Mafia (party game)

• 1. Introduction

  ›

  Mafia, also called Werewolf, was created in 1986 by Dmitry Davidoff, a psychology student at Moscow State University. It pits a small group of players who know exactly who their allies are against a larger group who know nothing at all. Everyone sits together, everyone talks, and every player holds a secret. The only fuel the game needs is suspicion.

  Three questions run through this documentary. How did a classroom experiment from the Soviet Union end up at technology conferences and on television? Why do the honest players so often beat the liars, even when the mathematics says the odds are closer than that? And how does a game made entirely of conversation become a research subject for mathematicians and computer scientists?

  12413

• 2. From Moscow To The World

  ›

  Davidoff dates the very first game of Mafia to the spring of 1987, in the Psychology Department where he studied. He says he brought it into classrooms for research purposes. From there it spread like a meme, first to dormitories and, probably during the following summer, to student summer camps.

  Lev Vygotsky, a psychologist who did pioneering work in the 1920s, and the Turing test are the two influences Davidoff credits for his game-based method. He designed it so that his psychology research could sit alongside his duties teaching high school students.

  The television series La Piovra first aired in 1986 and was hugely popular. Mafia became closely associated with it as the game passed through other colleges and schools across the Soviet Union.

  In the 1990s the game began to be played in other parts of Europe, in some countries under the name City of Palermo. It then crossed to the United States. By the mid 1990s a version had become a Latvian television series with a parliamentary setting, played by Latvian celebrities.

  Andrew Plotkin, who is also known as Zarf, added the werewolf theme in 1997. He argued that the mafia carried less cultural resonance. A werewolf, he felt, matched the idea of a hidden enemy who looks perfectly normal in daylight.

  The Werewolf version became widespread at major technology events, including the Game Developers Conference, ETech, Foo Camps and South By Southwest. France adopted the same theme in its own adaptation, The Werewolves of Millers Hollow.

  In 1998 the Kaliningrad Higher school of the Internal Affairs Ministry published a methodical textbook on nonverbal communications. It built role-playing games around Mafia and a companion game called Murderer, for a course on Visual psychodiagnostics. Its purpose was to teach students to read body language and other nonverbal signals. In September of that year Mafia reached the Graduate College at Princeton University, where several variants were developed.

  A Russian film based on the game, Mafia: The Game of Survival, followed in 2016 and received negative reviews. The game itself never needed a screen, only a moderator and a handful of cards.

  23478

• 3. A Night And A Day

  ›

  A card handed across the table, or a physical tap on the shoulder, is how a live game assigns secret identities. The moderator does not play but runs the proceedings. Every mafioso is told who the other mafiosi are, while the innocents learn only how many mafiosi are in the game.

  Players also need to know how much to trust the setup. In an open setup, everyone knows how many of each special role are in play. A closed setup hides that information, and a semi-open setup reveals only limited or tentative details.

  Night comes first in the rhythm of play. The moderator tells everyone to close their eyes, then asks the mafiosi alone to open theirs and acknowledge each other with a tap on the shoulder. They choose a victim by silently gesturing at a target, showing that they agree, and then close their eyes again.

  Other roles with nightly actions follow the same pattern. A seer, for example, might learn a target's innocence or guilt through a nod or a shake of the moderator's head. Players may tap gently on the table to cover the sound of all this gesturing.

  Day begins when the moderator tells everyone to open their eyes and announces who died overnight. The survivors then argue. At any moment a player can accuse someone of being a mafioso and ask the others to vote. If more than half agree, the accused is eliminated and night falls again. Otherwise the debate simply goes on.

  House rules differ on what happens to the dead. Some reveal an eliminated player's role. Others keep it secret, so that nobody learns, for instance, that the protector has died. In every version the dead are not allowed to influence the survivors. Daytime tends to run longer than night, because the living are free to deliberate.

