Okay, I'm here. I've only skimmed because I've got work to do but obligatory mechanics post you guys seem to love so much:
There are 9 players, with 6 town. This gives a 66% chance of lynching town.
After the first lynch and subsequent night kill (assuming town) we will have 7 players with 4 town. This gives a 57% chance of lynching town.
After the next lynch and subsequent night kill (assuming town) we will have 5 players with 2 town. This gives a 40% chance of lynching town, and is effectively lylo.
This is obvious but it points out something important: scum, meaning mafia and the SK, can literally leave lynches up to chance and have a large chance at winning.
Strategy for the mafia is simple. They should cooperate every Night and focus on staying in the background so they don't get lynched, leaving the "compete" option only for when there is a small number of players left and they can effectively guess the night kill.
While it is tempting for the mafia to agree to cooperate but instead compete every night, this done by both parties means that there is a 22%, to 29%, to 40% chance of both scum dying. In other words, if both are stupid enough to choose compete then they have a 1 in 3 chance of losing entirely due to random chance at any stage in the game, give or take a little. This is assuming random night kills; this can change based on the SK's patterns.
The optimal strategy for an individual mafia member would be to say they will "cooperate" when they really say "compete", but this is ONLY the case when their PARTNER is believed to be a prominent night kill target.
If a mafia members believe that THEY THEMSELVES are a prominent night kill target, their best option is still "cooperate" as it is the most likely to make them bulletproof; if their teammate is going to choose compete, there is nothing that the mafia member can do to make themselves bulletproof.
This means the default status for mafia not under night kill suspicion is "cooperate".
This strategy again changes if one of the teammates is considered a prominent lynch candidate. If mafia is lynched, this means the other mafia member is boned. As far as we know they can't win with only one mafia member unless they get to a 3 man lylo and the SK and mafia work together to lynch a townie; highly unlikely. This means that if someone thinks their teammate is weak and will get lynched and NOT night killed, the best option for that individual mafia member would be to say "compete" on the sheer chance that it could occur. While it is possible the compete option could get them killed, that individual mafia member's chance of winning is incredibly slim if their teammate gets lynched so they should compete as many times as possible the moment they believe their teammate will be lynched as their overall winning chance is the same in this case.
Now that we've got our head screwed on straight for all of that, know this:
It is in town's best interest for both mafia to survive and cooperate, but not for the reasons you think.
In other words, if someone claims mafia we should let them live until later in the game. This will allow for a one in three chance of the SK missing his shot. With at least 4 phases for town, it can be assumed that the SK will miss a shot due to BP, statistically speaking. To WHO is hard to predict, but it'll happen.
If the SK misses a shot on N1 for example:
D1- 9
D2 - 8
D3 - 6
D4 -4 (lylo)
If the SK doesn't miss a shot on N1:
D1 - 9
D2 - 7
D3 - 5
D4 -3 (lylo)
however
With "No Lynch" we can create a mathematical certainty of an extra Day phase if the SK misses his shot.
D1 - 9
D2 - 8
D3 - 6
D4 -4 (NO LYNCH)
D5 - 3 (lylo)
But guess what? In both scenarios we get 4 opportunities to catch mafia and the SK, meaning if the SK doesn't kill mafia we have to get 3/4 lynches correct. Assuming a Day One mislynch as the standard, this means that we have to hit at 100% accuracy. That's bad, but crazier odds have been overcome (Liar game, yeahyuhz).
So why keep mafia around and have them cooperate?
There's one last variable:
D1- 9
D2 - 8 (misses shot)
D3 - 5 (discovers scum, kills them both)
D4 -3 (lylo)
or
D1 - 9
D2 -7
D3 - 4 (discover scum, kills them both, No Lynch)
D4- 3 (assuming scum kills)
The nightmare scenario for town is that we mislynch today, mislynch tomorrow, and then it's down to 4 players. We can no lynch and get down to 3, but that's 'bout the best we can do and that's only IF the SK kills (stalemate, technically).
So strategy time:
In addition to that, if the SK hits a mafia member it is then obvious to the SK that mafia is cooperating in addition to who mafia is. SK will want that mafia member lynched, so be very cognizant of people who start a day or use an opportunity to push a lynch on someone heavily only to have them flip mafia. This makes them more likely to be SK than town.
