Happy New Year everyone! When I first made this video I had NO idea it would get this many views what on earth. Anyway, I thought I'd put together a comment on FAQs I've seen so far and what my takes are on everything. I'm not saying these are objectively correct answers, but just this way people can see a centralized response list. I also want to clarify that this is by no means a perfect video and I've been trying to take everyone's feedback as seriously as possible for future videos. Q: Why'd you say "2-3 Mafia per Town"? A: That was a typo in the script my bad Q: Isn't an optimal strategy to mix up the probabilities of doing either this strategy or strategy [INSERT HERE]? A: Technically, yes. However, the actual weights and values of those probabilities themselves is unknown to me and I'm really not sure if anyone could ever simulate it with programming (if you can please drop a link). Yes, mixed Nash Equilibrium strategies exist, but since I don't believe it's possible to get the optimal weights, I'm not really sure where that discussion takes us beyond a fun hypothetical. Q: If people watch this video doesn't this mean they would account for this strategy and it wouldn't be the optimal strategy? A: Also yes. However, in my mind that's kind of like saying "if I'm playing Rock-Paper-Scissors and my opponent knows I'll always do Rock, doesn't that mean I'll always lose?" Following this analogy, this video is more trying to inform you of the fact that you could throw Rock Paper or Scissors and that you have multiple options. However, if you have clearly rational plays, it still is good to establish this baseline. Q: What if people don't believe me during the day if I say [INSERT SOMETHING ELSE]? A: I did try to stress in the video that I couldn't really account for social deduction skills. For instance, if a cop outs with a check on the Mafia but the Mafia is so persuasive, then like yeah you can't really do anything about it either. It's unfortunate, but you can't really account for everything so I tried to focus on things you can control. Q: Can you make a video on [INSERT GAME HERE]? A: I'll do my best to take account everyone's recommendations! Again, I didn't really expect this video to blow up, but my general focus for content was really just about probability applications. I'll definitely look into games (Spyfall, Secret Werewolf, etc...) but I have no real timeline on when future content will be. Q: Is this really the optimal strategy? A: I think this video (at least in my mind) is actually optimal if you walked into a room with 6 other players you'd never met before and no one had any prior information on each other. If you then played hundreds of games with the same 6 other players, obviously some adaptations would probably arise.
I play Town of Salem but I imagine it would be a lot harder to do this kind of thing there because there's so many moving parts. That, and people mostly play the "all any" role list nowadays.
I think this question is still valid: "Q: What if people don't believe me during the day if I say [INSERT SOMETHING ELSE]?" Rather, the question to be asked should be what if 2 people claim to be a certain role. I think these cases need to be considered in order to have the complete strategy. e.g. 2 people claim sheriff, 2 people claim doctor, real sheriff stays silent but mafia claims sheriff, 1 sheriff 2 doctor, etc edit: I realize in other comment thread you mention it is psychological, but it is purely statistical just like how you model chance of mafia killing each role. you would have to account for all paths. For example, 2 people claim sheriff and each other as mafia. Is it better for townspeople to randomly decide between the 2, some other person, or skip entirely. For each of these scenarios we would calculate the probability of a town win, then town would pick the highest win rate option. e.g. let's say town picks to vote one of the 2 players claiming sheriff, 50% sheriff is eliminated, then from then on what would be paths from there, then next day mafia attempts to reveal their supposed investigation during the night, what are the chances they get it right, what if they choose to say a role of their fellow mafia, and that mafia agrees, or maybe the other mafia disagrees, each of these options then need to be explored. As you can see there's no psychological aspect to any of the above scenarios, just pure statistics, and each player would consider all those option since it is given that they are purely logical.
The real best way to play mafia is to send this video to one or more players beforehand, and then play totally illogically. If I don't know what I'm doing, they sure as hell can't.
I think you missed quite a few cases and strategies. First, the mafia can claim to be the Doctor and/or Sheriff, even when they are still alive. This is HUGE. Theres also the strategy where the Doctor saves someone else specifically because they knows that people will assume they saved themselves in the first round. This frees them up to save themselves when they know they're going to be attacked. These are both potentially rational decisions, as it's actually irrational to only act in your immediate self interest rather than maximising long term expected win rate.
Thanks for your input! I definitely do agree that there are other psychological factors and do address them briefly at the end of the video like the Mafia counter-claiming roles. You're obviously correct that in a scenario where, say you're with your friends, you might know that the most logical person might be targeted on night 0 the most. However, the video itself is a more generalized take on Mafia where we don't include meta-gaming/long-term win rates. Also, while I do think that making predictions is definitely a core part of the game, it's really hard to contextualize. For example, what if the Mafia knew the doctor would think that they (the Mafia) would target a specific individual and chose to target someone more innocuous instead? The levels of thinking ends up becoming circular, so it's really hard to say what the "best" first move is, but I would still contend that the doctor saving themselves is definitely the "safest" move. Let me know your thoughts though.
@@Poly_morphia I don't think those strategies really count as psychological factors/meta-gaming, though. Because mafia is an imperfect information game, I'd bet the "mathematical best way to play" is a mixed strategy where the doctor sometimes heals themselves, sometimes doesn't, and the mafia sometimes counter-claims sheriff, and sometimes doesn't. The analogy here would be to something like poker, where game-theory optimal (GTO) play requires you to randomize your strategy in certain positions. As far as I know, the game of mafia hasn't been "solved" yet (at least, not with this ruleset), so can't say for sure, but I doubt the approach presented in this video is mathematically optimal. Admittedly, it's still probably better than what most people do though
@@nicholas8288 Yes! You're absolutely correct that you do have to have some randomization. However, I think the conditions at the point where you need to implement randomness in your strategy is where we likely differ slightly. For example, if you walked into a room with 6 random people you had never met and were assigned the role of the Doctor, it becomes way more difficult to optimize on what to do because you lack the necessary priors to make these structurally randomized decisions. In contrast, if you have played hundreds of games with the same 6 other people for years, it becomes a lot easier to develop new strategies. If you know that, say everyone was following the strategy listed in this video, then you could actually create structured randomness rather than pure guess-in-the-dark moves. If we relate this to your poker analogy, I think this would be my best comparison. It's a lot easier for me to bluff if I 3-bet someone pre-flop and the board comes out AKQ rather than everyone at the table checking pre-flop, assuming you're playing say at the Worlds Series of Poker. However, if you're playing with people with 0 poker experience, they are far more likely to just forget the action before the flop came out to begin with, making a bet on the flop itself far less intimidating. You'd still be doing the same action in both scenarios, it's just a question of how receptive your audience is to your message. Also, thank you so much for your comment! I'm really glad you do appreciate the video enough to leave your feedback.
Definitely the case, especially since otherwise like they kind of just roll over if they get accused by the cop. From a Mafia POV, definitely better to just cause some chaos while you're alive and already under suspicion, but I didn't really want to handle social deduction in the video since that becomes subjective.
Here is the thing. 1: This assumes SUPERRATIONALITY. That is, everyone is rational, and everyone also KNOWS that everyone else is rational. 2: With this level of rationality, irrational plays can tip the scales. In the scenario where The doctor and the sherrif out themselves, the OPTIMAL play for the doctor is indeed to protect the sheriff. However, this means the mafia ALWAYS target a townsperson, ironically meaning that the doctor can actually safely NOT protect the sherrif(cause the mafia won't target him, assuming that the doctor will play rationally and save him) and get a 50/50 on protecting a innocent. 3: HOWEVER HOWEVER the mafia would expect this, and target the sheriff, killing him. But the doctor would ALSO expect that, and protect him, bringing us to sqaure 1. So yea, it just turns into a good game of rock paper & scissorss
All social deduction games do eventually devolve it’s kind of like that CalebCity video on “when the hero is just as smart as the villain” (which I would recommend as a good humorous watch). However it’s definitely better to be aware of all the options too. Wish I had the skill to be able to simulate this though.
For number 2, my understanding is that since the doctor protected themselves in the first round, the mafia always eliminate the doctor in the second round because they are aware that the doctor cannot save themselves 2 times in a row. This means that the mafia will always target the doctor, not a non-power townsperson in order to ensure that they get someone out. However, your reasoning of irrationality still stands because the doctor could have chosen not to protect themself round 1.
@almighty_clod8188 yep, the last statement was exactly my argument. Basically, a LOT of game theory boils down to rock paper scissors style guessing. Including the prisoner's dilema. It all depends on your group.
@@almighty_clod8188 But if the doctor chooses not to protect themselves round 1, then you have a lower winrate, so this does not matter. The chance of getting a "nobody died night 0" situation is much lower than if doctor protects themselves, thanks to the chance of protecting Mafia. If the doctor dies night 1 then there's the bad case of sheriff revealing and dying night 2, and if the doctor DOES successfully protect someone, it actually doesn't put them in enough of a better situation than successfully protecting themselves to justify doing. In the end, this kind of mixed strategy doesn't make sense because it can only ever decrease your odds.
@@kitsunin4690 Yeah I was saying it was irrational but just saying that the situation could have possibly happened if you weren't playing by the guide to metagame and throw off other players if they had seen this or just like the superrationality assumption. Sorry I'm ready this again and it made sense in my head but I don't know how else to put it so sorry if you don't understand it
An interesting wrinkle to the strategy would be in the case where no one dies night 1. I think it is actually most beneficial for a townsperson who isn't the doctor to lie about being the doctor. The mafia would obviously try to kill them, but the doctor can save them instead. Which means that the sheriff gets 2 free checks before a single villager has died. Though the existence of this strategy implies that its not necessarily optimal for the mafia to immediately kill someone who reveals themselves as doctor, which complicates things even more.
Wait that's actually super smart I should have included this as a scenario in the end of the video as an example of unoptimal play being optimal. Granted, it does rely on every single person playing to have watched this video or know this strategy since no town would claim doctor without having some baseline. Something to consider is actually the reaction of the doctor in that case: obviously the true doctor would know the other person is lying. Following the example of the video, if Grace did this after Charlie died night 0, then from Eve's POV she could also be a mafia just claiming doctor. This also would imply that a semi-optimal move for the Mafia is to claim doctor during the day 1. Obviously, it depends on how many layers of thinking are going into the game, hence the focus of the video as a baseline strategy. Thanks for your comment though, that is a much more interesting take too.
That's a pretty good strategy. When I play social deduction games with friends, we typically immediately call each other out if someone is obviously lying because it doesn't happen all too much, so it's the only time for "the epic play."
This is a very unique ruleset, one I've never seen before in fact. No counterclaiming, no roles revealed on death, the doctor clause, as well as the doctor being able to save themselves makes this version pretty different from how mafia is typically played in my eyes. Follow the Cop/Sherriff is a breaking strategy without the doctor clause in this setup, but I would love to see a version of this video for different setups i. e. roles revealed on death, no confirmed claiming, no selfdocs, and no doctor clause while the cop can't be protected. Or even an analysis of Vanilla, with no power roles. Sorry for the wall of text, I play a TON of online mafia so I love this stuff lol
Glad you enjoyed the video! Maybe down the line I might remake this video on the very minor chance this channel explodes. I actually played tons of Mafia growing up too and this was actually the ruleset we followed, but since most of the games were during camping trips, I'm not surprised house rules are different. I will say that roles revealed on death actually probably make the game a lot simpler, since it basically destroys any chance Mafia have of claiming cop (since all their "found mafia" checks would just be confirmed fake), so it would probably follow the logic from the video and act as an accelerator in the game pace (e.g. if cop died night 0 the town would probably realize to just vote on 5/3). But hey, maybe if the sub count takes off I'll come back to this one day. Thanks again for the feedback!
