Mafia, also known as Werewolf, is a social deduction game created in 1986 by Dmitry Davidoff, then a psychology student at Moscow State University. 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-phase, during which those with night-killing-powers may covertly kill other players, and second, a day-phase, in which all surviving players debate 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. Davidoff says that he brought Mafia into the Psychology department classrooms for research and it spread (as a meme) from there to dormitories and likely over next summer, through student summer camps. He credits this game-based methodology to pioneering 1920s psychologist Lev Vygotsky and the Turing test. He developed the game to combine psychology research with his duties teaching high school students. It became popular in other colleges and schools in the Soviet Union, often associated with hugely popular TV series La Piovra, which first ran in 1986. In the 1990s, it began to be played in other parts of Europe (in some countries under the name City of Palermo) 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.
In 1997, the werewolf theme was added to the game by Andrew Plotkin (also known as Zarf), arguing that the mafia had less cultural resonance, and that the werewolf concept fit the idea of a hidden enemy who looked normal during the daytime.
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 reading body language and nonverbal signals.Петров С.В., Холопова Е.Н. «Невербальная коммуникация. Развивающие ролевые игры „Мафия「 и „Убийца「». Учебно-методическое пособие – Калининград: КВШ МВД России, 1998 In September 1998, Mafia was introduced to the Graduate College at Princeton University, where several variants were developed. The werewolf theme was also incorporated in the French adaption of Mafia, The Werewolves of Millers Hollow.
In 2016, a film, Mafia: The Game of Survival was made in Russia based on the game; however, it received negative reviews.
Gameplay
In its simplest form, Mafia is played by two teams: the mafiosi and the villagers. Live games require a moderator who does not participate as a player, and identities are assigned by handing out cards, or by other non-verbal methods such as physically tapping players. At the start of the game, every mafioso is given the identities of their teammates, whereas the innocents only receive the number of mafiosi in the game.
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.
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 mafiosi have been eliminated or they reach numerical parity with the innocents.
Some players may be given roles with special abilities (see below). Common special roles include an investigative role, a protector role, and some association roles.
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 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 are told to close their eyes. The moderator then instructs all mafiosi to open their eyes and acknowledge their accomplices via tap on the shoulder. The mafiosi 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 mafioso 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 should be revealed; according to others, for example, if the protector dies, nobody should know that. 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 . 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.The single detective publishes a large list of innocents, and asks to be lynched to guarantee its veracity (under the standard rules in which the detective's role is revealed after she is killed, no strategic interference from the Mafia is possible):
In 2008, Erlin Yao derived specific analytical bounds for the mafia's win probability when there are no detectives.Derivation is by recursion on decreasing numbers of players in the following round, see:
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. (equality in the limit of the infinite number of players).
In 2023, a modification to the strategy of Braverman et al., termed the Modified Braverman Strategy (MBS), was proposed to increase the Mafia's probability of winning. When the numbers of Mafia and citizens are equal and greater than one, the MBS allows the Mafia to coordinate their votes against a predetermined citizen if the randomized resident vote selects a Mafioso, rather than voting to eliminate the selected Mafia member. Under the original Braverman strategy, for , the Mafia's probability of winning is ; under the modified strategy it is . Thus, within the model, the modified strategy weakly dominates the original strategy. Computer simulations reported in the thesis also produced higher Mafia win probabilities under the MBS than under the original strategy across the game sizes tested, with increases ranging from 1% to 13%.
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: The physiological stress of sustained lying degrades the initial ability of mafioso to deceive the innocents, much more than a model of perfect play would predict, especially if the innocents can get the town emotionally involved in the game's outcome:
The information revealed by the mafiosi voting patterns tells against them later in the game. One of the game's fans, Max Ventilla, has said that "If the villagers are allowed to keep a pencil and paper, they always win." As players get more experienced, their strategic sophistication and ability to spot and use deception increases. They will typically get better at the skills needed for playing innocents faster, being villagers more often than mafiosi. The Metagame aspect: Dimma Davidoff has said past connections will always lose to future collaborations. When playing several Mafia games with the same people, it's more helpful to be known for honesty than for deceit. Davidoff considers that so important that he thinks the advantages of playing the mafioso role honestly outweigh the disadvantages.
Laboratory results have not necessarily shown the same pattern. In a 2023 study in which players were not permitted to communicate, there was no statistically significant difference between observed and theoretically predicted win rates. The Mafia won 43 of 80 games (53.8%), compared with a theoretical win probability of 51.8% (); excluding one nine-player session, the Mafia won 37 of 70 games (52.9%), compared with a theoretical probability of 49.2% ().
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