The Psychology, History & Math of Social Deduction Games

By mrixrt | MRIXRT | 25 Mar 2021




One of 2020’s biggest games is Among Us, a truly massive game that just broke four million concurrent players--making it one of the largest and most successful games of all time. Have you heard it’s success story? It was released in 2018, something a lot of players find surprising, and sat in relative obscurity for two years. There’s even a tweet from one of the developers talking about how they had 8 players online once, and they were pretty thrilled. Seemingly destined to die, it got a lot of attention in Brazil, followed by a lot of memes building their way into the culture, finally ending up with a stream by AdmiralBulldog which led to it’s introduction to the masses, and then a massive stream by Sodapoppin that tipped it over the edge. And within three months, it explodes and becomes one of the biggest games in the world. In fact, it became so large and so popular, that they unintuitively cancelled the sequel to maintain their player base and provide updates to the game for the newest players.

And it totally deserves it too, there’s really no question that it’s a great and simple game, well designed, cute, totally perfect for today’s Permanently At Home gamer. It’s become such a large presence that maybe you’re starting to ask the question: Well, how long is it going to stay? When will Among Us be ejected? After all, games come and go. They’re number one on Twitch one day, and empty wastelands the next.

However, Good News Everyone! Okay, I’m not Billy West, but good news regardless: If you love Among Us, you’ll love the next game in the genre! Yes, you may not have realized it if this is your first time on the carousel, but Among Us is actually part of the “Social Deduction” genre. 

Social Deduction, that is deductive reasoning, or the logical process of figuring things out based on evidence. Take that and add it to a social setting, so logically figuring things out based on evidence from other people. Probably the earliest such game that people played was Cluedo, or Clue if you’re a heathen North American, a murder mystery game that spawned movies and about a thousand different branded versions. Created in the 1940s, you’ve probably played the game, or seen it played, and the goal is to determine who killed whom with what and where. This format was updated by games like Scotland Yard, which introduced a competitive aspect to the gameplay, where detective players try to capture a criminal player, or The Fury of Dracula! Which adds even more to this formula by introducing combat.

Of course one of the biggest problems with boardgames is the need to have a board, and so a more social party game aspect was introduced by the game Mafia--the first and easily most copied Social Deduction game. Stop me if you’ve heard this one, you’ve got two groups of people, the citizens and the mafia. The mafia can kill citizens during the night, and the citizens can vote out people they think are in the mafia in a meeting during the day. It’s really prototypical, to the point that it’s basics are the basics of social deduction. A group of people who have various roles and various win states based on those roles. Mafia was developed in the Psychology Department of Moscow State University, and it should surprise absolutely nobody to find out that this was done as psychology research. The creator, Dimitry Davidoff, was an overworked college student making side-cash teaching high school students about psychology, and he needed a way to be more efficient: So he developed a game that could appeal to his younger student but also provide fodder for his term papers.

This was taken later and refined and expanded by game developer Andrew Plotkin into Werewolf, a version of the game that adds all sorts of roles like detectives, psychics, witnesses, doctors, hunters, and many many many more. One of the most interesting quotes from Andrew that I think magically describes Social Deduction games entirely is this: “It was what poker would be if you didn't play with a deck of cards, but bet solely on other people's bets.” Fascinating.

Now there is no evidence of this, but I have sneaking suspicion that 1982’s The Thing had to play at least a small role in the ideation of this game, and certainly others thought so too since there are several variations of Werewolf based on the movie.

And speaking of movies, they also made a movie about Mafia, and boy it looks legitimately terrible, I can’t wait to watch it.

