the Godfather or a designated mafioso) must send in the kill.
Another variant requires the night-time vote to be secret and unanimous, but allows multiple players to be added to the execution queue to ensure unanimity.
Multiple families.
Multiple, independent groups of mafia or werewolves act and win independently, giving faster game-play and the potential for cross-fire between the factions.
Attributes.
In this variant, players are given two cards: the first contains their role, the second an attribute. Attributes were originally derived from roles that could apply to both Mafia and Innocent alignments such as "Bulletproof" (cannot be killed at night), "Mayor" (has two votes in the elimination), and "Siamese Twins" (more commonly known as Siblings or Lovers).
Quantum Werewolf.
This variant was developed by Steven Irrgang and used for a puzzle in the 2008 CISRA Puzzle Competition. The difference from a standard game of Mafia is that players are not initially assigned roles, but rather on each day are given the probabilities describing the game's current quantum state. Each player with a non-zero probability of being a seer or a werewolf performs the appropriate night actions (which may not be effective if it is later determined that the player did not have that role). When a player is killed, the wave function collapses and the players are given updated probabilities.
Train Mafia.
Traditional Mafia re-envisioned and heavily modified by the Copenhagen Game Collective to be played in a subway metro. In this variation, players who are eliminated are kicked off the train (at the next stop), and must wait in shame for the following train – a kind of 'afterlife' train – to join a second, interwoven game.
Invisible City: Rebels vs. Spies.
A location-based mobile gaming variant for Android, designed for city center play. The two factions are: the Rebels, the majority; and the Spies, the informed minority. The rule-set replaces expulsions with scoring by round. Each player is assigned an individual mission each round. Some missions are critical and if one of those fails, the round goes to the Spies, but only one player knows which missions are critical.
Ultimate Werewolf.
In this version of Mafia, the main enemies are the werewolves, as opposed to the mafia. The werewolves wake at night to kill a player, who is usually a Villager. Other helpful roles such as the Seer, Bodyguard, and Witch exist to help purge the village of werewolves, but other neutral roles exist such as the Tanner, lovers (if Cupid is in the game and the lovers are from different teams), and a third major faction: Vampires.
One Night variant.
In this standalone game published by Bezier Games, players only "sleep" and close their eyes for a single night at the beginning of the game. They then have a single day of discussion, with a single elimination. No players are eliminated as the game progresses. There is no moderator, so everyone gets to participate as a member of the town or village. When playing this game, three more role cards are used than the number of players; when everyone is randomly dealt out their card the three extra ones placed in the middle of the table. To begin the game one of the players, with eyes closed, will act as the "caller" on the single starting night, going through the nighttime roles once: Werewolves and Minions (if in play) will identify each other, the Seer will examine one player's card or two of the middle cards, the Robber will steal another player's role card and replace it with their own, the Troublemaker will blindly swap two players' role cards, the Insomniac wakes up to check if their role card has been swapped, etc. The game ends on a single elimination vote, with the villagers winning if a single werewolf is caught, and the werewolves winning if no werewolves are killed. This game can be played with as few as three players. Play time can be as quick as five minutes per game.
Town of Salem.
"Town of Salem" is an advanced online version of Mafia that takes place during the Salem witch trials. It involves several different roles from multiple factions. The game was updated on June 6, 2017, to add a new faction: the Coven, which mainly consists of witches and is similar in function and goal to the more traditional Mafia.
Online play.
Mafia can also be played online. Games can be played on IRC channels, where a bot assumes the role of a game moderator and the interaction of players is conducted via textual communication. Being that IRC is not a widespread way of communication, these Mafia games are restricted to limited number of people. Since 2008, many other Mafia game sites were formed. These sites are attempts at reproducing the live Mafia games, and the duration and the mechanics of the games are about the same as when the game is played traditionally.
Playing mafia-like games online opens the possibility of long lasting games, such as the ones on forums. In such games, one day in real life usually corresponds to one day within the game, so players log in each morning to see who was killed during the night phase.
The online games have several advantages. There is no need to gather many people in the same room, so organizing and playing a game of Mafia is faster and more convenient. Removing the human moderator and the need for players to close their eyes removes the possibility of accidental revelation of information. Online play also allows role mechanics which would be too cumbersome to use in a physical version of the game.
A drawback of online play is the lack of direct face-to-face communication, which many consider the most important aspect of Mafia. Some sites organize Mafia games with web cams, so that face-to-face communication is preserved. The long lasting online mafia games that are usually played via online forums do not necessarily have this drawback. People who communicate via forums usually do not know each other in real life.
In a traditional Mafia game, all of the players are in one room. There is no way to communicate with another player in private. With online games, this is not the case. Many Mafia game forums and game sites have rules that mandate that only one channel of communication must be used for all game related discussion.
Artificial intelligence.
Werewolf is a subject of artificial intelligence research due to its unique features such as persuasion and deception. The game requires several AI technologies such as multi-agent coordination, intentional reading, and understanding of the theory of mind.
Deep learning has been used in an attempt to develop agents that can win the game as werewolves or as villagers. Regular expressions have been used to parse utterance logs for divulgence (or "coming-out" as a role) and decision information, although one difficulty has been that a statement such a "Player A is a werewolf" could be based on either the player's ability (e.g. as seer) or just speculation.