[SETUP] Silent Night

[usesPython]

2 Mafia Loyal Neighborizers

7 Vanilla Townies

No scum PT, mafia do NOT know who their partner is

If scum submit differing nightkills before they're in the hood together a coin is flipped to determine which nightkill happens (Otherwise if there's a scum hood resolve as normal)

[usesPython]

Doing the math the chances of scum finding each other with random picks is about:

N1: 1 - ((6/7)^2) ~= 26.5%
N2: 1 - ((6/7)^2 * (4/5)^2) ~= 53%

(Numbers are slightly off since I'm not correctly accounting for how likely a n1 neighborizer target being alive n2 is)

Mostly just looking for opinions on balance (Maybe adding Bulletproof or N1 Bulletproof to scum to stop swing from NKing scum if it's too town sided, or adding 2/4 more VT if it's too scum sided)

[BBmolla]

Can scum kill each other?

[usesPython]

If they're not in the hood scum can kill each other yes

[yessiree]

N1: 1 - ((6/7)^2) ~= 26.5%
N2: 1 - ((6/7)^2 * (4/5)^2) ~= 53%

why was 6/7 used and not 7/8?

[Skygazer]

N1: 1 - ((6/7)^2) ~= 26.5%
N2: 1 - ((6/7)^2 * (4/5)^2) ~= 53%

why was 6/7 used and not 7/8?

Presumably because the mafia isn't going to try and neighborize themselves N1

[yessiree]

oops i forgor about the d1 lim

[usesPython]

Spoiler: Hand calculated EV

11P: 9-2 Hoodless day
2/11 GOTO 9P: 8-1 (187/315 Town win)
9/11 GOTO 10P: 8-2 Hoodless night (4187179/11252115 Town win)

(2/11 * 187/315 + 9/11 * 4187179/11252115 = 1134317/2750517) 41.2% Town win
(1616200/2750517) 58.8% Scum win

---

10P: 8-2 Hoodless night
1/9 GOTO 9P: 8-1 (187/315 Town win)
136/729 GOTO 9P: 7-2 (94/315 Town win)
512/729 GOTO 9P: 7-2 Hoodless day (367/1029 Town win)

(1/9 * 187/315 + 136/729 * 94/315 + 512/729 * 367/1029 = 4187179/11252115) 37.2% Town win
(7064936/11252115) 62.8% Scum win

---

9P: 7-2 Hoodless day
2/9 22.2% GOTO 7P: 6-1 (19/35 Town win)
7/9 77.8% GOTO 8P: 6-2 Hoodless night (3643/12005 Town win)

(2/9 * 19/35 + 7/9 * 3643/12005 = 367/1029) 35.7% Town win
(662/1029) 64.3% Scum win

---

8P: 6-2 Hoodless night
1/7 GOTO 7P: 6-1 (19/35 Town win)
78/343 GOTO 7P: 5-2 (8/35 Town win)
216/343 GOTO 7P: 5-2 Hoodless day (29/105 Town win)

(1/7 * 19/35 + 78/343 * 8/35 + 216/343 * 29/105 = 3643/12005) 30.3% Town win
(8362/12005) 69.7% Scum win

---

7P: 5-2 Hoodless day
2/7 28.6% GOTO 5P: 4-1 (7/15 Town win)
5/7 71.4% GOTO 6P: 4-2 Hoodless night(1/5 Town win)

(2/7 * 7/15 + 5/7 * 1/5 = 29/105) 27.6% Town win
(76/105) 72.4% Scum win

---

6P: 4-2 Hoodless night
1/5 20% GOTO 5P: 4-1 (7/15 Town win)
4/5 80% GOTO 5P: 3-2 (2/15 Town win)

(1/5 * 7/15 + 4/5 * 2/15 = 1/5) 20% Town win
(4/5) 80% Scum win

For ease of calculation no attempt was made to prevent scum from neighborizing someone they neighborized a previous night or to only shoot people who they've failed to neighborize. The formula used to calculate if scum neighborize for NP: (N-2 : 2) Hoodless night was:

Code: Select all

(1 - (((N-2)/(N-1))^2))*((N-2)/(N-1))

e.g. for 10P: 8-2 Hoodless night:

Code: Select all

(1 - ((8/9) ^ 2))*(8/9)

Implementing these strategies would make the numbers slightly more scumsided but it should be counterbalanced by the lack of scum coordination making dayplay slightly more townsided. For reference 11-2 Mountainous has a 39.5% town winrate with random lims so 7-2 is expected to be slightly more scumsided and 9-2 slightly more townsided. I'd figure a test run with 7-2 and then doing 9-2 with a n0 neighborizer action if it's too townsided would probably work fine

[yessiree]

A lot of numbers to digest but from what I've gathered I don't think it's apt to compare this setup to 2:N mountainous since it plays drastically differently when 2 scums don't know each another. It's probably closer to some fringe variant of multiball or N vs 1 even night sk + 1 odd night sk depending on the NK rng

It also feels wrong when there's still a chance for scum to not be neighbours at ELO in the 7:2

[usesPython]

A lot of numbers to digest but from what I've gathered I don't think it's apt to compare this setup to 2:N mountainous since it plays drastically differently when 2 scums don't know each another. It's probably closer to some fringe variant of multiball or N vs 1 even night sk + 1 odd night sk depending on the NK rng

For EV calculations I don't think that multiball/SK calcs are correct here since scum want to only hit town during the night (since hitting scum always lowers their EV) whereas in multiball there's cases when you want to hit scum.
Likewise dayplay is better represented without using multiball if you run under the assumption that in that case scum will just play survivalistic d1 and then d2 onwards push town since they should be using their neighborizer ability on scummy people (either they find their partner at which point standard mountainous calcs or they find out it's town in which case it's safe to push them during the day at which point standard mountainous calcs)

D1's kind of a wildcard there as well as games where a neighborizer target dies during the night but as a rough estimate it's fine I think?