  The game ends when all mafiosi are eliminated or when they reach numerical parity with the innocents. Davidoff's original rules call for roughly a third of the players to be mafiosi, rounded to the nearest whole number. Plotkin recommends exactly two. For his Werewolf rules, Plotkin also suggests starting with a night and having an odd number of players, counting the moderator. That way votes cannot tie, and the game finishes on a dramatic elimination rather than on a murder everyone saw coming.

  12131429

• 4. The Mathematics Of Suspicion

  ›

  In 2006 the computer scientists Braverman, Etesami and Mossel proved something striking about perfect play. With no detectives and flawless players, a randomized strategy is optimal for both the citizens and the mafia. Neither side can do better than to behave unpredictably.

  Mafia is hard to model, so most analyses of optimal play make two simplifying assumptions. There are only townsfolk and mafiosi, and the townsfolk never identify the mafia with a probability better than chance. Early work relied on simulation. More recent studies have tried to derive closed-form equilibrium solutions for perfect play.

  Braverman and his colleagues also asked how many mafiosi make the game fair. To give both groups a similar chance of winning with a large crowd, the number of mafiosi must be proportional to the square root of the total number of players. Their simulation confirmed that 50 mafiosi among 10,000 players would win almost half the time.

  Detectives change the arithmetic. Once they are added, the same researchers showed, the mafia's share of the table must stay a fixed proportion of all players if their winning chance is to remain constant.

  In 2008 Erlin Yao derived specific analytical bounds on the mafia's chance of victory when there are no detectives. A paper from 2010 went further and found the exact formula for that probability.

  The 2010 result also revealed that the parity of the starting player count matters a great deal. Suppose the number of mafiosi is fixed, ties are settled by coin flips, and one odd extra player joins. The mafia's winning chance does not fall. It rises.

  All of these models imagine players who lie without strain and read each other no better than random guessing. Real tables rarely behave that way.

  151718195

• 5. Why Innocents Win

  ›

  Max Ventilla, one of the game's fans, put the villagers' advantage bluntly: "If the villagers are allowed to keep a pencil and paper, they always win." His point is that the mafiosi's voting patterns give them away as the game goes on, and written notes make those patterns easy to track.

  In live play, whether in a room or over videoconference, the innocents usually win more often than game theory predicts. One explanation is physiological. Sustained lying is stressful, and that stress erodes the mafioso's ability to deceive far more than a model of perfect play would expect. Faking shock or anger over a long period is especially hard. An accused player may begin with feigned outrage, along the lines of "How dare you ask me that?" Over time that outrage tends to slide into plain objection, because mimicking emotion is psychologically difficult.

  Experience pushes in the same direction. As players grow more sophisticated, they get better at spotting and using deception. They also tend to be villagers more often than mafiosi, so they sharpen the skills that innocents need faster.

  Davidoff points to a metagame. In his view, past connections always lose to future collaborations. When the same group plays many rounds together, a reputation for honesty is worth more than a reputation for deceit. He considers this so important that he believes the advantages of playing the mafioso honestly outweigh the disadvantages.

  The mafia can still win. Their best chance comes when a mafioso bonds with innocent neighbours and persuades them to value that bond over cold analysis. The game designers Salen and Zimmerman have written that the deep emergent social play in Mafia, combined with the fear of elimination, creates ideal conditions for exactly this.

  11524135

• 6. A Village Of Roles

  ›

  Davidoff's original game had no special abilities at all, yet modern versions carry a long cast of roles. Names shift between versions for thematic flavor or historical reasons, and the same name can mean different things in different games.

  The Detective is the best known investigator. It is also called the Seer, Sheriff or Commandant. Detectives are allied with the innocents and learn whether a chosen player is a mafioso. Every commercial card game version includes one, as do almost all internet versions. Because nobody knows who the detective is, anyone may pretend to be one.

  The Little Girl in Werewolf and The Werewolves of Millers Hollow gets a different gift. She may secretly peek while the werewolves choose a victim. If they catch her at it, she dies of fright.

  The Doctor protects one person each night, and that person survives any night attack. Doctors are commonly allowed to protect themselves but barred from protecting the same target on consecutive nights. A Guardian Angel, by contrast, can only protect others.