Our basic house rule was role reveal on day death (town vote), no role reveal on night death (mafia kill). Sometimes we had a special role, like a coroner, who could identify roles of previously eliminated people.
clicked on video, identified the really good quality of video, checked channel to see more videos, perplexed that there are only three videos, baffled there are only 538 subscribers. subscribed
Great video! I grew up playing with no sheriff and (usually) only one mafioso and this version is definitely a lot more strategic and a lot less random voting
This is a really interesting analysis. And funnily enough, mafia is one of the favorite games on the Mexican Math Olympiad, I think I'm sending this to the group chat as I think they'll enjoy it 😅
As already mentioned prior by people, both the doctor saving themselves as an assumption on N1 as well as the complete dismissal (tbf this is the “layer 1” mafia video so it’s fine) of the probabilities of when a mafia counterclaims sheriff especially, or even claims initially as sheriff not being included. Of course the amount of players being so low as well is another thing, given that revealing information is stronger as the group shrinks. I’ll explain why the doctor saving themselves on day 1 isn’t the most optimal decision. The chance the doctor saves themselves from the specific mafia hit is the same as them saving anyone else from a specific mafia hit. If everyone assumes that the doctor saved themselves on N1, then the mafia can be assured that their will be a higher chance of hitting either A the doctor or B the sheriff on N2, with the hit on the doctor being un-defendable. The doctor also knows this. It’s precisely why the greater expected outcome of winning increases the longer they hold their self-save, as it would have a higher chance of saving themselves the less players there are. We also need to take into consideration that even if the doctor saves themselves N1, they could end up revealed and dead N2 as you say, Or a mafia could make the jump and the same claim on D2 leading to a paralysis where you either keep both alive or kill both, which requires multiple days with a 50% chance the sheriff would die within the same period > or you waste investigations on the members which could also lead to the exact same jump of the mafia, leading to 4 revealed roles of Mafia vs Power role, while the next 4 days where you have to coinflip the votes (I’m sure there’s probability diagrams that can be done of this), the remaining 3 town members have a 66% of dying on N2, (other 33%) 100% chance of dying if no one died on N3- 50% chance of dying if someone died on N2 (33% and 33% of the 66%), on D4 if there are 3 members left (33% chance of happening- doctor, mafia doctor and town), then it is a 50% chance of town/mafia winning dependent on the vote, getting to a 50% chance of victory is a dream for the mafia. If there are 4 members left (33% chance of happening), there is again, a 50% chance of victory, as the shot is still 50/50, with the wrong 50 = an instant loss for town in N4. Again finally if no one died on N2 -> 100% chance of someone dying on N3, we are left with 4 members and the exact same conditions -> even if someone is saved on N4 it is useless as the chances of victory are still 50%. This is all for if both Sheriff and Doctor reveal themselves on D2 -> leading to 50/50 every time if they are counter-claimed. This if of course only playing at the 2nd layer, ignoring town false claims, false claims of a sheriff immune mafia, as well as many other conditions/situations that could happen. If Sheriff reveals themselves on D3 however, that’s a different story -> or if only 1 claims sheriff and town specifically knows that counter claiming or even claiming in the initiate with the option of someone counter claiming leads to a 50/50 outcome. This leads to another scenario where someone who knows all this information as a town would counterclaim/false claim on the mafia’s “sheriff”, with again a complete 50/50 on knowing if the information they possess is correct, but with the real sheriff in the background of the ability to check 1 and know the roles of both. I really wish someone made an exact chart of all these routes maybe I will check in my spare time, but I’m of good confidence that fake claiming as town of a power role is a good play, assumed that the other players are also of high game knowledge. The most important thing to note is that the correct play differs to the level of play that players are at, playing 3 layers deep could be game losing in a lobby where you only need to go 1 or 2 layers deep. And the “doctor saving themselves N1” in short, is playing 1 layer deep -> arguably debatable as to whether it is surface level, or whether randomly saving someone N1 is surface level, even despite this I still believe saving someone at random is of the higher value play, as well as not simplifying the game straight away with a reveal. But of course you’d need to chart out everything to be completely certain. Post 3rd layers with base mafia conditions there’s honestly not much other gameplay, maybe the doctor false claiming as sheriff -> saving themselves -> mafia wasting a kill, this would be dependent on the actual sheriff knowing this is a false claim at the 4th layer to not bother checking and get free checks on townies/mafia while the mafia wastes 2 nights on the false sheriff, or for the mafia to realise this precisely and target everyone but the doctor, but then the doctor can realise this for 1 night and gamble on them not targeting them until the night after -> mafia reading that and just targeting the doctor straight away -> the real sheriff in these circumstances still gets 1 check off with a lower chance of getting hit (66%) than normal, 33% chance of 2 checks, which can win the game in late game mafia. Just a bunch of these conditions need to be looked at, of course this is also with only the reduced set of roles for that matter.
I commented along the same lines a day ago and arrived at similar conclusions. In my bones I feel that doctor should be playing a mixed, randomized strategy on at least some nights. If mixed strategies are not allowed, then at least the pure strategy of Eve saving someone else should be analyzed and the resulting win % compared to Eve saving herself to find which pure strategy is better. I think it would still be cool to analyze the optimal strategy for a very simplified mafia game (this video analyzes the town win rate for one such strategy), same rules as in the video with the unstated ones below 1. only sheriff and doctor can claim, no one else can claim 2. no mixed strategies are allowed - the players' strategies are all known to everyone beforehand and assumed optimal. The strategies can be conditional, but cannot involve randomization, except for randomly choosing between symmetrical options. This way it's much simpler to test claims like "doctor saving herself on night 0 is better than saving a random on night 0".
@@ygojudge3129also the assumption that the doctor will save themselves off in of itself is a paradox, especially the greater the amount of players there are and the greedy doctor clause. If this gamestate was reached of 1 sheriff, 2 mafia, 1 doctor, 3 townies, from a greater gamestate of lets say 3 mafia, 1 serial killer, 6 townies, 2 sheriff, 1 bodyguard, 1 vigilante, 1 doctor -> 1st sheriff 1 for 1’d with the serial killer, 3rd mafia died alongside the bodyguard, vigilante shot a townie and died alongside them (the extra roles being dead in the ways they died practically confirmed what they were, so it’s not relevant for the simulation since we reached the same gamestate) -> due to the greedy doctor clause, the doctor either would’ve have had to have saved themselves the Night before this gamestate, or someone else, yet again they are limited in the options as to which they can choose based on these factors. Of course this simulation assumes we are playing with 7 players, but lets be real, most people who have played this game played it with more than only 7, as to which 7 is also a bold assumption to be making on the amount of players every time. It’s also more “solved” -> for example in a situation of 3 townies, 1 mafia, the game is solved in that there is a 66% chance for mafia to win (considering on N1 a townie dies at random -> 33% chance that they shoot the mafia). If there were 1 townie, 1 confirmed townie, 1 mafia in the final 3 -> the chance for mafia and town to win are now split 50/50. Of course these to instances aren’t fun at all given that the deception is all gone, we are simply playing roulette, or spin the bottle, which is why layers upon layers of deception with roles are added, with of course the option to lie about things and create networks of stories which the town must navigate logically to try and reach the best decisions. In short- the proposition/issues I have with this video is that if we just ignore the fact that someone can lie, it isn’t mafia, it’s truthia, or rather playing the game at the surface level. Taking into the account the very facts that people will lie, because lying statistically will help out your chances -> instead of being voted out guaranteed + person who called you out will live for a round or even more potentially -> it’s a trade while your partner gets to kill more -> you get to sow misinformation that the town is forced to then ignore both stories or possibly buy it -> for example outing ur partner as mafia if they really think ur completely lying can work as a double bluff play alongside other villagers and ur other partner as innocent. That was meant to be in short but w/e u get the point, making a mathematical model of mafia and then avoiding the conclusions of counterclaims, initiate claims, false townie/role claims as well as the assumption that the doctor should save themselves on N1, is ludicrous. Especially as we add more roles, for example if there are ever 2 doctors, theoretically they can alternate from saving themselves and saving the other. Of course letting it be known that there are 2 doctors itself is arguably low elo -> the mafia can abuse this and counter claim to endup killing both doctors potentially -> or they waste their heals while the rest of the town dies. The doctor saving someone -> no one dies -> is almost as guaranteed information as the sheriff finding out someones’ role -> given that saving someone would mean that they know X person is guaranteed townie. If the ruleset allows the doctor to save other people multiple times in a row, even more power to them because it essentially gives them agency to 1 and a half saves the next night, given that the mafia know that X person was just saved. Of course if there is a lobby where the mafia doesn’t have to kill someone every night, it can add another mindgame of them not shooting -> doctor saving a mafia mistakenly -> thinks they’re confirmed innocent because no one died -> later reveals this information and both are confirmed as “innocent”. And of course if we are assuming the doctor has to save themselves N1 every time this simply means the Mafia just doesn’t kill on even Nights, to gamble that they can get a free pass, works even moreso with more doctors and a dumber lobby. Of course allowing evil members the ability to not kill is something that only happens in groups that play a lot, big groups or ones with Neutral Killers as well such as an SK or Arsonist, etc etc. That’s another thing that completely breaks the “Doctor must save themselves” clause. Also by revealing themselves and luring the Mafia into shooting them and blocking it, it can waste a shot. However if the mafia knows when the doctor is saving themselves, it defeats the whole purpose of potential outplays the doctor has and is given a set lifespan. I wrote a lot because I was addicted to the web version when I was younger (Town of Salem) and calling flaming the shit out of people for misplaying. The most low elo thing to do is just Role force calling aka “vote for rolling” (VFR) and it still annoys the fuck out of me that it is the strategy of preference, but then again most people can’t think beyond 1 layer deep. It’s fine to do in the late game for extra time/to force someone to speak, but especially in early game when there’s 0 information that can be confirmed, VFR is just plain idiocy. Times where it is acceptable-> when no one is talking useful information at all (surprise surprise low elo specialty) -> late game to get extra time + by now it’s at a point where people *should* start to make claims (obviously it’s contextual based off of information).
The way we play in Romania (at least in my circle of friends), is the following: There are 4 main roles: the Killer, the Butcher, the Doctor & the Sheriff. They all mantain the roles and rules you specified in the video, but no one is allowed to claim to be any role. Also, the Butcher is part of the Mafia, same as the Killer, but both of them do not know who else is part of the mafia. The role of the Butcher is this: before every round, they can choose to hurt someone's hands or mouth. If they hurt someone's hands, that person cannot vote for the next elimination, but can still talk and influence the vote. If they hurt that person's mouth, they cannot talk for the next round, but can vote at the end of it. A fun dynamic is also allowing the Butcher to hurt their own hands/mouth so as not to draw suspicion on themselves, and so that they can pretend to be innocent (but this rule is usually optional). This adds a whole other layer to the game, given that the Killer can eliminate the Butcher without even knowing, and the Butcher can hurt the Killer without knowing.
I used to play a TON of town of salem (great game, highly recommended) and i loved adding roles from that to home mafia, especially with my whole family so we had a bunch of people, adding neutral roles like werewolf and vampire makes it so fun, i also love the social deduction aspect more than perfect logic
Small issue: you assume when the sheriff is eliminated that the doctor will save a towns person, but they don’t know the townspeople. There’s another case where they save a mafia.
If everyone knows everyone's perfectly logical, then saving someone at random then outing day 1 would be better - in the majority of cases, you reveal yourself, everyone thinks you're unprotected night 1, and mafia wastes a kill then, essentially confirming you especially if you went up against a mafia counterclaim, and it's also better because a wasted kill then means the sheriff can get pretty close to sealing the game
I think it depends on the deduction skills and how far down the rabbit hole the doctor is thinking. If they do this, the Mafia and the Doctor are essentially playing mind games about whether the doctor is going to save themselves or save the sheriff. This also creates more metas where the doctor could be like "I anticipated you anticipating me saving myself so I actually saved some random person" or even cases where the doctor pretends they're caught in a lie (e.g. saying they saved the person who clearly was just eliminated night 0). I think it is a little circular to think about this though, and it is less volatile to just save yourself night 0. Obviously the strategy you listed has high reward but it also does have high risk of the doctor just immediately dying night 0. The reason why that's bad is because then the cop outing themselves day 1 is terrible since they would have thought they get at least another check, but they don't since the doctor tried playing mind games and is dead from night 0. You're definitely correct about the last part of your comment though. Thanks for leaving feedback!
@@Poly_morphia "This also creates more metas where the doctor could be like "I anticipated you anticipating me saving myself so I actually saved some random person" or even cases where the doctor pretends they're caught in a lie (e.g. saying they saved the person who clearly was just eliminated night 0). I think it is a little circular to think about this though, and it is less volatile to just save yourself night 0." Mixed strategies with defined ratios exist in Nash Equilibrium, nothing circular about them. In a game of Rock-Paper-Scissors between mind-readers, the mixed strategy of mixing the pure strategies with ratios 1/3,1/3,1/3 is an equilibrium strategy.
Wait I'm actually so happy to hear someone mention mixed Nash! Most people don't even know about it so I decided not to really mention it but the reason why I keep saying "circular" is because it's really hard to determine the accurate weights since it's (in my mind, at least) impossible to simulate many games over and over quickly without rational agents choosing to pick up on different things each time. For instance, in RPS, it's already known that every single possibility is equally likely if you just map out the state space and observe that you win 1/3 of the time, lose 1/3 of the time, and tie 1/3 of the time. Unfortunately in Mafia, there are so so many events occurring all at once especially with multiple nights that each day would almost have its own mixed Nash strategy, so in my mind it's not worth mentioning or pursuing out of raw difficulty. From my best understanding, a mixed Nash strategy is still only really valuable if you know the weights, otherwise you're kind of just randomly guessing. I think you probably are correct though; from like a pure pure game theory standpoint, it might exist floating in the universe, but unfortunately I don't think I'm remotely skilled enough to derive the solution. As a result, I just decided to make a video on a baseline strategy. Really glad to see someone finally comment something about it though!
