Sometimes the simplest of games have the most powerful lessons to teach us. There are a lot of real-world dynamics that can be understood through very simple game theory models like the Prisoner’s Dilemma, Rock-Paper-Scissors, Chicken, and so forth. Often, these models are too simple to be much fun to play, and are more like thought experiments. One notable exception, however, is the party game originally known as Mafia, but perhaps more familiar these days as Werewolf.
I’ve been meaning to write about Mafia in my Beyond Poker column for a while now, but the political events now unfolding in the US bear enough similarity to the game’s dynamics that I’d like to look at it from that perspective instead. Don’t worry, though, there’s plenty in here that can be applied to poker as well.
Mafia was invented by Dmitry Davidoff, who was a teacher and researcher in the psychology department of Moscow State University at the time. The year was 1987, just around the time that the Soviet Union was beginning to disintegrate. For those who’d grown up behind the Iron Curtain, questions of dubious loyalty, deception and paranoia were a front-and-center concern, and this was both the subject of Davidoff’s research and the inspiration for the game of Mafia.
In its original form, Mafia is an almost absurdly simple game. The game begins with each player being secretly assigned to a team, originally known as innocents and mafia, though for this article I’ll use the more contemporary equivalents Town and Scum. The number of Scum can vary, but for the game to work properly must be at least two, but fewer than the number of Town players. Ideally, the game is played with a minimum of seven players, and roughly one Scum per two-to-three Town. In live play, a non-participant moderator is required.
Naturally, very little equipment is needed to play. Quite often, playing cards are used, with red suits to indicate Town and black suits to indicate Scum.
Once players receive their affiliations, the Scum identify themselves to one another. In live play, this is accomplished by everyone putting their heads down, then the moderator instructing the Scum to lift their heads quietly so they can see one another. This established the basic dynamic of the game, which is that of an informed minority versus a uninformed majority.
Play then consists of an alternating series of Day phases and Night phases, beginning with Day. During the day, the players must collectively decide, by majority vote, who will be removed from the game. In contemporary jargon, this is known as the Lynch. Typically there is a time limit, and if agreement can’t be reached by that point, the day ends with no lynch.
The player who is lynched is eliminated from the game and their affiliation is revealed: Town or Scum. Next, the Night phase occurs. During this time, the Scum secretly decide amongst themselves which Town player to eliminate; this is called the Night kill. In a live environment, verbal discussion between the Scum is naturally impossible, so the deliberation is done with hand gestures and facial expressions while the Town players keep their heads down at the direction of the moderator.
As with the lynch, the night kill eliminates the chosen player and their identity is revealed, although in the game’s basic form, this identity is of course always Town.
That is all there is to the game. The Town wins if all the Scum players are eliminated, and the Scum win if they ever equal or exceed the Town players in number; at that point, the Scum would be able to control the vote to Lynch, which makes the Town’s demise inevitable.
Even plain “Vanilla” Mafia is a fun game, but it can become a little bit dry after a few plays. Various house rules and commercial variants – the first of which was Andrew Plotkin’s Werewolf – have expanded the game’s strategy and fun factor by providing Town (and sometimes Scum) players with special roles that provide extra powers.
The constraints of live play mean that commercial versions of the game have a relatively limited set of powers. The most common are the Doctor and the Cop. The former gets to choose one Town player to protect each Night; if that player is chosen as the Night kill by the Scum, then the kill is averted. The latter selects one player to investigate each Night, whereupon the moderator informs the Cop of the target’s affiliation.
Mafia has become very popular in certain forums communities online, however, and here, a moderator with access to a random number generator and private communication with every player has much more leeway to craft original roles. Often, the game is played “closed setup,” meaning that the players do not even know which roles are in the game, and may encounter some they’ve never even seen before.
Regardless of how many special roles there are and how bizarre they can be, the strategy in a well-designed Mafia setup is largely the same as that of the basic version. At first, the Town have no information to go on, and will be casting votes largely randomly, or based on gut hunches. In live play, players can look for visible signs of nervousness, whereas online, the game typically begins with a “joke phase,” in which players vote each other for frivolous reasons, while watching for signs that someone’s joking doesn’t seem quite natural.