The Werewolf concept doesn’t stop there, it expands well outside of board games, well outside of even movies, and into tech, obviously into video games, but also into board rooms and conventions. It’s studied and researched and mathed into the ground, with people using the gameplay to learn how to lie better, and how to spot lies better. For example, the first reaction that people tend to have when they’re accused of being the bad guy? Aggression. Outrage! Why? Because that’s the easiest emotion to fake, it’s hard mimicking emotions, mimicking real interpersonal behavior. You lie, and your heart rate goes up, your blood pressure rises, you breath a little faster--it’s all physiologically tied up with the act of creating falsehoods. So psychologically, the easiest out? It’s not shock, it’s not logic, it’s anger--how dare you ask me that, I am absolutely not a bad guy!

This was a game that transcended just the usual thinky-thinky nerd types and really moved into a cultural phenomenon, and party games almost inevitably become video games simply because it’s easy. Everyone knows how to play them already, and they’re good for groups gathered around a console. And eventually, they proved good for groups gathered around a internet. 

In 2006, Garry’s Mod was released on Steam as a standalone product, and eventually in 2009 a contest was held to determine what game modes should be added. Unceremoniously added just about a year later, Trouble in Terrorist Town was alive. This is essentially Werewolf, or Mafia, mixed with a little bit of Counter-Strike, and it proved remarkably successful. GMod has now sold over 15 million copies, and I somehow doubt they’d suggest that people RDMing their way through TTT wasn’t responsible for a good portion of that.

Soon after, Town of Salem would show up as a free-to-play browser game and later Steam game, and to date is likely the second largest Werewolf game in existence, with a reported 8 million players. This follows the traditional Mafia-style of gameplay pretty closely--a group of people in a circle talking about what they’re doing, and lynching someone. I think the fact that there is a free-to-play version and yet people will still choose to pay for the premium version says all that needs to be said about how enjoyable, and might I even suggest, addictive this gameplay is. 

Now neither of these were the first, but they’re some of the most successful video game adaptations, and some of the most faithful. Space Station 13 is another very popular but perhaps slightly less polished Werewolf-esque game. It certainly falls into the category, though it’s on the edges. Barotrauma is a submarine game that’s awfully similar as well, and so is Stationeers. All games that seem to be a divergent branch of the Social Deduction tree, and all with major changes to the gameplay in an effort to address the ever-present issues inherent in the Mafia style gameplay, and I wonder if you haven’t identified them for yourself already.

Imagine it, you’re sitting in a circle with strangers, and your goal is to either survive or kill them, which means that either you are being lied to or you are lying to people. Imagine where the most fun actually takes place, and where the most stress takes place. Being a citizen and having no idea who’s out to kill you, who’s lying to you, is stressful. There’s nothing to do except lay your head down and hope you’re not chosen to be killed, and then be prepared to defend yourself when someone wrongly accuses you of being a killer and therefore worthy of death yourself. Imagine doing all of that, and then spending 30 minutes or more in a dead state because you lost. And what is the win state outside of killing everyone? Either the werewolves eat everyone, or the citizens lynch enough innocents to have accidentally killed the bad guys. You have players sitting around doing nothing at all both when they are alive, and when they are dead. If you’re not leading the discussion and you have nothing valuable to add, you’re just sitting there until someone kills you. And when you’re dead, you sit there and watch other people have fun. You have players with no clear win state outside of betrayal, and no goal to cooperate. These are the issues with the format, and it’s why so many changes have been made, so many other games in diverging branches.

Speaking of diverging, there’s a lot of math study around these types of games. It’s really mindblowing, actually, and during my research I came to the conclusion that I can’t share most of this because boy--it’s not interesting unless you’re a psychopath like me. And I promise, I won’t get into the actual math of it, but the studies are in the description and if you’d like a taste, they go into pure death processes of markov chains, a stochastic model that is used here to determine the approximated probability that the mafia will win any given game. And it’s really fascinating, it’s fascinating to see how these studies relate to mass hysteria and uninformed majority decisions, and there are 3 really really cool takeaways from this.