@@Poly_morphia a) if no doctor outs then the cop just shouldn't out, do things in order b) you're also functioning on no person lying about having a power role
good video. I used to play classic mafia in Russia and there are certain rules there. For example, there are only 10 players including 3 mafias (one of them is a mafia boss or don how we call it) 6 civilians and one sheriff. This kind of mafia is very popular in Russia and there are many tournaments and professional players. Also I'd like to share some thoughts about mafia variation suggested in the video. I'm not sure how many people can play in your variation and I don't know if players are allowed to vote out suspects on the first day. From my perspective 6 players are not enough, considering that there are two mafias. I mean that after the first night there will be only 3 civilians and two mafias and civilians do not have a chance to be wrong and vote out a wrong person. In Russian classic mafia(10 players, 3 mafias) after the first night, civilians have that chance to make a mistake and not to lose immediately. There are more balance in the game. I've read a couple of comments and some people mentioned a strategy where mafia claims to be a sheriff or doctor. It seems good at the first glance, however it won't work on practice in your version of the game. I'll try to explain it and sorry for my English. So, when a true sheriff exposes himself and one of the mafias decides to do the same, then all civilians just simply vote out them one by one. Therefore, one of the mafias is eliminated and citizens do not even need to think too much. Now the same scenario happens when a true doctor says he is the doctor of the game. If mafia decides to counterclaim to be the doctor, both the true doctor and another mafia will be voted out one by one. This is a mathematical win for civilians. So, I think it is understandable. Actually, I'm curious if you could make the same video about classic mafia. It would be really great. As for the rules, I could explain them to you. Thanks for the great video!
Trying to write the rules and assumptions in a more comprehensive way, outlining ways in which opportunities for logical deduction have been ignored: 1. Players know who is still alive and whether the game has ended. 2. The Mafia may attack a non-Mafia player each night. 3. The Doctor may heal a player each night, but may not heal the same player twice in a row. 4.The Sheriff may check a player at night, and will know the alignment of each player they have checked. 5. Doctor and Sheriff may prove their role. 5a. Nobody may claim to be a Doctor or Sheriff without proving it. 5b. Once the Sheriff proves their role, the Sheriff's checks are public knowledge and can not be lied about. 6. Players may vote out a player during the day. 6a. Players cannot threaten to vote out a player in order to provoke a player into proving their role. 7. Players cannot whisper information to a subset of other players. 8. Players may only gain information from the legal moves outlined above. For example, they may not use social deduction to target a player for communicating a strategy. 9. Players perform the legal moves in a logically optimal way. Would be interesting to see a fast-forward overview over the other strategies that Town could employ under these assumptions. This might be done by working backwards from the "known 3", "blind 3", and other simple scenarios, and constructing the 7-player setup in reverse chronological order
With rule 5 it actually simplifies the game significantly since Mafia counterclaims are basically worthless so it probably becomes more town sided. Otherwise, it’s probably similar to the video.
I play mafia competitively, with a unique rule set. Even with money on the line there is no meta to be found, because whatever citizens do, mafia counteracts with. There are ways for the city to achieve a mathematical win, but it requires mafia to miss, therefore when every team plays optimally the best way to win is non existent.
I didn’t realize there were tournaments woah. Can I ask how the games were structured and if there are consistent “good players” who always win? If so, is the metric of winning primarily through staying alive or just your side winning?
I played a fare share of professional mafia: 10 people, 3 mafia (one of them don), 7 citizens (one of them is sheriff), and mafia is not allowed to communicate past 0 night, so they have to secretly agree on who they want to kill, so a city has an actual logical clue on mafia besides intuition/emotional clues. And this version of the game is far more complex: you can eliminate 2, 3 or even 5 members at once, or eliminate no one (by splitting votes equally). And almost every game has a false-sheriff (usually don), and occasionally even two of them, and sometimes a false sheriff can be citizen who is trying to cover up for an actual sheriff. So the game is very complex, and it's not possible to apply this simple statistics. In some very limited situations there is a mathematically best way to play it, but they are pretty rare to occur. And the game is always changing: it was considered a best practice for some time to split table on the second day (3 votes for 3 people), and eliminate all of them (because there is around 70+% chance that one of them is mafia, and sheriff has far less candidates to pick from). Buuuut than mafia realized they can can do it too, and since they know who is who, vote 3 citizen at once and win the game, and if someone vocally disagrees, well, it's probably sheriff and he will be killed next night. So this strategy only has been discovered recently (even so the game in it's current iteration is like 20 years old), and some communities actually banned it by rules.
This was a really interesting rundown of the theory behind a game! I have been working on and off to make a Discord bot that can automate games of Mafia. One of the hardest things to do is to generate fair but interesting games, given just a number of players. Watching something like this makes me want to create some kind of agent simulator to simulate how games will play out with different role generation and player counts!
My bad, my bad, was a misread voice line in the script I somehow did not catch. Did notice this one someone else commented oops, but yes it is supposed to be the other way around. Sorry about that.
@@Extramrdo yeah but it's backwards lol, funny mistake there. We got 9 killers and 3 townspeople here! Unless you were making a joke. In which case I completely missed it
This is a neat way of looking at the game, but since the maths assumes totally random eliminations (because it can't account for the social deduction), it would probably be more valuable comparing different game scenarios - e.g. the power roles claiming Day 1 vs not, or different numbers or roles. It's not very valuable to know that with random eliminations and precise meta-play that the town has a 49% win chance, but it could be useful to know that some scenarios have a better or worse baseline. For example, I think it's valuable to know that the cop dying N0 has a massive negative impact on the theoretical town win rate, because it tells you as a game designer a key area to look at to improve long-term game balance. Also cop + doc is an overpowered combination that leads to this kind of boring gameplay!
That is definitely true! Even though overall there is a 49% winrate if town plays this optimally, the reason why is because edge cases of the cop being eliminated night 0 dramatically tank the odds of winning. Honestly, I'm not really experienced in game design at all. Someone earlier just mentioned something about tournament rulesets though? That could also be a possibility.
I can't use this guide because you can't rule out meta-gaming, where if a player is heard moving during the mafia phase, a nearby player may accuse them for that reason. This opens the door for mafia false claims of being the doctor or sheriff in the earlier rounds in scenarios where the real sherrif doesn't have enough information, as the fake sheriff can claim to get additional information from meta-gaming, making it the rational play to reveal themselves earlier. Also, we don't play a strict doctor clause, and they may get away with saving someone twice in a row. That being said, a lot of these strategies have been picked up by players, like doctor self-save being the safest pick, the no-vote in earlier rounds when there's not enough information, or voting at the crucial round with 4-5 players but not enough information to optimize the odds. All the rules that assume a more general strategy still apply.
Meta-gaming is a tragic but unfortunate reality if you're playing in person with friends. However, I do think online websites offer some protection against this.
I’d love to see a follow-up video which expands the probability to include other common roles, like the Vigilante, the Kamikaze, the Sniper, the Godfather and the Fool.
This is interesting, but I've never played Mafia where doctor can self-target and generally speaking, anon-death is usual. But I've spent most of my time on epicmafia. I wish there were more standard rules for mafia to avoid stuff like this.
15:27 Here you said that the doctor is saving Charlie. But there is a chance that the doctor will come out to save the mafia (40%), and you did not take it into account.
In Italy the game is called Lupus In Tabula and: The mafia becomes : I lupi mannari ( The werewolves ) The doctor becomes : La guardia del corpo ( The Bodyguard ) The sheriff becomes : La veggente ( The seer )
@@goldenwarrior1186 It's the same social deduction game but with different names for the roles. In America I think Werewolf is more popular but it is acknowledged that Mafia is the original.
this is a really nice video! I'd say maybe make the background music a little quieter next time. I can see this channel doing really great, this was a nicely edited and scripted video
People are, of course, commenting on the doing the mafi variants that give everyone some sort of role, like Blood on the Clocktower and Town of Salem, and I'd be interested in seeing that, but perhaps easier to do the math on, I'd be interested in seeing the math on Avalon. It's a much different type of social deduction game, since it's not about player elimination, but moreso, getting 3 missions to succeed (or fail, if you're the bad guys), but there's a lot more public information, even if that information isn't as much of a smoking gun as with the mafia sherrif (or the implicit information of a no-death night 1)
Can't say I'd really enjoy a table of 20 people; I make the animations on Google Slides (not joking, unfortunately) so you can already imagine the hassle 7 people took. Thanks for the comment though!
Now this would be a sisyphean tale for real. Even limiting to the base scripts, the number of possibilities. Not to mention all the really weird interactions and that the storyteller makes many choices throughout. Seems like it would be a fun video, but boy would it be long
The light green on most backgrounds is very difficult to make out. I can only imagine how hard it is to see if someone is colorblind or vision impaired.
Ooh you’re right that’s my bad. Did not account for that at all. I’ll try to fix this for future videos hopefully. I also might switch more to manim for the future depending on how much time I have with balancing this and school.
It would be interesting to see how a "perfectly logical" game turns out in other scenarios: - Greedy doctor clause is not in effect - Greedy doctor clause is not in effect, but doctor cannot save themself - There is only, say, a 50% chance there is a sheriff, doctor, or second mafia - More players, etc. - Player's roles are revealed upon death etc etc.
My best guess is that absent greedy doctor it’s super town skewed since the cop outs instantly just get spam saved (regardless if doctor can save themselves). The doctor would never out since it increases uncertainty on whether they are alive to save the cop. The counterplay is that the Mafia would try to claim cop too, but that would devolve if they still stay alive afterward since either their checks are lies (which the “investigated” town know or the real cop dies). More players probably shifts the vote spreads e.g. 5/3 -> like 7/5/3 or something idk. For probabilistic role spreads, having just one mafia makes it much more likely you just hit a known final 3. For 50% power roles, if the cop doesn’t out day 1 if someone dies it’s either no cop or the cop died, but both of those roles are basically the same anyway. Doctor definitely worse for the town though. Lastly, player reveals just make counterclaiming impossible cause when the real cop dies the mafia is probably going to be voted out. Sorry this is a bit long, but hope that helps. That’s just my initial takes though could be wrong too.
Wow, a mafia video that doesn't mention WIFOM. I never considered that possible. (Note: for those wondering, WIFOM stands for 'wine in front of me', named after a scene from the Film 'The Princess Bride', and describes any kind of speculation as to whether someone did something genuinely, or whether they did so because they anticipated how another player would react to it. )
I would love to see a version of this with like 10 people that includes a 4th role: the jester. The jester wins by getting voted out, and makes everything way trickier bc everyone starts to second-guess everything - it is a social deduction game after all
10 people is really hard to draw arrows with. However Jester is actually a really interesting role. Most people don’t realize that Jester actually hurts town too which is fun. My first instinct is probably that Mafia would want to keep them alive since Jesters wouldn’t want to vote out Mafia (or the game gets more likely to end in certainty). Beyond that, I’m not too sure the exact dynamics.
@@Poly_morphia the font and animation style were kind of the first clue in but I honestly think you take a lot of the best parts of his delivery and passing and really make them your own its quite impressive
Many people mentioned that cases are missed which is a clear issue, but I'd like to point out that even on top of that the cases presented have many false assumptions. Most importantly, when person X claims to have role Y, everyone believes them. This is not trivial from the fact that everyone is logical, and I'm pretty sure given that everyone is logical this is not the case, since this would mean that in the early game under certain scenarios mafia has a pure NE, but there is actually a surprising amount of literature discussing why this is not the case (and the mixed NEs of the cases). For the analysis to hold you'd have to assume (on top of other things) that people can't lie about their role, (I guess mafia is allowed to pretend to be villager but not special role?) but I think most people would agree being able to lie is literally the point of mafia and I find it hard to believe any set of "house rules" would restrict anyone from lying (other than the narrator ofc).
I don't see why you would save yourself as doctor then sacrifice yourself. Why not take the chance of death on night 1 by saving at random 5hen revealing on night 2 while saving yourself that night?
Hi yes, this is a very popular question I've been getting so I'll paste a response to a comment from earlier, just make sure to subtract 1 from all the day numbers since the person who originally commented used a different numbering system. The reason why the doctor out should come on this version of day 2 is because they essentially make the cop's check more efficient. You already covered this at the start of your comment on how you can guarantee a win via process of elimination. In the case where you have a mafia check as the cop, I'm pretty sure it makes things worse (let me know if you catch an error here). We can kinda break down the meta game here: Day 2 end [if cop checks a mafia and the town believe them, with no doctor out]: 1 Mafia / 1 Cop / 1 Doc / 2 unchecked Town Without a doc out, mafia have no reason to kill the cop, but doc has every reason to save them. Here, there's a 25% chance the town just win if cop finds the Mafia Night 2 (as opposed to 33% in the video where the doc outs). Otherwise, in the case where there is no mafia check, there is also a 3/9 chance that the Mafia also just kills the person the cop checks, and of that 3/9, 1/9 is when the Mafia also killed the doctor that night, which means the town actually are cooked since the cop is guaranteed to die the next night. Otherwise, the Mafia just kill the doc anyway and its still just a known final 3 since the doctor survives once the Mafia waits out the day and kills the cop. I know obviously there's the whole "well if the doctor realizes the Mafia thinks this they'll act differently" and there's already been tons of other comments talking about how the video isn't optimal cause people could play differently, but I hope my replies to those other comments show that thinking along that route isn't really fruitful. TLDR: Doc outing earlier makes cop's checks more efficient and lowkey acts as a magnet away from the cop. Sorry this was really long, but I'm really glad you enjoyed the video overall and I'd really enjoy to have you in future comment sections too.