The Scum, on the other hand, know everyone’s alignment, and have a strong incentive to make sure a Town player gets lynched, rather than someone on their own team. This is simultaneously an advantage and their potential downfall, in that if they’re too overt in trying to sway the vote, they can raise the Town’s suspicions and end up lynched themselves.
The simplicity of Vanilla Mafia makes it a very pure exercise in game theory. Scum would like to vote for a Town player most of the time. However, this means that Town players should be more inclined to vote for players who have participated in lynching other Town players on previous days, and less inclined to vote for players who helped in lynching Scum. That, in turn, means that Scum must occasionally vote for other Scum, to avoid giving Town too much information.
As a game with more than two players, Mafia likely has multiple equilibria, rather than a single solution; however, all will share this basic dynamic, that Scum should usually but not always vote for Town, and Town should usually but not always base their voting on other players’ voting history and the alignments of the dead (“flipped”) players people have voted for.
A similar dynamic is at work with the Night kill; Scum will usually want to kill a Town player who has been persistent but unsuccessful in trying to get a Scum player lynched. However, this can likewise give the Town too much information if done consistently. To avoid allowing the Town to simply vote for whoever the night-killed player was suspicious of, the Scum must occasionally kill someone who was barking up the wrong tree.
It’s in this regard that Mafia can be good practice for poker. Both games have the feature that any pure strategy (that is, doing the same thing every time in a given scenario) can and will be exploited, yet the potential payoff for one play is higher than the others. In the case of poker, the desirable play is to put money into the pot when strong and to check or fold when weak, while in Mafia, as Scum, it is to vote for Town players and kill players whose suspicions are accurate. In both games, the key is in determining the frequency with which one needs to take the counterintuitive option (bluffing or slowplaying in poker) in order to avoid being exploitable, and then to identify the most convincing spots to exercise that option.
Mafia 101: Bussing
The act of a Scum player voting for another Scum player is so fundamental to the game’s strategy that it has its own term: “bussing,” which is short for “throwing your partner under the bus.” Scum must be willing to bus one another occasionally in order to avoid detection, but if they do it too frequently, then they may forfeit their informational advantage, or even be their own downfall.
If there were no discussion during Day phase, and only a single chance for each player to cast a vote, then the game could be approached mathematically, and bussing or not bussing would be a simple yes-or-no proposition with calculable probabilities. However, players can negotiate and speculate amongst themselves, and move their votes around until a majority is reached or the deadline expires. This means that there is more than one way for Scum to bus a teammate. There are actually a whole variety of tactics, but often, to simplify the discussion, they’re categorized as either a soft bus or a hard bus.
The soft bus
Soft bussing is bussing without the expectation that the partner in question will actually be lynched that day. It can range from verbal accusations or aggressive questioning without a vote (“You were on Joe all of Day One and he flipped Town, can you remind me why you were so sure he’d be Scum?”) to voting for the teammate early in the day with the intention of finding an excuse to switch one’s vote later. There’s even a variation where, when it seems inevitable that another player will be lynched, to push very aggressively to have one’s teammate lynched instead, counting on the Town to be unwilling to switch their votes at the last moment.
Real world equivalents to soft bussing are very common. When two or more people are conspiring unethically, it’s a natural reflex for them to want to distance themselves from one another, especially if it’s likely that the discovery of one conspirator could lead the rest of the group to connect the dots.
A fictional poker example is seen in the classic movie Rounders, in the scene in which Worm (Ed Norton) is bottom-dealing in a game of Stud to his friend Mike (Matt Damon). Knowing that Mike’s improbably good run of luck will eventually raise suspicions, Worm attempts some pre-emptive soft-bussing, drawing attention to Mike’s luck and establishing fake antagonism between the two of them with the line, “Fuck you and your never-ending string of boats, okay?”
Of course, the ploy is a bit heavy-handed, and an experienced Mafia player (or cheat-catcher) would likely find Worm more, rather than less suspicious because of it. Indeed, another player at the table begins to keep an eye on him after this, resulting in the pair being exposed as cheaters when Worm “catches a hanger.”
