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 (russian: Дми́трий Давы́дов, ''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.Plotkin quotes a 2005 email in which Davidoff explains 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 Vygotskiy. ''Wired'' attributes the creation to Davidoff and also dates the first game to 1987. He developed the game to combine psychology research with his duties teaching high school students. It became popular in other Soviet colleges and schools, 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).

Andrew Plotkin gave the rules a werewolf theme in 1997, is Plotkin's own description of the original Werewolf version 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. Mafia and a variant called ThingIn which the antagonists are Things, shape-shifting aliens that can turn humans into other Things. For the rules of the original variant, see: . For a detailed description of another variant of this game, see: . For the most recent variant using web-enabled devices, see: 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 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.. Retrieved 2014-05-16. 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 is one of the 50 most historically and culturally significant tabletop games since 1800 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, or by other non-verbal methods such as physically tapping players. 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:

* ''seer'' — a villager who may learn the team of one player every night;
* ''protector'' — a villager who may protect a player from being killed every night, but can only do so once in each game;
* ''masons'' — village-aligned players who can recognize each other

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 should not 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

$W(m, P) \approx \frac ,$

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. $\sqrt$ (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:
* 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

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