I'm a bit confused. Why would the doctor claim come D2? I understand process of elimination, but let's go with the world where the cop for example checks a town. They always claim they checked x as town, this leaves Doctor / Cop / Two VT / Two mafia. The understanding here is that mafia will always check the player who was checked by the cop as town, given the doctor is always on the cop. In the event that the doctor was not the checked person, the game is won by town in every single world. In the event that cop checks a mafia, at the end of the day if mafia does not hit the 1/3 chance for doctor to die and cop checks outside of their as well it is just once again a win. Obviously, the cop risks the chance of checking the doctor, which is a 20% chance (assuming the cop checked the N1 kill), assuming they didn't it's a 25% chance. By comparison, the mafia's chance of killing a VT is a 66% chance. Is it not just safer for the doctor to not out in this world? Even ignoring that chain of logic - the only way cop checking the doctor is -effective value (if we run under the assumption the doctor is an innocent child), would be if mafia cold called the doctor in the same night, which is
Thanks for the encouragement! As for your first scenario, I'm not really sure what you mean by the doctor claim coming on Day 2, my thoughts were that the doctor should usually out after the cop does, but if the cop ever dies night 0 then they have no reason to, which is the only scenario I can imagine where a doctor day 2 out comes? Unless you're assuming that there is a Day 0 (I think you call it day 1 in your comment)? If that's the case, I'll use your day indexing for the reply (just subtract 1 if you want to cross reference for the video). The reason why the doctor out should come on this version of day 2 is because they essentially make the cop's check more efficient. You already covered this at the start of your comment on how you can guarantee a win via process of elimination. In the case where you have a mafia check as the cop, I'm pretty sure it makes things worse (let me know if you catch an error here). We can kinda break down the meta game here: Day 2 end [if cop checks a mafia and the town believe them, with no doctor out]: 1 Mafia / 1 Cop / 1 Doc / 2 unchecked Town Without a doc out, mafia have no reason to kill the cop, but doc has every reason to save them. Here, there's a 25% chance the town just win if cop finds the Mafia Night 2 (as opposed to 33% in the video where the doc outs). Otherwise, in the case where there is no mafia check, there is also a 3/9 chance that the Mafia also just kills the person the cop checks, and of that 3/9, 1/9 is when the Mafia also killed the doctor that night, which means the town actually are cooked since the cop is guaranteed to die the next night. Otherwise, the Mafia just kill the doc anyway and its still just a known final 3 since the doctor survives once the Mafia waits out the day and kills the cop. I know obviously there's the whole "well if the doctor realizes the Mafia thinks this they'll act differently" and there's already been tons of other comments talking about how the video isn't optimal cause people could play differently, but I hope my replies to those other comments show that thinking along that route isn't really fruitful. TLDR: Doc outing earlier makes cop's checks more efficient and lowkey acts as a magnet away from the cop. Sorry this was really long, but I'm really glad you enjoyed the video overall and I'd really enjoy to have you in future comment sections too.
I'm trying to follow closely, but the order of play for each night-day is confusing me. How exactly is information (like who the doctor saves and the sheriff revealing himself) revealed?
Biggest problem so far is you're saying the doctor can "out themself". How? By saying they're the doctor assumedly. But why should they be believed? You didn't specify a rule that says you're only allowed to claim to be a role if you are that role.
If the doctor can out themselves, then why can't the citizens? And at that point, the whole game is trivial. Giving the doctor the ability to confirm themselves breaks the standard of "minimal information". I would be interested in an analysis where only the sheriff outs themselves - they need to out themselves to have an effect, and further play can go on the assumption of Frank either being Sheriff or Mafia. You could also do an analysis where a mafia always counter claims, so you know that Frank/Bob are always a Sheriff/Mafia pair (with Alice remaining an anonymous mafia).
Ah I think I get the confusion here. The doctor isn't "confirmed" but it would be a very risky play for a member of the mafia to claim to be a doctor, as that leaves a 50/50 between the actual doctor and that mafia. Then again, this would probably depend on who the more convincing person is which can't really be mathematically accounted for.
@@shrekiscool4743 In case 1, there are 6 people left, 2 mafia & 4 townsfolk. If Mafia manage to persaude town to kill a townsfolk, they can then kill the doctor (or any townsfolk if the doctor is dead), and then it is 2/2 and evil wins (evil can tie all votes). Considering that the video presents case 1 probability to win for mafia as below 50%, taking a 50/50 of believe Alice/Eve is the doctor is clearly better than the case presented in the video (and it is slightly better than 50% for Mafia, because there is still a probability for mafia win if town guess Alice).
I believe there are missing aspects here. 1. You assumed that the sheriff and doctor are capable of convincingly revealing themselves, as if flipping their role cards. In some rule variations, this may in fact be the case. But you didn't specify this in the game's description. In other rule variations, a sheriff and doctor revealing themselves plays out no differently from a mafia lying about their role, which means such revelations are not necessarily convincing. 2. This is the more important part: You failed to establish a rigorous model of cooperation. This would be important, since the game does rely on players working together. The actions of players may be motivated by their expectations of other players' future actions. To elaborate on cooperation, consider a simple game: Alice and Bob must each write down a word on a piece of paper. They then individually submit their words to a judge. If the words match, they both win. Otherwise they both lose. We could examine two variants of this game. In the first variant, imagine that you are Alice, and you aren't allowed to communicate with Bob. What is the optimal strategy? That's right. *The problem is ill-posed.* The only way one of Alice's possible strategies could be evaluated is by knowing Bob's strategy-distribution beforehand. The problem description contains nothing to illuminate us in this regard, so the problem is unsolvable due to a lack of information. In the second variant, imagine that Alice and Bob are allowed to (bindingly) strategise before the game. What is the optimal strategy? That's right. They write the same word. Now how Mafia should be modelled is a pretty good question. I'm not sure. Most likely, there should be a town "meta" and a mafia "meta". Those who receive town roles play according to the town meta, and those who receive mafia roles play according to the mafia meta. The goal should then be to evaluate the effectiveness of different metas. There's many pitfalls, such as: - How exactly is daytime communication modelled? - What happens when two players attempt to hold an infinite conversation? - Should players be aware of what meta the opposing side is currently using? - What even is a meta? Is it like a computer program? Or just an arbitrary, possibly uncomputable strategy? - If metas are computable, are there any computation theoretical hazards due to metas possibly requiring players to evaluate the opposing meta in play? And probably more.
Hey, thanks for commenting your feedback! I'll try to go in order of generally what you said, but I'm curious about your further thoughts. Generally, yes you are correct that verification is the name of the game and that in social deduction games like Mafia, that is usually impossible. As a result, this also makes true cooperation impossible, since there is no guarantee from the perspective of a town. I apologize for not being more clear on the rules, but this is what I tried to cover. At 1:45, I tried to set up that an implication of minimal information from the narrator was that anyone could claim roles with ambiguity, including the Mafia (see 17:37 for more). This might have been unclear with the lack of visuals, but I'll try to improve on that in future videos. Generally, the goal of the video is to establish a logically sound baseline strategy. Obviously, if people are aware that every other participant is on this level, then new strategies would develop (similar to your paper game example). The difference between Mafia and your example, in my mind, is that the game is competitive rather than cooperative. So yes, it is true that strategies can build off each other, but in my mind, the video is meant to be an initial strategy that has some method of maximizing the chances of winning by analyzing all possible outcomes. I guess for the sake of the "dual metas", the reason why I chose not to cover this more in detail is that it becomes infinitely circular. If we take examples of mind-readers playing Rock-Paper-Scissors, obviously it becomes regressive to the point where the best move is just not to play. We have to suspend some disbelief and accept the possibilities of being outplayed with new strategies, but I don't think that's a reason to not think about strategy at all. I do really appreciate your feedback though, please don't read this as me disregarding it. If you choose to reply, I'm more than happy to continue discussing.
In games where i plays mafia, usually there is either a town person or even the mafia itself sort of playing mindgames and act suspicious intentionally, e.g. moving intentionally, etc, after a few games his/her behaviour was normalized by us, but turns out when we normalize it, he was it, whats the best logic strategies againts that, you think? In his POV whats the chance of him winning? And was it a good strats? Cause everytime he do it, he was almost always kept alive by the mafia, was this actually a good way to play e.g. the sheriff or other power plant, then you can out yourself later or? Thanks thanks
Love the idea to analyse Mafia via math. But You lack understanding of the most META strategies for this game: for example, one of Blacks allways has to challange the Sheriff claim to deny Reds free information. Better do it under the tournament standarts: 10 players 6 townfolks 1 sheriff 2 mafias+1don. I would love to see more in depth analysis of different strategies for every team with early and late Sheff reveals, Sheff reveal 1 turn after fake Sheff, table splits to pass or to raise 2 or even 3/4 players etc.
Woah, I actually didn't know that there even were tournaments for Mafia! I only played the game during camping trips really, but that's actually super interesting. Thanks for sharing!
Will think about it for the future but I'm honestly not even sure if its possible, especially with roles like Medium (I think?) where you can communicate with the dead.
I'm sorry you feel that way, but I do genuinely believe that being a more engaged player tends to make it more fun for everyone though. I'm sure we can agree to disagree though.
In reality, you can understand the mathematics while still having fun, depending on how you play. I played a lot of video mafia a few years back and the vibe of those games very much is "everyone understands the statistics and purposefully plays suboptimally, still playing to win but moreso trying to look like you're Light Yagami at the same time". Intentionally playing a wide game psychologically to obfuscate statistics for both the town and the mafia. That is the real skill ceiling - not knowing what the chances are, but knowing what the chances are and trying to tell your opponent the chances aren't what they think they are, even without knowing who your opponent is.
If a game can be ruined by overanalysing the maths it wasnt very good anyways. If you assume the other guys follow this strategy, the mafia can win a lot more. Same goes for the other guys. If the mafia always follows this strategies, the other guys can win a lot more
@@ChillKillaBeta Sure! I'll try to keep this in mind for the future. Right now, I have several general ideas on probability schema/interesting logic puzzles coming up for uploads next week/the following week, so it might have to wait a month or so, but I think we can definitely try to find some for 2025. I do know that a lot of the logic puzzles have probably been already covered on youtube though, so I've made a great effort to look for niches that people haven't made videos on yet. Hope to see you in future comment sections too!
Happy New Year everyone! When I first made this video I had NO idea it would get this many views what on earth. Anyway, I thought I'd put together a comment on FAQs I've seen so far and what my takes are on everything. I'm not saying these are objectively correct answers, but just this way people can see a centralized response list. I also want to clarify that this is by no means a perfect video and I've been trying to take everyone's feedback as seriously as possible for future videos.
Q: Why'd you say "2-3 Mafia per Town"?
A: That was a typo in the script my bad
Q: Isn't an optimal strategy to mix up the probabilities of doing either this strategy or strategy [INSERT HERE]?
A: Technically, yes. However, the actual weights and values of those probabilities themselves is unknown to me and I'm really not sure if anyone could ever simulate it with programming (if you can please drop a link). Yes, mixed Nash Equilibrium strategies exist, but since I don't believe it's possible to get the optimal weights, I'm not really sure where that discussion takes us beyond a fun hypothetical.
Q: If people watch this video doesn't this mean they would account for this strategy and it wouldn't be the optimal strategy?
A: Also yes. However, in my mind that's kind of like saying "if I'm playing Rock-Paper-Scissors and my opponent knows I'll always do Rock, doesn't that mean I'll always lose?" Following this analogy, this video is more trying to inform you of the fact that you could throw Rock Paper or Scissors and that you have multiple options. However, if you have clearly rational plays, it still is good to establish this baseline.
Q: What if people don't believe me during the day if I say [INSERT SOMETHING ELSE]?
A: I did try to stress in the video that I couldn't really account for social deduction skills. For instance, if a cop outs with a check on the Mafia but the Mafia is so persuasive, then like yeah you can't really do anything about it either. It's unfortunate, but you can't really account for everything so I tried to focus on things you can control.
Q: Can you make a video on [INSERT GAME HERE]?
A: I'll do my best to take account everyone's recommendations! Again, I didn't really expect this video to blow up, but my general focus for content was really just about probability applications. I'll definitely look into games (Spyfall, Secret Werewolf, etc...) but I have no real timeline on when future content will be.
Q: Is this really the optimal strategy?
A: I think this video (at least in my mind) is actually optimal if you walked into a room with 6 other players you'd never met before and no one had any prior information on each other. If you then played hundreds of games with the same 6 other players, obviously some adaptations would probably arise.