The lack of communication and organization definitely makes it more townsided until scum neighborize (since scum can accidentally bus/shoot each other/nk a pocket/etc.) but representing that in EV calcs is pretty arbitrary (Does it make scum 10% scummier? 20%? Or even

less

scummy than normal if townies are used to associative reads) so I just left it as is instead and only looked at the "Scum can NK each other" part.

It also feels wrong when there's still a chance for scum to not be neighbours at ELO in the 7:2

It actually doesn't really matter in that case I think?

Someone's

getting limmed that day and unless you're saying scum are inherently more likely to get limmed there it should be an even distribution when you look at EV (Just assume that scum slow-roll and justify even a hammer vote)

[yessiree]

A lot of numbers to digest but from what I've gathered I don't think it's apt to compare this setup to 2:N mountainous since it plays drastically differently when 2 scums don't know each another. It's probably closer to some fringe variant of multiball or N vs 1 even night sk + 1 odd night sk depending on the NK rng

For EV calculations I don't think that multiball/SK calcs are correct here since scum want to only hit town during the night (since hitting scum always lowers their EV) whereas in multiball there's cases when you want to hit scum.
Likewise dayplay is better represented without using multiball if you run under the assumption that in that case scum will just play survivalistic d1 and then d2 onwards push town since they should be using their neighborizer ability on scummy people (either they find their partner at which point standard mountainous calcs or they find out it's town in which case it's safe to push them during the day at which point standard mountainous calcs)

For looking at EV Dayplay wise, it should be the same as any normal setup, what each actor wants to do shouldn't matter since we're modelling the behavior of the entire playerlist as a whole, and using that to calculate the outcome. You are using randomness to abstract away what each individual actor might do and how they might play.

Nightplay follows the same logic for modelling outcome, I dont think you should be looking at what each actor wants to do, only what they

can

do given the info they have at a given moment in time (with the assumption they still always play to their wincon)
For mountainous, the scum team has complete info of the identities of every town/scum players so they could only ever hit town during the night making it easy to model
For multiball, each scum team has incomplete info, so only guarantee is scum won't shoot themselves, anyone else is fair game
For this setup, it should be the same as multiball iff scum are not neighbors, and mountainous otherwise, which might not be hard to model now that I think about it

D1's kind of a wildcard there as well as games where a neighborizer target dies during the night but as a rough estimate it's fine I think?

The lack of communication and organization definitely makes it more townsided until scum neighborize (since scum can accidentally bus/shoot each other/nk a pocket/etc.) but representing that in EV calcs is pretty arbitrary (Does it make scum 10% scummier? 20%? Or even

less

scummy than normal if townies are used to associative reads) so I just left it as is instead and only looked at the "Scum can NK each other" part.

It also feels wrong when there's still a chance for scum to not be neighbours at ELO in the 7:2

It actually doesn't really matter in that case I think?

Someone's

getting limmed that day and unless you're saying scum are inherently more likely to get limmed there it should be an even distribution when you look at EV (Just assume that scum slow-roll and justify even a hammer vote)

Not talking about EV here, I just feel like it wouldn't be a proper game of mafia at that point. There are no associative reads for town to use to sort potential scum pairs which means town isn't really hunting for an informed minority, more like semi-informed team of two acting out of their own interests. So I guess town is just hunting for scummy players but then that'll have an effect in how scum approaches the game too so I think I'd prefer if the scum team becomes neighbors at ELO automatically. There is precedence where setups with unique mechanics revert to mountainous during ELO

[usesPython]

For mountainous, the scum team has complete info of the identities of every town/scum players so they could only ever hit town during the night making it easy to model
For multiball, each scum team has incomplete info, so only guarantee is scum won't shoot themselves, anyone else is fair game
For this setup, it should be the same as multiball iff scum are not neighbors, and mountainous otherwise, which might not be hard to model now that I think about it

Oh I misunderstood you mb, the EV above already takes into account the chance that scum can nightkill each other

Not talking about EV here, I just feel like it wouldn't be a proper game of mafia at that point. There are no associative reads for town to use to sort potential scum pairs which means town isn't really hunting for an informed minority, more like semi-informed team of two acting out of their own interests. So I guess town is just hunting for scummy players but then that'll have an effect in how scum approaches the game too so I think I'd prefer if the scum team becomes neighbors at ELO automatically. There is precedence where setups with unique mechanics revert to mountainous during ELO

Loyal Neighborizers N2 Informed

maybe? It punishes scum for not being accurate n1 since they have to mind read their partner for the nk n2 while still letting them communicate during ELO and giving town a co-ordinated nightkill to analyse