  Some roles exist to confuse investigators. The Miller is an innocent who looks guilty. The Godfather is the opposite: the mafia leader, who looks innocent. The Traitor works for the mafia and wins only if the mafia does, yet never wakes at night and does not show up as a mafioso. The Undercover Cop is a mole inside the mafia who wins with the innocents.

  The Baker gives out loaves of bread at night. If the Baker dies, the innocents have just three nights to get rid of the mafia, or they starve and the mafia win. The Thief, in Werewolves, can steal another player's role on the first night or take an unused card. In Werewolf, Cupid chooses a pair of Lovers, and if one dies, the other dies too. The Lovers can win together as the last two standing.

  Many moderators invent new roles for each game, and some commercial variants ship with blank cards to make that easy.

  5933343642

• 7. Rule Variants And Spinoffs

  ›

  A shape-shifting alien is the villain of the variant called Thing. The antagonists there are Things that can turn humans into more Things. Players have rewritten nearly every other part of the rules too.

  One famous quirk involves refusing to kill. In the original Mafia rules, if there are as many mafiosi as innocents during the day phase, the mafia win immediately. The innocents may also choose to eliminate no one. That generally favors the mafia, but not always. With three innocents and one mafioso left, skipping the vote gives a 1 in 3 chance of killing the mafioso the next day, instead of a 1 in 4 chance today, assuming random choices.

  Several variants change how the mafia kill. Some require every mafioso to choose the same victim independently, which can be done by waking them separately or by calling out each name and watching for raised hands. In another method, innocents write the word honest on a slip of paper while the mafia write a name. A kill succeeds only if every mafia slip matches. Davidoff's original Mafia even allowed several daytime executions per day, each needing only a plurality.

  The Copenhagen Game Collective reimagined the game as Train Mafia, played on a subway. Eliminated players are kicked off at the next stop and must wait for a second train, a kind of afterlife, to join a second, interwoven game.

  Steven Irrgang developed Quantum Werewolf for a puzzle in the 2008 CISRA Puzzle Competition. Players start with no assigned roles. Each day they receive the probabilities describing the game's current quantum state, and when a player is killed, the wave function collapses and the numbers update.

  Invisible City: Rebels vs. Spies is a location-based game for Android, designed for play in city centers. The One Night variant from Bezier Games compresses everything into a single night and a single elimination vote. It needs no moderator, can be played by as few as three players, and a round can finish in five minutes.

  Town of Salem is an advanced online version set during the Salem witch trials. On the 6th of June 2017 it added a new faction, the Coven, which consists mainly of witches. Town of Salem 2 reached Steam on the 26th of May 2023 and removed the Mafia faction entirely, handing most of its functions to the Coven.

  6648767579

• 8. Screens And Schools

  ›

  Internet Relay Chat channels were an early home for online Mafia. A bot takes the part of the moderator, and the players do all of their talking in text.

  In June 2006 a school inquiry began in Rockingham County, New Hampshire. A parent had complained that classroom Mafia was traumatizing her fifth-grade daughter. She described the girl as having "sleepless nights, crying before bed because she's afraid that she'll sleep walk and relive the tragic events they talked about in class".

  Davidoff replied as a parent who had studied child psychology for 25 years. He argued that the game could "teach kids to distinguish right from wrong". In his view, the positive message of being honest could outweigh any harm from an "evil narrator" who moderates the game as though telling a scary story. The incident led to a teacher's resignation.

  Werewolf has also become a subject for artificial intelligence research, thanks to its persuasion and deception. Playing it well requires multi-agent coordination, intentional reading and an understanding of the theory of mind.

  Researchers have used deep learning to build agents that try to win as either werewolves or villagers. They have also used regular expressions to scan logs of what players said, looking for divulgence, the act of announcing a role, and for decision information. One difficulty keeps recurring. A statement such as "Player A is a werewolf" might come from a seer's real ability, or it might be nothing more than a guess.

  4782868885