I play Town of Salem but I imagine it would be a lot harder to do this kind of thing there because there's so many moving parts. That, and people mostly play the "all any" role list nowadays.
I think this question is still valid: "Q: What if people don't believe me during the day if I say [INSERT SOMETHING ELSE]?"
Rather, the question to be asked should be what if 2 people claim to be a certain role. I think these cases need to be considered in order to have the complete strategy.
e.g. 2 people claim sheriff, 2 people claim doctor, real sheriff stays silent but mafia claims sheriff, 1 sheriff 2 doctor, etc
edit: I realize in other comment thread you mention it is psychological, but it is purely statistical just like how you model chance of mafia killing each role. you would have to account for all paths. For example, 2 people claim sheriff and each other as mafia. Is it better for townspeople to randomly decide between the 2, some other person, or skip entirely. For each of these scenarios we would calculate the probability of a town win, then town would pick the highest win rate option. e.g. let's say town picks to vote one of the 2 players claiming sheriff, 50% sheriff is eliminated, then from then on what would be paths from there, then next day mafia attempts to reveal their supposed investigation during the night, what are the chances they get it right, what if they choose to say a role of their fellow mafia, and that mafia agrees, or maybe the other mafia disagrees, each of these options then need to be explored.
As you can see there's no psychological aspect to any of the above scenarios, just pure statistics, and each player would consider all those option since it is given that they are purely logical.
Just one question
What happens if there are TWO sheriff claims on day 1?
its not like wolvesille where you have village killer roles
Why didn’t you make Eve the sheriff? (In cryptography, the name “Eve” to refer to an eavesdropper.)
(Not a criticism obviously, just curious.)
The real best way to play mafia is to send this video to one or more players beforehand, and then play totally illogically. If I don't know what I'm doing, they sure as hell can't.
TRUE this is the true best way to play.
I think you missed quite a few cases and strategies. First, the mafia can claim to be the Doctor and/or Sheriff, even when they are still alive. This is HUGE. Theres also the strategy where the Doctor saves someone else specifically because they knows that people will assume they saved themselves in the first round. This frees them up to save themselves when they know they're going to be attacked. These are both potentially rational decisions, as it's actually irrational to only act in your immediate self interest rather than maximising long term expected win rate.
Thanks for your input! I definitely do agree that there are other psychological factors and do address them briefly at the end of the video like the Mafia counter-claiming roles. You're obviously correct that in a scenario where, say you're with your friends, you might know that the most logical person might be targeted on night 0 the most. However, the video itself is a more generalized take on Mafia where we don't include meta-gaming/long-term win rates.
Also, while I do think that making predictions is definitely a core part of the game, it's really hard to contextualize. For example, what if the Mafia knew the doctor would think that they (the Mafia) would target a specific individual and chose to target someone more innocuous instead? The levels of thinking ends up becoming circular, so it's really hard to say what the "best" first move is, but I would still contend that the doctor saving themselves is definitely the "safest" move. Let me know your thoughts though.
@@Poly_morphia I don't think those strategies really count as psychological factors/meta-gaming, though. Because mafia is an imperfect information game, I'd bet the "mathematical best way to play" is a mixed strategy where the doctor sometimes heals themselves, sometimes doesn't, and the mafia sometimes counter-claims sheriff, and sometimes doesn't. The analogy here would be to something like poker, where game-theory optimal (GTO) play requires you to randomize your strategy in certain positions.
As far as I know, the game of mafia hasn't been "solved" yet (at least, not with this ruleset), so can't say for sure, but I doubt the approach presented in this video is mathematically optimal. Admittedly, it's still probably better than what most people do though
@@nicholas8288 Yes! You're absolutely correct that you do have to have some randomization. However, I think the conditions at the point where you need to implement randomness in your strategy is where we likely differ slightly. For example, if you walked into a room with 6 random people you had never met and were assigned the role of the Doctor, it becomes way more difficult to optimize on what to do because you lack the necessary priors to make these structurally randomized decisions.
In contrast, if you have played hundreds of games with the same 6 other people for years, it becomes a lot easier to develop new strategies. If you know that, say everyone was following the strategy listed in this video, then you could actually create structured randomness rather than pure guess-in-the-dark moves.
If we relate this to your poker analogy, I think this would be my best comparison. It's a lot easier for me to bluff if I 3-bet someone pre-flop and the board comes out AKQ rather than everyone at the table checking pre-flop, assuming you're playing say at the Worlds Series of Poker. However, if you're playing with people with 0 poker experience, they are far more likely to just forget the action before the flop came out to begin with, making a bet on the flop itself far less intimidating. You'd still be doing the same action in both scenarios, it's just a question of how receptive your audience is to your message.
Also, thank you so much for your comment! I'm really glad you do appreciate the video enough to leave your feedback.
In optimally played mafia, the mafia basically has to counter-claim doctor or sheriff every time the doctor or sheriff claims.
Definitely the case, especially since otherwise like they kind of just roll over if they get accused by the cop. From a Mafia POV, definitely better to just cause some chaos while you're alive and already under suspicion, but I didn't really want to handle social deduction in the video since that becomes subjective.
Here is the thing.
1: This assumes SUPERRATIONALITY. That is, everyone is rational, and everyone also KNOWS that everyone else is rational.
2: With this level of rationality, irrational plays can tip the scales. In the scenario where The doctor and the sherrif out themselves, the OPTIMAL play for the doctor is indeed to protect the sheriff. However, this means the mafia ALWAYS target a townsperson, ironically meaning that the doctor can actually safely NOT protect the sherrif(cause the mafia won't target him, assuming that the doctor will play rationally and save him) and get a 50/50 on protecting a innocent.
3: HOWEVER HOWEVER the mafia would expect this, and target the sheriff, killing him. But the doctor would ALSO expect that, and protect him, bringing us to sqaure 1.
So yea, it just turns into a good game of rock paper & scissorss
All social deduction games do eventually devolve it’s kind of like that CalebCity video on “when the hero is just as smart as the villain” (which I would recommend as a good humorous watch). However it’s definitely better to be aware of all the options too. Wish I had the skill to be able to simulate this though.
For number 2, my understanding is that since the doctor protected themselves in the first round, the mafia always eliminate the doctor in the second round because they are aware that the doctor cannot save themselves 2 times in a row. This means that the mafia will always target the doctor, not a non-power townsperson in order to ensure that they get someone out. However, your reasoning of irrationality still stands because the doctor could have chosen not to protect themself round 1.
@almighty_clod8188 yep, the last statement was exactly my argument.
Basically, a LOT of game theory boils down to rock paper scissors style guessing. Including the prisoner's dilema.
It all depends on your group.
@@almighty_clod8188 But if the doctor chooses not to protect themselves round 1, then you have a lower winrate, so this does not matter.
The chance of getting a "nobody died night 0" situation is much lower than if doctor protects themselves, thanks to the chance of protecting Mafia. If the doctor dies night 1 then there's the bad case of sheriff revealing and dying night 2, and if the doctor DOES successfully protect someone, it actually doesn't put them in enough of a better situation than successfully protecting themselves to justify doing. In the end, this kind of mixed strategy doesn't make sense because it can only ever decrease your odds.
@@kitsunin4690 Yeah I was saying it was irrational but just saying that the situation could have possibly happened if you weren't playing by the guide to metagame and throw off other players if they had seen this or just like the superrationality assumption. Sorry I'm ready this again and it made sense in my head but I don't know how else to put it so sorry if you don't understand it
Instructions unclear, outed myself as the mafia Day 1
An interesting wrinkle to the strategy would be in the case where no one dies night 1. I think it is actually most beneficial for a townsperson who isn't the doctor to lie about being the doctor. The mafia would obviously try to kill them, but the doctor can save them instead. Which means that the sheriff gets 2 free checks before a single villager has died.
Though the existence of this strategy implies that its not necessarily optimal for the mafia to immediately kill someone who reveals themselves as doctor, which complicates things even more.
Wait that's actually super smart I should have included this as a scenario in the end of the video as an example of unoptimal play being optimal. Granted, it does rely on every single person playing to have watched this video or know this strategy since no town would claim doctor without having some baseline.
Something to consider is actually the reaction of the doctor in that case: obviously the true doctor would know the other person is lying. Following the example of the video, if Grace did this after Charlie died night 0, then from Eve's POV she could also be a mafia just claiming doctor. This also would imply that a semi-optimal move for the Mafia is to claim doctor during the day 1. Obviously, it depends on how many layers of thinking are going into the game, hence the focus of the video as a baseline strategy. Thanks for your comment though, that is a much more interesting take too.
That's a pretty good strategy. When I play social deduction games with friends, we typically immediately call each other out if someone is obviously lying because it doesn't happen all too much, so it's the only time for "the epic play."
Pretty ironic that Eve is the Doctor, considering how “An apple a day keeps the doctor away”…
"2-3 mafia per towns person"
Oops yes see the pinned comment
me when 9 mafia vs 3 town
This is a very unique ruleset, one I've never seen before in fact. No counterclaiming, no roles revealed on death, the doctor clause, as well as the doctor being able to save themselves makes this version pretty different from how mafia is typically played in my eyes.
Follow the Cop/Sherriff is a breaking strategy without the doctor clause in this setup, but I would love to see a version of this video for different setups i. e. roles revealed on death, no confirmed claiming, no selfdocs, and no doctor clause while the cop can't be protected. Or even an analysis of Vanilla, with no power roles.
Sorry for the wall of text, I play a TON of online mafia so I love this stuff lol
Glad you enjoyed the video! Maybe down the line I might remake this video on the very minor chance this channel explodes. I actually played tons of Mafia growing up too and this was actually the ruleset we followed, but since most of the games were during camping trips, I'm not surprised house rules are different. I will say that roles revealed on death actually probably make the game a lot simpler, since it basically destroys any chance Mafia have of claiming cop (since all their "found mafia" checks would just be confirmed fake), so it would probably follow the logic from the video and act as an accelerator in the game pace (e.g. if cop died night 0 the town would probably realize to just vote on 5/3).
But hey, maybe if the sub count takes off I'll come back to this one day. Thanks again for the feedback!
Our basic house rule was role reveal on day death (town vote), no role reveal on night death (mafia kill).
Sometimes we had a special role, like a coroner, who could identify roles of previously eliminated people.
No, that is the standard ruleset I have played with.
I think you meant 2-3 townspeople per Mafia, not the other way around
clicked on video, identified the really good quality of video, checked channel to see more videos, perplexed that there are only three videos, baffled there are only 538 subscribers. subscribed
Thanks for the support!
Great video!
I grew up playing with no sheriff and (usually) only one mafioso and this version is definitely a lot more strategic and a lot less random voting
Erm actually you forgot to mention the most powerful role, which is the cookie man who does nothing except give people cookies. Lots of strategy there
True true
Loved the video. Animations were great. I'd love to see more mafia content. (Commenting to boost the video in algorithm)
Thanks so much for the support!
This is a really interesting analysis.
And funnily enough, mafia is one of the favorite games on the Mexican Math Olympiad, I think I'm sending this to the group chat as I think they'll enjoy it 😅
Woah, that's actually really cool! I was not aware of that at all but thanks for sharing both your comment and for sharing the video!
As already mentioned prior by people, both the doctor saving themselves as an assumption on N1 as well as the complete dismissal (tbf this is the “layer 1” mafia video so it’s fine) of the probabilities of when a mafia counterclaims sheriff especially, or even claims initially as sheriff not being included. Of course the amount of players being so low as well is another thing, given that revealing information is stronger as the group shrinks.
I’ll explain why the doctor saving themselves on day 1 isn’t the most optimal decision. The chance the doctor saves themselves from the specific mafia hit is the same as them saving anyone else from a specific mafia hit. If everyone assumes that the doctor saved themselves on N1, then the mafia can be assured that their will be a higher chance of hitting either A the doctor or B the sheriff on N2, with the hit on the doctor being un-defendable. The doctor also knows this. It’s precisely why the greater expected outcome of winning increases the longer they hold their self-save, as it would have a higher chance of saving themselves the less players there are. We also need to take into consideration that even if the doctor saves themselves N1, they could end up revealed and dead N2 as you say,
Or a mafia could make the jump and the same claim on D2 leading to a paralysis where you either keep both alive or kill both, which requires multiple days with a 50% chance the sheriff would die within the same period > or you waste investigations on the members which could also lead to the exact same jump of the mafia, leading to 4 revealed roles of Mafia vs Power role, while the next 4 days where you have to coinflip the votes (I’m sure there’s probability diagrams that can be done of this), the remaining 3 town members have a 66% of dying on N2, (other 33%) 100% chance of dying if no one died on N3- 50% chance of dying if someone died on N2 (33% and 33% of the 66%), on D4 if there are 3 members left (33% chance of happening- doctor, mafia doctor and town), then it is a 50% chance of town/mafia winning dependent on the vote, getting to a 50% chance of victory is a dream for the mafia. If there are 4 members left (33% chance of happening), there is again, a 50% chance of victory, as the shot is still 50/50, with the wrong 50 = an instant loss for town in N4. Again finally if no one died on N2 -> 100% chance of someone dying on N3, we are left with 4 members and the exact same conditions -> even if someone is saved on N4 it is useless as the chances of victory are still 50%.