First, as counter-intuitive as it may seem, the best thing to do is to randomly vote with absolutely no preconceptions immediately. Literally as soon as the game starts, you should vote someone out. You’d think this means you have high chance of killing a civilian, but the bad guys are going to kill people too--so best to just take a shot. Those werewolves have an equal chance of being removed as anyone else. And as with a lot of probabilities, it sounds wrong but it is right. Now this only works if there’s no information, no detectives telling you who is or isn’t, and no outside information--as in no one’s seen anything yet. But at the start of a game, of course no one’s seen anything. Instead, you should just lynch someone at random. As often as possible. So, everytime you get a chance, vote someone out and you’ll most likely win.

Secondly, don’t play games with odd numbers, because that tips the balance of power unfairly into the hands of the enemy. You want as many even numbers as possible, and as often as possible, because when there is an odd number you give the coin toss to the enemy. Let’s say that we have 9 people. 2 are bad guys. 4 people want to vote out a bad guy, and 3 people want to vote out a good guy. Well, those two bad guys just have to vote with the minority and it becomes a 5-4, and the bad guys win that vote. Now they’ve lynched a good guy and they still get to kill more good guys. Wait for even numbers whenever possible, and if the game comes down to 9 players, wait for a tenth. In fact, adding in an odd player tips the probabilities towards the bad guys by over half--to the point that just by starting with an odd number of players you’ve basically guaranteed a bad guy win. 

Finally, with any information, the citizens will vote--properly--almost 70% of the time. Given any good intel, citizens will kill the right person. This is combined with the fact that almost all players will approach their decisions pessimistically, meaning they assume every player is a bad guy--and by the math, when players make the wrong decision, they tend to do so because they assume the other player had bad intentions. This means that as a good guy, you need to be as honest as possible if you want to win--just lay it all out and don’t hide things. Be cooperative, and helpful, and transparent--and if you are, then other players will hopefully overcome their natural pessimism and see the information you’re providing as good--and therefore make the right decision and kill the other guy. 

So how does Among Us fit into all of this? Well, it’s a natural progression from Mafia, to be more real-time and not turn based. A faster, faster kill pussycat version of a very traditional Mafia game. There’s no detectives, there’s no special roles, but everyone always has their head up looking around. There are goals to complete, so when you’re alive you feel like there is a win state--complete all your tasks and win. And when you’re dead, there’s something to do that actively contributes to your team: Either completing tasks and therefore getting the good guys closer to winning, or sabotaging the still alive players in order to influence their votes against their teammates and provide opportunity for your own team to score kills. This addresses some of the major issues in the original format, while maintaining the day-night cycle of the game by limiting conversation to emergency meetings held around the finding of a corpse. 

Yes, Among Us is certainly a very good Mafia game, one that takes the failings and improves upon them to the point that it’s almost obvious why it would become so popular. It’s also inevitable that it will be replaced, not just as one of the most played games, or one of the most watched on Twitch, but also as the next generation of Mafiwolves. In fact, Among Us came out in 2018, and since then some very good Were-ia games have come out--including Unfortunate Spacemen, a Mafia style game that has iterated on the format by allowing the Mafia character to change skins and imitate and mimic other players--giving a whole new dimension to the lies and tricks, and really ratcheting it up another level. If anything, the biggest complaints I have about Spacemen is that they haven’t taken the lessons from Among Us with regards to giving dead players more to do. It would be great to see some very smart new implementation here that makes it so dead players aren’t floating around the map for 15 minutes in some material way that helps the civilian players. This is the revolutionary upgrade that Among Us brings to the genre.

Thank you to all my patrons who kindly help me pay for this content, and of course thank you for watching and sharing this video, it really helps me out because the only way new people find my content is if you decide to share it. And, as always, I’ll see you on the next one.

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mrixrt
mrixrt

MRIXRT is Moriarty


MRIXRT
MRIXRT

Completely Biased. Video Game Critic & Digital Connoisseur. MRIXRT is Moriarty, and I create visual thinkpieces, or "Video Essays." My most popular videos focus on delivering complete histories of studios, genres, events, or specific games and their franchises. Articles are scripts of videos with minor additional editing.

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