Murmurings in the Fortress

[implosion]

So I was thinking about Guardians of the Fortress and I just came up with an absolutely ridiculous idea. And I'm like, kind of convinced it's a good idea, and if people think so I might run it (assuming that the other listmods agree with me that it actually counts as mafia!) What if we took that setup... and crossed it with conspiracy?

Murmurings in the fortress

0, 2, 4 or 6 Mafia Goons

9, 7, 5 or 3 Vanilla Townies

During setup generation, the moderator randomly picks 0, 2, 4, or 6.

The way they do this is important:

they should flip three coins. For each heads, they add two mafia. There will be this many mafia. The rest of the player list will be town. This method makes 0 and 6 less likely than 2 and 4, and is important for the same reason as "The Pie Observation" in the Conspiracy wiki page is important.

There are three locations: the Hearth, the Bunker, and the Atrium. These names are purely for flavor, and a mod could modify them as they please; the three are equivalent, unlike in Guardians of the Fortress. Like Guardians there's a lot of room for mods to potentially get creative with flavor (so long as they're careful not to spoil any information) and I think Guardians has a nice history of having good handwritten flavor, at least in the two runs of it I've played.

On day one, players assign themselves to locations much like in Guardians. At the end of the day phase, the mafia must choose two players to swap. If there are no mafia, the mod will choose two players to swap at random. Like in Guardians, there is a condition that must be met after the swap: in Guardians, that condition was that each location must have 1 mafia. Here, the condition is that

every location must have exactly 0 or 2 mafia.

If this condition is impossible to meet with a single swap, the town automatically win (I believe this will only be impossible in the case where there are 6 mafia

and

the 3 town pick the same location).

On day two, all three locations play simultaneous games of conspiracy: from each town member's perspective, either both other players in their location are town, or both are mafia. Every townie must eventually declare "my location contains 3 town" or "my location contains me and 2 mafia". This could be done publicly or privately, I think; it shouldn't matter, but should be consistent. Whenever all townies in a given location have made declarations, that location is flipped, and all players from that location may no longer post.

There is some single deadline for day two; if that deadline passes and any townie has not made a declaration, the game immediately ends in a mafia win. On d1 if deadline passes with anyone unassigned, town lose if any townies are unassigned and win if only mafia are unassigned.

Locations are scored as follows: if there is a single townie and 2 mafia, the town earn 3 points if the townie is correct, and the mafia earn 3 points if they are incorrect. If there are 3 townies, every correct townie earns 1 point for the town, every incorrect townie earns 1 of a point for the mafia. The first team to reach 5 points is victorious. If a team reaches 5 points, the game immediately ends even if it's in the middle of resolving an area (i.e. if the town has 3 points from the first location and 2 townies in the second location get it right, the game should just end immediately, since the outcome is guaranteed).

It seems to me like there

has

to be some kind of breaking strategies but for the life of me I can't figure out what they could possibly be. E.g. if the town has 4 points and mafia has 2 points with one location left, then it feels like the town should have a breaking strategy because if all 3 in the last location are town, then all town has to do is have one person be right. So they could do something like demand that a specific player that they agree is scummiest declare that everyone is town. But on the flip side, from the perspective of each individual townie, if they say "town" and are wrong, they just lose the whole game, so it's a matter of if you're willing to be the person who says that... and you might not be willing to!

Regarding the math behind the setup generation: you can think of it as the mod flipping 3 independent coins to decide whether each individual location will have a conspiracy or no conspiracy (and then the locations get shuffled to decide which ones are actually which). If you, for instance, randomly picked 0, 2, 4, or 6 with equal probability, then it'd turn out that e.g. if the town has seen two locations with conspiracies, the third location is actually more likely than not to also have a conspiracy.

[implosion]

I just thought of some arguments against this working, that I want to preempt and discuss.

Argument 1: you might look at this and think "well, if I'm a townie and I win 3 points for declaring a conspiracy, and only win 1 point for declaring no conspiracy (and conversely, that you risk losing 3 points by declaring no conspiracy and only risk losing 1 point by declaring a conspiracy) and say "optimal strategy for townies is to just say there's a conspiracy, or at least heavily bias themselves that way".

Argument 2: you might look at this and say "well, if you look at it closely from the perspective of any individual townie, they're actually much more likely to

not

be in a conspiracy. Each location has a 50% chance to have a conspiracy - ergo, we can pretend that each location's status is decided by a coin flip, and the fact that you are a townie in a location makes it more likely that that location has no conspiracy by Bayesian statistics, or by the Pie Observation. Thus, you might say "optimal strategy for townies is just to say there's no conspiracy, or at least heavily bias themselves that way".

So which of these is correct, and which is wrong? Well, both, and both! Both of them are correct, and both of them are wrong. In fact, they cancel each other out. If you are a townie in a given location, you can work out that the probability of there being a conspiracy is 1/4. Ergo, the expected point gain for the town by you saying "conspiracy" is (1/4) * 3 + (3/4) * (-1) = 0, and the expected point gain for the town by you saying "no conspiracy" is (1/4) * -3 + (3/4) * 1 = 0. In other words, since points are what matters, there is actually no mechanical advantage to guessing either way - a smart townie has no reason to bias themself in either direction.

[implosion]

But I thought that there are usually more than 0 scum.

Indeed. It's also usually the case that town outnumber scum. In this case these will each

usually

be true (it's only 1/8 that there are 0 and 1/8 that there are 6 scum), and the expected value is 3 scum, so

on average

it looks like a normal ratio. And hence, the average amount of suspicion a townie should have on a player is sort of similar to a 3:6 game.

[implosion]

In a 0 mafia setup the town wincon is effectively that at least 5/9 townies will have to declare no-conspiracy. If at least 5/9 declare conspiracy, then no one will win.

[implosion]

Yes, that is one important difference between this and conspiracy - townies have incentive to convince other townies that they are town.

[implosion]

Would this still function if the 0 mafia possibility was axed?

There would be a major flaw, namely that if two locations were resolved and revealed to not have any scum, the townie in the third location would know what to do.