This is all for if both Sheriff and Doctor reveal themselves on D2 -> leading to 50/50 every time if they are counter-claimed. This if of course only playing at the 2nd layer, ignoring town false claims, false claims of a sheriff immune mafia, as well as many other conditions/situations that could happen.
If Sheriff reveals themselves on D3 however, that’s a different story -> or if only 1 claims sheriff and town specifically knows that counter claiming or even claiming in the initiate with the option of someone counter claiming leads to a 50/50 outcome. This leads to another scenario where someone who knows all this information as a town would counterclaim/false claim on the mafia’s “sheriff”, with again a complete 50/50 on knowing if the information they possess is correct, but with the real sheriff in the background of the ability to check 1 and know the roles of both.
I really wish someone made an exact chart of all these routes maybe I will check in my spare time, but I’m of good confidence that fake claiming as town of a power role is a good play, assumed that the other players are also of high game knowledge. The most important thing to note is that the correct play differs to the level of play that players are at, playing 3 layers deep could be game losing in a lobby where you only need to go 1 or 2 layers deep. And the “doctor saving themselves N1” in short, is playing 1 layer deep -> arguably debatable as to whether it is surface level, or whether randomly saving someone N1 is surface level, even despite this I still believe saving someone at random is of the higher value play, as well as not simplifying the game straight away with a reveal. But of course you’d need to chart out everything to be completely certain. Post 3rd layers with base mafia conditions there’s honestly not much other gameplay, maybe the doctor false claiming as sheriff -> saving themselves -> mafia wasting a kill, this would be dependent on the actual sheriff knowing this is a false claim at the 4th layer to not bother checking and get free checks on townies/mafia while the mafia wastes 2 nights on the false sheriff, or for the mafia to realise this precisely and target everyone but the doctor, but then the doctor can realise this for 1 night and gamble on them not targeting them until the night after -> mafia reading that and just targeting the doctor straight away -> the real sheriff in these circumstances still gets 1 check off with a lower chance of getting hit (66%) than normal, 33% chance of 2 checks, which can win the game in late game mafia. Just a bunch of these conditions need to be looked at, of course this is also with only the reduced set of roles for that matter.
I commented along the same lines a day ago and arrived at similar conclusions. In my bones I feel that doctor should be playing a mixed, randomized strategy on at least some nights. If mixed strategies are not allowed, then at least the pure strategy of Eve saving someone else should be analyzed and the resulting win % compared to Eve saving herself to find which pure strategy is better.
I think it would still be cool to analyze the optimal strategy for a very simplified mafia game (this video analyzes the town win rate for one such strategy), same rules as in the video with the unstated ones below
1. only sheriff and doctor can claim, no one else can claim
2. no mixed strategies are allowed - the players' strategies are all known to everyone beforehand and assumed optimal. The strategies can be conditional, but cannot involve randomization, except for randomly choosing between symmetrical options.
This way it's much simpler to test claims like "doctor saving herself on night 0 is better than saving a random on night 0".
@@ygojudge3129also the assumption that the doctor will save themselves off in of itself is a paradox, especially the greater the amount of players there are and the greedy doctor clause. If this gamestate was reached of 1 sheriff, 2 mafia, 1 doctor, 3 townies, from a greater gamestate of lets say 3 mafia, 1 serial killer, 6 townies, 2 sheriff, 1 bodyguard, 1 vigilante, 1 doctor -> 1st sheriff 1 for 1’d with the serial killer, 3rd mafia died alongside the bodyguard, vigilante shot a townie and died alongside them (the extra roles being dead in the ways they died practically confirmed what they were, so it’s not relevant for the simulation since we reached the same gamestate) -> due to the greedy doctor clause, the doctor either would’ve have had to have saved themselves the Night before this gamestate, or someone else, yet again they are limited in the options as to which they can choose based on these factors. Of course this simulation assumes we are playing with 7 players, but lets be real, most people who have played this game played it with more than only 7, as to which 7 is also a bold assumption to be making on the amount of players every time. It’s also more “solved” -> for example in a situation of 3 townies, 1 mafia, the game is solved in that there is a 66% chance for mafia to win (considering on N1 a townie dies at random -> 33% chance that they shoot the mafia). If there were 1 townie, 1 confirmed townie, 1 mafia in the final 3 -> the chance for mafia and town to win are now split 50/50. Of course these to instances aren’t fun at all given that the deception is all gone, we are simply playing roulette, or spin the bottle, which is why layers upon layers of deception with roles are added, with of course the option to lie about things and create networks of stories which the town must navigate logically to try and reach the best decisions.
In short- the proposition/issues I have with this video is that if we just ignore the fact that someone can lie, it isn’t mafia, it’s truthia, or rather playing the game at the surface level. Taking into the account the very facts that people will lie, because lying statistically will help out your chances -> instead of being voted out guaranteed + person who called you out will live for a round or even more potentially -> it’s a trade while your partner gets to kill more -> you get to sow misinformation that the town is forced to then ignore both stories or possibly buy it -> for example outing ur partner as mafia if they really think ur completely lying can work as a double bluff play alongside other villagers and ur other partner as innocent.
That was meant to be in short but w/e u get the point, making a mathematical model of mafia and then avoiding the conclusions of counterclaims, initiate claims, false townie/role claims as well as the assumption that the doctor should save themselves on N1, is ludicrous. Especially as we add more roles, for example if there are ever 2 doctors, theoretically they can alternate from saving themselves and saving the other. Of course letting it be known that there are 2 doctors itself is arguably low elo -> the mafia can abuse this and counter claim to endup killing both doctors potentially -> or they waste their heals while the rest of the town dies. The doctor saving someone -> no one dies -> is almost as guaranteed information as the sheriff finding out someones’ role -> given that saving someone would mean that they know X person is guaranteed townie. If the ruleset allows the doctor to save other people multiple times in a row, even more power to them because it essentially gives them agency to 1 and a half saves the next night, given that the mafia know that X person was just saved. Of course if there is a lobby where the mafia doesn’t have to kill someone every night, it can add another mindgame of them not shooting -> doctor saving a mafia mistakenly -> thinks they’re confirmed innocent because no one died -> later reveals this information and both are confirmed as “innocent”. And of course if we are assuming the doctor has to save themselves N1 every time this simply means the Mafia just doesn’t kill on even Nights, to gamble that they can get a free pass, works even moreso with more doctors and a dumber lobby. Of course allowing evil members the ability to not kill is something that only happens in groups that play a lot, big groups or ones with Neutral Killers as well such as an SK or Arsonist, etc etc.
That’s another thing that completely breaks the “Doctor must save themselves” clause. Also by revealing themselves and luring the Mafia into shooting them and blocking it, it can waste a shot. However if the mafia knows when the doctor is saving themselves, it defeats the whole purpose of potential outplays the doctor has and is given a set lifespan.
I wrote a lot because I was addicted to the web version when I was younger (Town of Salem) and calling flaming the shit out of people for misplaying. The most low elo thing to do is just Role force calling aka “vote for rolling” (VFR) and it still annoys the fuck out of me that it is the strategy of preference, but then again most people can’t think beyond 1 layer deep. It’s fine to do in the late game for extra time/to force someone to speak, but especially in early game when there’s 0 information that can be confirmed, VFR is just plain idiocy. Times where it is acceptable-> when no one is talking useful information at all (surprise surprise low elo specialty) -> late game to get extra time + by now it’s at a point where people *should* start to make claims (obviously it’s contextual based off of information).
The way we play in Romania (at least in my circle of friends), is the following:
There are 4 main roles: the Killer, the Butcher, the Doctor & the Sheriff.
They all mantain the roles and rules you specified in the video, but no one is allowed to claim to be any role. Also, the Butcher is part of the Mafia, same as the Killer, but both of them do not know who else is part of the mafia. The role of the Butcher is this: before every round, they can choose to hurt someone's hands or mouth. If they hurt someone's hands, that person cannot vote for the next elimination, but can still talk and influence the vote. If they hurt that person's mouth, they cannot talk for the next round, but can vote at the end of it.
A fun dynamic is also allowing the Butcher to hurt their own hands/mouth so as not to draw suspicion on themselves, and so that they can pretend to be innocent (but this rule is usually optional).
This adds a whole other layer to the game, given that the Killer can eliminate the Butcher without even knowing, and the Butcher can hurt the Killer without knowing.
I was somehow entirely sure that you would teach me how to manage a real mafia upon clicking on this video
I used to play a TON of town of salem (great game, highly recommended) and i loved adding roles from that to home mafia, especially with my whole family so we had a bunch of people, adding neutral roles like werewolf and vampire makes it so fun, i also love the social deduction aspect more than perfect logic
Very nice video! I have always enjoyed playing mafia, and it is interesting to see it analyzed assuming perfect play from all players!
Thank you very much! I'm glad you enjoyed it.
Small issue: you assume when the sheriff is eliminated that the doctor will save a towns person, but they don’t know the townspeople. There’s another case where they save a mafia.
Saving a non attacked towns person is functionally identical to saving a mafia since there is no town killing role
@ yes but the probability is not factored accordingly
If everyone knows everyone's perfectly logical, then saving someone at random then outing day 1 would be better - in the majority of cases, you reveal yourself, everyone thinks you're unprotected night 1, and mafia wastes a kill then, essentially confirming you especially if you went up against a mafia counterclaim, and it's also better because a wasted kill then means the sheriff can get pretty close to sealing the game
I think it depends on the deduction skills and how far down the rabbit hole the doctor is thinking. If they do this, the Mafia and the Doctor are essentially playing mind games about whether the doctor is going to save themselves or save the sheriff. This also creates more metas where the doctor could be like "I anticipated you anticipating me saving myself so I actually saved some random person" or even cases where the doctor pretends they're caught in a lie (e.g. saying they saved the person who clearly was just eliminated night 0). I think it is a little circular to think about this though, and it is less volatile to just save yourself night 0. Obviously the strategy you listed has high reward but it also does have high risk of the doctor just immediately dying night 0. The reason why that's bad is because then the cop outing themselves day 1 is terrible since they would have thought they get at least another check, but they don't since the doctor tried playing mind games and is dead from night 0. You're definitely correct about the last part of your comment though. Thanks for leaving feedback!
@@Poly_morphia "This also creates more metas where the doctor could be like "I anticipated you anticipating me saving myself so I actually saved some random person" or even cases where the doctor pretends they're caught in a lie (e.g. saying they saved the person who clearly was just eliminated night 0). I think it is a little circular to think about this though, and it is less volatile to just save yourself night 0."
Mixed strategies with defined ratios exist in Nash Equilibrium, nothing circular about them. In a game of Rock-Paper-Scissors between mind-readers, the mixed strategy of mixing the pure strategies with ratios 1/3,1/3,1/3 is an equilibrium strategy.
Wait I'm actually so happy to hear someone mention mixed Nash! Most people don't even know about it so I decided not to really mention it but the reason why I keep saying "circular" is because it's really hard to determine the accurate weights since it's (in my mind, at least) impossible to simulate many games over and over quickly without rational agents choosing to pick up on different things each time. For instance, in RPS, it's already known that every single possibility is equally likely if you just map out the state space and observe that you win 1/3 of the time, lose 1/3 of the time, and tie 1/3 of the time. Unfortunately in Mafia, there are so so many events occurring all at once especially with multiple nights that each day would almost have its own mixed Nash strategy, so in my mind it's not worth mentioning or pursuing out of raw difficulty. From my best understanding, a mixed Nash strategy is still only really valuable if you know the weights, otherwise you're kind of just randomly guessing.
I think you probably are correct though; from like a pure pure game theory standpoint, it might exist floating in the universe, but unfortunately I don't think I'm remotely skilled enough to derive the solution. As a result, I just decided to make a video on a baseline strategy. Really glad to see someone finally comment something about it though!
@@Poly_morphia a) if no doctor outs then the cop just shouldn't out, do things in order
b) you're also functioning on no person lying about having a power role
good video. I used to play classic mafia in Russia and there are certain rules there. For example, there are only 10 players including 3 mafias (one of them is a mafia boss or don how we call it) 6 civilians and one sheriff. This kind of mafia is very popular in Russia and there are many tournaments and professional players. Also I'd like to share some thoughts about mafia variation suggested in the video. I'm not sure how many people can play in your variation and I don't know if players are allowed to vote out suspects on the first day. From my perspective 6 players are not enough, considering that there are two mafias. I mean that after the first night there will be only 3 civilians and two mafias and civilians do not have a chance to be wrong and vote out a wrong person. In Russian classic mafia(10 players, 3 mafias) after the first night, civilians have that chance to make a mistake and not to lose immediately. There are more balance in the game.