The hard bus
And then there’s the hard bus. Naturally, this is when the player doing the bussing does actually intend to get his teammate lynched. It’s a major gambit, because most reasonably-sized games only have two or three Scum players to begin with, so sacrificing a member of the team has a significantly negative direct impact on the odds of victory, and so one has to be confident of building a huge amount of “Town cred” in doing it.
It’s also a bad way to make friends, as it’s imperative that the teammate do a convincing job of kicking and screaming, and the best way to ensure that is to bus someone who hasn’t agreed to the plan. But if you’re playing Mafia to make friends, you’ve already made a terrible mistake.
Hard bussing is actually much more common in life than it is in Mafia (usually referred to as setting someone up to “take the fall”), and this is one of those places that game-as-model-for-reality breaks down.
In Mafia, the Town players know the game contains multiple Scum, and often the exact number. In a closed-setup game, there can be some uncertainty, but assuming that the setup is fair, it’s usually easy to guess quite closely. By contrast, real-life scenarios can involve one deceptive party or many, or even zero. That makes it much easier to give people a pass simply because they seem to be making an effort to catch “bad guys.”
As with soft bussing, there are several sub-variations of the hard bus, and these vary considerably in how convincing they are. Sometimes, what began as a soft bus early in the Day phase becomes a hard bus because the bussing player comes under scrutiny themselves and can’t find a non-suspicious way to move their vote later. Conversely, once it seems inevitable that a teammate is going down, the remaining Scum tend to try to find plausible moments to join the bandwagon rather than drawing attention to themselves by fighting to the end.
The most convincing – and consequential – hard bussings come midway through the deliberations, when it’s most up in the air whether this player or that player will be lynched that day. For instance, if there are nine players remaining and it will take five votes for a successful lynch, there may be two or even three players with three votes on them as deadline approaches. Quite often, in that situation, a single shifted vote will create the decisive momentum.
To borrow a term from the business world (which stole it from the mathematics world), we could describe these tense moments as “inflection points.” Although each player’s vote carries the same weight in theory, the combination of time pressure and the consequences to the Town of letting a day end with no lynch create situations in which a player can single-handedly force the vote to go a certain way.
Of course, it’s hard to determine when that point is reached, sometimes even with the benefit of hindsight. One player may judge a certain vote to have been the tipping point, but others might point to the one just before or just after. As a result, hard-bussing strategies that fall close to the actual inflection point tend to get a lot of credit, but the effective cost to the Scum team can be very high or zero, depending on whether or not the vote could still have been swung another way. The ideal timing for the Scum, then, is to identify the exact moment that one of their members is doomed, and to begin bussing as soon as possible after that point.
The political connection
At this point, it should be fairly clear what the connection is between Mafia strategy and the events that are unfolding in the United States. Since his election, it’s been a major question whether Donald Trump will find himself impeached or worse, and as time goes on, those odds have been steadily increasing.
Although it may still be some time before we know for sure whether that is what is going to happen or not, it’s likely that we are either approaching the inflection point, or have just passed it. For the time being, the majority of Republicans in congress still support Trump or are at least not actively resisting him, but this is beginning to change. It’s going to be important for the public to watch and keep track of who comes down against him, when and how hard.
It’s popular among a certain segment of the left to claim that every Republican politician is morally bankrupt and supremely cynical, but this is probably not the case. Even if one believes that most conservative policies are wrong-headed, it’s disingenuous to claim that every Republican is knowingly attempting to further enrich upper class white people at the expense of all others; some surely are, but others are presumably attempting to do their best for the country even if I, and perhaps you, believe they’re going about it the wrong way.
Many of those who voted for Trump did so not because they supported the man himself, but saw him as a wrecking ball to send swinging into the entrenched corruption of Washington insider politics. That, at least, is certainly coming to pass, but regardless of how and when Trump’s term in office ends, the next step is going to be to rebuild the two parties, and the government itself.
If Americans would like things not to go back to the way they were before Trump, distinguishing heroes – misguided or otherwise – from villains is going to be necessary. When it comes to the Republican party, one big clue is going to be what each man and woman does right around now.
Not everyone who resists Trump is going to be doing it for the right reason; watch the timing and intensity, and ask yourself whether the person is doing so for the good of the country, or simply because they’ve realized that continuing to support him will make them look bad. That’s how the Town catches the Scum.
Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.