I repeat: if there is no Night Kill and then someone miraculously lynches a mafia member out of nowhere the next day, that person likely has inside info and is the serial killer.
Think of it this way:
3 man lylo between 2 mafia and SK means SK loses as mafia wins ties. This means a 4 man lylo between town, mafia, mafia, SK will result in a mafia win unless mafia is lynched and the SK kills the other mafia. There shouldn't be any claim shenanigans at the end as it is in everyone's best interest this game to claim mafia (even town!) as it makes you less of a lynch target and more of a night kill target, but town being hit by a NKill instead of mafia is preferrable to town given the possibility of a 3 Day phase game, at least early on.
Because of all this, SK can't give up trying to kill mafia. So if he misses one NKill, he's more likely to miss another one. It isn't sheer odds anymore because he wants to kill that scum. That means he's going to want a lynch if he can. Knowing the prisoners dilemma, it means if Mafia knows who was targeted it is in the best interest to compete if it was their teammate which means the SK is more likely to attack that same guy again, but the SK doesn't want to miss two kills in a row so he will go for a lynch.
TL;DR
1) All claims should be "mafia", so claiming is irrelevant. If you are forced to claim, claim mafia. Town claiming mafia, being left alive, then night killed is better than accidentally losing two mafia members. If you say "no that is horrible" then congratulations, now everyone is forced to claim town and we have no way of directing the SK's nkill. It isn't a boon to mafia for town to claim mafia anymore than it is a boon for town for mafia to claim town. The SK has his own prisoners dilemma when someone claims mafia, everyone claiming town just means the only people who benefit from claiming town are mafia. Town is who benefits by claiming mafia but only if mafia aren't lynched.
But because claims are irrelevant that won't matter, but it's a fun thought exercise all the same.
2) The SK really wants to lynch mafia. Town wants to lynch the SK. Enemy of my enemy is my friend and all that, we don't want to hunt mafia we want to hunt the serial killer.
3) Mafia should always cooperate unless they believe strongly that their teammate will be a night kill target, in which case they will inevitably both compete which makes cooperation the best choice anyway
Sorry if this was confusing, but this game is a fun logic puzzle. Not as fun as liar game mafia, but fun.
Finding the SK or mafia is going to be the same as other games, so no difference there. Only major difference is that mafia has no reason to distance whatsoever. They don't want to announce anything, but claiming a strong defense for their teammate doesn't put them in any extra danger because if one of them are lynched they will likely both lose so it's an all-or-nothing thing.
The SK's best chance of winning is making himself a strong town force as mafia have no NKill and this makes it the least likely for him to be lynched. A weak SK will probably hide in the background, but I'd imagine the majority of this game would simply try to take control.
This means town's best strategy at finding a weak SK is to lynch inactives while the best strategy to find a strong SK is to lynch prominent town players. For the SK, it is best to kill the opposite of how he is playing so he isn't sticking out like a sore thumb; this does make inactive SK a bit stronger as it'll make lylo a bit easier for the SK, but he still would have a weaker early game and would not control if mafia was lynched (which he has to).
KevinM actually has the best strategy in the game so far in that buddying with someone is the best way to prevent you getting NKilled.
1) Mafia won't openly buddy with their partner, so if you openly buddy with someone it makes it seem less likely you are mafia
2) If you buddy with someone openly and are antagonistic towards someone else and you survive and your buddy survives but those antagonistic towards you die, it is incredibly likely that one of those two could be considered the Serial Killer if viewed at a banal level.
While very low-level thinking, the SK would want to avoid suspicion at all costs and probably wouldn't dare to attack their direct competitor. I guess that means the most townie players in this game are going to be mafia and the Serial Killer.
There's more to all this, but I think you guys got the gist. Lots of WIFOM in this game. LEGITIMATE WIFOM for once.
I'll get to the actual thread later today. This post isn't really for discussion as most of it is pretty cut and dry; disagreeing with it gives the SK more information so... I wouldn't say anything. If you're town and you want to say town should claim town or something, just let it slide and we might get lucky and mafia will claim mafia, get shot at, and be bulletproof.
Did not proofread this sorry for any errors