I've read a couple of comments and some people mentioned a strategy where mafia claims to be a sheriff or doctor. It seems good at the first glance, however it won't work on practice in your version of the game. I'll try to explain it and sorry for my English.
So, when a true sheriff exposes himself and one of the mafias decides to do the same, then all civilians just simply vote out them one by one. Therefore, one of the mafias is eliminated and citizens do not even need to think too much. Now the same scenario happens when a true doctor says he is the doctor of the game. If mafia decides to counterclaim to be the doctor, both the true doctor and another mafia will be voted out one by one. This is a mathematical win for civilians.
So, I think it is understandable. Actually, I'm curious if you could make the same video about classic mafia. It would be really great. As for the rules, I could explain them to you.
Thanks for the great video!
Trying to write the rules and assumptions in a more comprehensive way, outlining ways in which opportunities for logical deduction have been ignored:
1. Players know who is still alive and whether the game has ended.
2. The Mafia may attack a non-Mafia player each night.
3. The Doctor may heal a player each night, but may not heal the same player twice in a row.
4.The Sheriff may check a player at night, and will know the alignment of each player they have checked.
5. Doctor and Sheriff may prove their role.
5a. Nobody may claim to be a Doctor or Sheriff without proving it.
5b. Once the Sheriff proves their role, the Sheriff's checks are public knowledge and can not be lied about.
6. Players may vote out a player during the day.
6a. Players cannot threaten to vote out a player in order to provoke a player into proving their role.
7. Players cannot whisper information to a subset of other players.
8. Players may only gain information from the legal moves outlined above. For example, they may not use social deduction to target a player for communicating a strategy.
9. Players perform the legal moves in a logically optimal way.
Would be interesting to see a fast-forward overview over the other strategies that Town could employ under these assumptions. This might be done by working backwards from the "known 3", "blind 3", and other simple scenarios, and constructing the 7-player setup in reverse chronological order
With rule 5 it actually simplifies the game significantly since Mafia counterclaims are basically worthless so it probably becomes more town sided. Otherwise, it’s probably similar to the video.
I play mafia competitively, with a unique rule set. Even with money on the line there is no meta to be found, because whatever citizens do, mafia counteracts with. There are ways for the city to achieve a mathematical win, but it requires mafia to miss, therefore when every team plays optimally the best way to win is non existent.
I didn’t realize there were tournaments woah. Can I ask how the games were structured and if there are consistent “good players” who always win? If so, is the metric of winning primarily through staying alive or just your side winning?
@@Poly_morphia Well, the answer would be too long for a youtube comment, where can I reach you?
I played a fare share of professional mafia: 10 people, 3 mafia (one of them don), 7 citizens (one of them is sheriff), and mafia is not allowed to communicate past 0 night, so they have to secretly agree on who they want to kill, so a city has an actual logical clue on mafia besides intuition/emotional clues. And this version of the game is far more complex: you can eliminate 2, 3 or even 5 members at once, or eliminate no one (by splitting votes equally). And almost every game has a false-sheriff (usually don), and occasionally even two of them, and sometimes a false sheriff can be citizen who is trying to cover up for an actual sheriff.
So the game is very complex, and it's not possible to apply this simple statistics. In some very limited situations there is a mathematically best way to play it, but they are pretty rare to occur.
And the game is always changing: it was considered a best practice for some time to split table on the second day (3 votes for 3 people), and eliminate all of them (because there is around 70+% chance that one of them is mafia, and sheriff has far less candidates to pick from). Buuuut than mafia realized they can can do it too, and since they know who is who, vote 3 citizen at once and win the game, and if someone vocally disagrees, well, it's probably sheriff and he will be killed next night. So this strategy only has been discovered recently (even so the game in it's current iteration is like 20 years old), and some communities actually banned it by rules.
This was a really interesting rundown of the theory behind a game! I have been working on and off to make a Discord bot that can automate games of Mafia. One of the hardest things to do is to generate fair but interesting games, given just a number of players. Watching something like this makes me want to create some kind of agent simulator to simulate how games will play out with different role generation and player counts!
1:01 2-3 mafia PER TOWNSPERSON ARE U CRAZY
they're not wrong, that's ideal setup for the majority of players
My bad, my bad, was a misread voice line in the script I somehow did not catch. Did notice this one someone else commented oops, but yes it is supposed to be the other way around. Sorry about that.
@@Extramrdo yeah but it's backwards lol, funny mistake there. We got 9 killers and 3 townspeople here!
Unless you were making a joke. In which case I completely missed it
Good breakdown with useful graphics.
Glad you liked it!
1:00 I think you meant, 2-3 townsperson per mafia
You are very correct, did not know how that slipped through
I really like your art style and music it goes really well with your interesting mathematical insights
I didn’t go to this video for any ulterior motive in mind.
Can’t believe I’m here this early. Ts oughta blow up fr. Great vid boss
This is a neat way of looking at the game, but since the maths assumes totally random eliminations (because it can't account for the social deduction), it would probably be more valuable comparing different game scenarios - e.g. the power roles claiming Day 1 vs not, or different numbers or roles. It's not very valuable to know that with random eliminations and precise meta-play that the town has a 49% win chance, but it could be useful to know that some scenarios have a better or worse baseline. For example, I think it's valuable to know that the cop dying N0 has a massive negative impact on the theoretical town win rate, because it tells you as a game designer a key area to look at to improve long-term game balance.
Also cop + doc is an overpowered combination that leads to this kind of boring gameplay!
That is definitely true! Even though overall there is a 49% winrate if town plays this optimally, the reason why is because edge cases of the cop being eliminated night 0 dramatically tank the odds of winning. Honestly, I'm not really experienced in game design at all. Someone earlier just mentioned something about tournament rulesets though? That could also be a possibility.
I can't use this guide because you can't rule out meta-gaming, where if a player is heard moving during the mafia phase, a nearby player may accuse them for that reason. This opens the door for mafia false claims of being the doctor or sheriff in the earlier rounds in scenarios where the real sherrif doesn't have enough information, as the fake sheriff can claim to get additional information from meta-gaming, making it the rational play to reveal themselves earlier. Also, we don't play a strict doctor clause, and they may get away with saving someone twice in a row.
That being said, a lot of these strategies have been picked up by players, like doctor self-save being the safest pick, the no-vote in earlier rounds when there's not enough information, or voting at the crucial round with 4-5 players but not enough information to optimize the odds. All the rules that assume a more general strategy still apply.
Meta-gaming is a tragic but unfortunate reality if you're playing in person with friends. However, I do think online websites offer some protection against this.
I’d love to see a follow-up video which expands the probability to include other common roles, like the Vigilante, the Kamikaze, the Sniper, the Godfather and the Fool.
This is interesting, but I've never played Mafia where doctor can self-target and generally speaking, anon-death is usual. But I've spent most of my time on epicmafia. I wish there were more standard rules for mafia to avoid stuff like this.
Yeah, it’s unlucky but the game has evolved so much with so many house rules it’s hard to cover everything.
Subbed - this video deserved it
Thanks so much!
15:27
Here you said that the doctor is saving Charlie. But there is a chance that the doctor will come out to save the mafia (40%), and you did not take it into account.
WOW crazy video. Keep up the good work.
In Italy the game is called Lupus In Tabula and:
The mafia becomes : I lupi mannari ( The werewolves )
The doctor becomes : La guardia del corpo ( The Bodyguard )
The sheriff becomes : La veggente ( The seer )
I think that’s a different social deduction game called Werewolf
@@goldenwarrior1186 It's the same social deduction game but with different names for the roles. In America I think Werewolf is more popular but it is acknowledged that Mafia is the original.
we also used to have a joker role, a person with that role wins if they get themselves voted out (dying wont work)
this is a really nice video! I'd say maybe make the background music a little quieter next time.
I can see this channel doing really great, this was a nicely edited and scripted video
Will do, thanks so much for your feedback!
People are, of course, commenting on the doing the mafi variants that give everyone some sort of role, like Blood on the Clocktower and Town of Salem, and I'd be interested in seeing that, but perhaps easier to do the math on, I'd be interested in seeing the math on Avalon. It's a much different type of social deduction game, since it's not about player elimination, but moreso, getting 3 missions to succeed (or fail, if you're the bad guys), but there's a lot more public information, even if that information isn't as much of a smoking gun as with the mafia sherrif (or the implicit information of a no-death night 1)
requesting "The Mathematically Best Way to Play Blood on the Clocktower"
have fun
(this is a joke)
Can't say I'd really enjoy a table of 20 people; I make the animations on Google Slides (not joking, unfortunately) so you can already imagine the hassle 7 people took. Thanks for the comment though!
Now this would be a sisyphean tale for real. Even limiting to the base scripts, the number of possibilities. Not to mention all the really weird interactions and that the storyteller makes many choices throughout. Seems like it would be a fun video, but boy would it be long
The light green on most backgrounds is very difficult to make out. I can only imagine how hard it is to see if someone is colorblind or vision impaired.
Ooh you’re right that’s my bad. Did not account for that at all. I’ll try to fix this for future videos hopefully. I also might switch more to manim for the future depending on how much time I have with balancing this and school.
Using this to get better at Town of Salem
Best of luck! Glad you liked it.
It would be interesting to see how a "perfectly logical" game turns out in other scenarios:
- Greedy doctor clause is not in effect
- Greedy doctor clause is not in effect, but doctor cannot save themself
- There is only, say, a 50% chance there is a sheriff, doctor, or second mafia
- More players, etc.
- Player's roles are revealed upon death
etc etc.
My best guess is that absent greedy doctor it’s super town skewed since the cop outs instantly just get spam saved (regardless if doctor can save themselves). The doctor would never out since it increases uncertainty on whether they are alive to save the cop. The counterplay is that the Mafia would try to claim cop too, but that would devolve if they still stay alive afterward since either their checks are lies (which the “investigated” town know or the real cop dies).
More players probably shifts the vote spreads e.g. 5/3 -> like 7/5/3 or something idk.
For probabilistic role spreads, having just one mafia makes it much more likely you just hit a known final 3. For 50% power roles, if the cop doesn’t out day 1 if someone dies it’s either no cop or the cop died, but both of those roles are basically the same anyway. Doctor definitely worse for the town though.
Lastly, player reveals just make counterclaiming impossible cause when the real cop dies the mafia is probably going to be voted out.
Sorry this is a bit long, but hope that helps. That’s just my initial takes though could be wrong too.
Wow, a mafia video that doesn't mention WIFOM. I never considered that possible.
(Note: for those wondering, WIFOM stands for 'wine in front of me', named after a scene from the Film 'The Princess Bride', and describes any kind of speculation as to whether someone did something genuinely, or whether they did so because they anticipated how another player would react to it. )
I would love to see a version of this with like 10 people that includes a 4th role: the jester. The jester wins by getting voted out, and makes everything way trickier bc everyone starts to second-guess everything - it is a social deduction game after all
10 people is really hard to draw arrows with. However Jester is actually a really interesting role. Most people don’t realize that Jester actually hurts town too which is fun. My first instinct is probably that Mafia would want to keep them alive since Jesters wouldn’t want to vote out Mafia (or the game gets more likely to end in certainty). Beyond that, I’m not too sure the exact dynamics.
Historia civilis for how to lose your friends
Wait I’m so glad someone caught the parallel; he’s one of my favorite RUclipsrs I love his Caesar series.
@@Poly_morphia the font and animation style were kind of the first clue in but I honestly think you take a lot of the best parts of his delivery and passing and really make them your own its quite impressive
massive brain moment if i do say so myself
Either I missed something, or this doesn't include cases where the doctor targets a mafia member
This analysis was, unfortunately, shallower than I expected
Have you ever heard of the social deduction game quest? The strategy of that game is very complex and I’d love to see a video on it.
Many people mentioned that cases are missed which is a clear issue, but I'd like to point out that even on top of that the cases presented have many false assumptions. Most importantly, when person X claims to have role Y, everyone believes them. This is not trivial from the fact that everyone is logical, and I'm pretty sure given that everyone is logical this is not the case, since this would mean that in the early game under certain scenarios mafia has a pure NE, but there is actually a surprising amount of literature discussing why this is not the case (and the mixed NEs of the cases).
For the analysis to hold you'd have to assume (on top of other things) that people can't lie about their role, (I guess mafia is allowed to pretend to be villager but not special role?) but I think most people would agree being able to lie is literally the point of mafia and I find it hard to believe any set of "house rules" would restrict anyone from lying (other than the narrator ofc).
I don't see why you would save yourself as doctor then sacrifice yourself. Why not take the chance of death on night 1 by saving at random 5hen revealing on night 2 while saving yourself that night?
Hi yes, this is a very popular question I've been getting so I'll paste a response to a comment from earlier, just make sure to subtract 1 from all the day numbers since the person who originally commented used a different numbering system.
The reason why the doctor out should come on this version of day 2 is because they essentially make the cop's check more efficient. You already covered this at the start of your comment on how you can guarantee a win via process of elimination.
In the case where you have a mafia check as the cop, I'm pretty sure it makes things worse (let me know if you catch an error here). We can kinda break down the meta game here:
Day 2 end [if cop checks a mafia and the town believe them, with no doctor out]: 1 Mafia / 1 Cop / 1 Doc / 2 unchecked Town
Without a doc out, mafia have no reason to kill the cop, but doc has every reason to save them. Here, there's a 25% chance the town just win if cop finds the Mafia Night 2 (as opposed to 33% in the video where the doc outs).
Otherwise, in the case where there is no mafia check, there is also a 3/9 chance that the Mafia also just kills the person the cop checks, and of that 3/9, 1/9 is when the Mafia also killed the doctor that night, which means the town actually are cooked since the cop is guaranteed to die the next night. Otherwise, the Mafia just kill the doc anyway and its still just a known final 3 since the doctor survives once the Mafia waits out the day and kills the cop.
I know obviously there's the whole "well if the doctor realizes the Mafia thinks this they'll act differently" and there's already been tons of other comments talking about how the video isn't optimal cause people could play differently, but I hope my replies to those other comments show that thinking along that route isn't really fruitful.
TLDR: Doc outing earlier makes cop's checks more efficient and lowkey acts as a magnet away from the cop.
Sorry this was really long, but I'm really glad you enjoyed the video overall and I'd really enjoy to have you in future comment sections too.
BRO. This video is amazing. Do a video over more stuff like Mole
I'll try to look into that!
Rule #1 is find a good game host/mod… some of them have no idea what they’re doing.
I'm a bit confused. Why would the doctor claim come D2? I understand process of elimination, but let's go with the world where the cop for example checks a town. They always claim they checked x as town, this leaves Doctor / Cop / Two VT / Two mafia. The understanding here is that mafia will always check the player who was checked by the cop as town, given the doctor is always on the cop. In the event that the doctor was not the checked person, the game is won by town in every single world.
In the event that cop checks a mafia, at the end of the day if mafia does not hit the 1/3 chance for doctor to die and cop checks outside of their as well it is just once again a win. Obviously, the cop risks the chance of checking the doctor, which is a 20% chance (assuming the cop checked the N1 kill), assuming they didn't it's a 25% chance. By comparison, the mafia's chance of killing a VT is a 66% chance. Is it not just safer for the doctor to not out in this world? Even ignoring that chain of logic - the only way cop checking the doctor is -effective value (if we run under the assumption the doctor is an innocent child), would be if mafia cold called the doctor in the same night, which is
Thanks for the encouragement!
As for your first scenario, I'm not really sure what you mean by the doctor claim coming on Day 2, my thoughts were that the doctor should usually out after the cop does, but if the cop ever dies night 0 then they have no reason to, which is the only scenario I can imagine where a doctor day 2 out comes?
Unless you're assuming that there is a Day 0 (I think you call it day 1 in your comment)? If that's the case, I'll use your day indexing for the reply (just subtract 1 if you want to cross reference for the video). The reason why the doctor out should come on this version of day 2 is because they essentially make the cop's check more efficient. You already covered this at the start of your comment on how you can guarantee a win via process of elimination.
In the case where you have a mafia check as the cop, I'm pretty sure it makes things worse (let me know if you catch an error here). We can kinda break down the meta game here:
Day 2 end [if cop checks a mafia and the town believe them, with no doctor out]: 1 Mafia / 1 Cop / 1 Doc / 2 unchecked Town
Without a doc out, mafia have no reason to kill the cop, but doc has every reason to save them. Here, there's a 25% chance the town just win if cop finds the Mafia Night 2 (as opposed to 33% in the video where the doc outs).
Otherwise, in the case where there is no mafia check, there is also a 3/9 chance that the Mafia also just kills the person the cop checks, and of that 3/9, 1/9 is when the Mafia also killed the doctor that night, which means the town actually are cooked since the cop is guaranteed to die the next night. Otherwise, the Mafia just kill the doc anyway and its still just a known final 3 since the doctor survives once the Mafia waits out the day and kills the cop.
I know obviously there's the whole "well if the doctor realizes the Mafia thinks this they'll act differently" and there's already been tons of other comments talking about how the video isn't optimal cause people could play differently, but I hope my replies to those other comments show that thinking along that route isn't really fruitful.
TLDR: Doc outing earlier makes cop's checks more efficient and lowkey acts as a magnet away from the cop.
Sorry this was really long, but I'm really glad you enjoyed the video overall and I'd really enjoy to have you in future comment sections too.
I'm trying to follow closely, but the order of play for each night-day is confusing me. How exactly is information (like who the doctor saves and the sheriff revealing himself) revealed?
I have a question: what if a villager claims one of the town special roles? what about that curveball?
Biggest problem so far is you're saying the doctor can "out themself". How? By saying they're the doctor assumedly. But why should they be believed? You didn't specify a rule that says you're only allowed to claim to be a role if you are that role.
fun video! thanks for this!
We need an online calculator for different setups!
Sadly this would be really hard to setup if someone more skilled than me at programming could that would be sick
Guys please please please play mafia42 it's a game on the app store and it's literally mafia but there's so many more roles
If the doctor can out themselves, then why can't the citizens? And at that point, the whole game is trivial. Giving the doctor the ability to confirm themselves breaks the standard of "minimal information".
I would be interested in an analysis where only the sheriff outs themselves - they need to out themselves to have an effect, and further play can go on the assumption of Frank either being Sheriff or Mafia. You could also do an analysis where a mafia always counter claims, so you know that Frank/Bob are always a Sheriff/Mafia pair (with Alice remaining an anonymous mafia).
Because the mafia could just as easily claim to be citizens - in fact that's what you'd generally expect
Ah I think I get the confusion here. The doctor isn't "confirmed" but it would be a very risky play for a member of the mafia to claim to be a doctor, as that leaves a 50/50 between the actual doctor and that mafia. Then again, this would probably depend on who the more convincing person is which can't really be mathematically accounted for.
@@shrekiscool4743 In case 1, there are 6 people left, 2 mafia & 4 townsfolk. If Mafia manage to persaude town to kill a townsfolk, they can then kill the doctor (or any townsfolk if the doctor is dead), and then it is 2/2 and evil wins (evil can tie all votes). Considering that the video presents case 1 probability to win for mafia as below 50%, taking a 50/50 of believe Alice/Eve is the doctor is clearly better than the case presented in the video (and it is slightly better than 50% for Mafia, because there is still a probability for mafia win if town guess Alice).
I believe there are missing aspects here.
1. You assumed that the sheriff and doctor are capable of convincingly revealing themselves, as if flipping their role cards. In some rule variations, this may in fact be the case. But you didn't specify this in the game's description. In other rule variations, a sheriff and doctor revealing themselves plays out no differently from a mafia lying about their role, which means such revelations are not necessarily convincing.
2. This is the more important part: You failed to establish a rigorous model of cooperation. This would be important, since the game does rely on players working together. The actions of players may be motivated by their expectations of other players' future actions.
To elaborate on cooperation, consider a simple game:
Alice and Bob must each write down a word on a piece of paper. They then individually submit their words to a judge. If the words match, they both win. Otherwise they both lose.
We could examine two variants of this game.
In the first variant, imagine that you are Alice, and you aren't allowed to communicate with Bob. What is the optimal strategy?
That's right. *The problem is ill-posed.* The only way one of Alice's possible strategies could be evaluated is by knowing Bob's strategy-distribution beforehand. The problem description contains nothing to illuminate us in this regard, so the problem is unsolvable due to a lack of information.
In the second variant, imagine that Alice and Bob are allowed to (bindingly) strategise before the game. What is the optimal strategy?
That's right. They write the same word.
Now how Mafia should be modelled is a pretty good question. I'm not sure. Most likely, there should be a town "meta" and a mafia "meta". Those who receive town roles play according to the town meta, and those who receive mafia roles play according to the mafia meta. The goal should then be to evaluate the effectiveness of different metas.
There's many pitfalls, such as:
- How exactly is daytime communication modelled?
- What happens when two players attempt to hold an infinite conversation?
- Should players be aware of what meta the opposing side is currently using?
- What even is a meta? Is it like a computer program? Or just an arbitrary, possibly uncomputable strategy?
- If metas are computable, are there any computation theoretical hazards due to metas possibly requiring players to evaluate the opposing meta in play?
And probably more.
Hey, thanks for commenting your feedback! I'll try to go in order of generally what you said, but I'm curious about your further thoughts.
Generally, yes you are correct that verification is the name of the game and that in social deduction games like Mafia, that is usually impossible. As a result, this also makes true cooperation impossible, since there is no guarantee from the perspective of a town.
I apologize for not being more clear on the rules, but this is what I tried to cover. At 1:45, I tried to set up that an implication of minimal information from the narrator was that anyone could claim roles with ambiguity, including the Mafia (see 17:37 for more). This might have been unclear with the lack of visuals, but I'll try to improve on that in future videos.
Generally, the goal of the video is to establish a logically sound baseline strategy. Obviously, if people are aware that every other participant is on this level, then new strategies would develop (similar to your paper game example). The difference between Mafia and your example, in my mind, is that the game is competitive rather than cooperative. So yes, it is true that strategies can build off each other, but in my mind, the video is meant to be an initial strategy that has some method of maximizing the chances of winning by analyzing all possible outcomes.
I guess for the sake of the "dual metas", the reason why I chose not to cover this more in detail is that it becomes infinitely circular. If we take examples of mind-readers playing Rock-Paper-Scissors, obviously it becomes regressive to the point where the best move is just not to play. We have to suspend some disbelief and accept the possibilities of being outplayed with new strategies, but I don't think that's a reason to not think about strategy at all.
I do really appreciate your feedback though, please don't read this as me disregarding it. If you choose to reply, I'm more than happy to continue discussing.
He he mathia
In games where i plays mafia, usually there is either a town person or even the mafia itself sort of playing mindgames and act suspicious intentionally, e.g. moving intentionally, etc, after a few games his/her behaviour was normalized by us, but turns out when we normalize it, he was it, whats the best logic strategies againts that, you think?
In his POV whats the chance of him winning?
And was it a good strats?
Cause everytime he do it, he was almost always kept alive by the mafia, was this actually a good way to play e.g. the sheriff or other power plant, then you can out yourself later or?
Thanks
thanks
Love the idea to analyse Mafia via math. But You lack understanding of the most META strategies for this game: for example, one of Blacks allways has to challange the Sheriff claim to deny Reds free information.
Better do it under the tournament standarts: 10 players 6 townfolks 1 sheriff 2 mafias+1don.
I would love to see more in depth analysis of different strategies for every team with early and late Sheff reveals, Sheff reveal 1 turn after fake Sheff, table splits to pass or to raise 2 or even 3/4 players etc.
Woah, I actually didn't know that there even were tournaments for Mafia! I only played the game during camping trips really, but that's actually super interesting. Thanks for sharing!
do this or salem please
Will think about it for the future but I'm honestly not even sure if its possible, especially with roles like Medium (I think?) where you can communicate with the dead.
ah, i love ruining simple games by overanalyzing the mathematics behind them
I'm sorry you feel that way, but I do genuinely believe that being a more engaged player tends to make it more fun for everyone though. I'm sure we can agree to disagree though.
In reality, you can understand the mathematics while still having fun, depending on how you play. I played a lot of video mafia a few years back and the vibe of those games very much is "everyone understands the statistics and purposefully plays suboptimally, still playing to win but moreso trying to look like you're Light Yagami at the same time". Intentionally playing a wide game psychologically to obfuscate statistics for both the town and the mafia. That is the real skill ceiling - not knowing what the chances are, but knowing what the chances are and trying to tell your opponent the chances aren't what they think they are, even without knowing who your opponent is.
Don't think I could have put it better, especially since I am also a fan of the Death Note show.
If a game can be ruined by overanalysing the maths it wasnt very good anyways. If you assume the other guys follow this strategy, the mafia can win a lot more. Same goes for the other guys. If the mafia always follows this strategies, the other guys can win a lot more
84 SUBS? THATS A CRIME
Haha, thanks! Is there any content you'd be interested in seeing in the future?
@@Poly_morphia idk, i guess i just find these 'best way to play (insert game)' videos just really interesting
@@ChillKillaBeta Sure! I'll try to keep this in mind for the future. Right now, I have several general ideas on probability schema/interesting logic puzzles coming up for uploads next week/the following week, so it might have to wait a month or so, but I think we can definitely try to find some for 2025. I do know that a lot of the logic puzzles have probably been already covered on youtube though, so I've made a great effort to look for niches that people haven't made videos on yet. Hope to see you in future comment sections too!
@@Poly_morphia thanks :3
Laughing in the Blood on the Clocktower tears 🥲
Awesome! Now can you do blood on the clock tower? Trouble Brewing is fine 🫡