[SETUP]Mafia Rebels

[Allomancer]

13 Vanilla Townies

3 Mafia Goons

2 Rebel Goons

Mafia and Rebels share a PT. Rebels know each other's identities, Mafia do not know who the rebels are. Setup is Nightless and PT has daytalk; from Day 2 onward, the mafia perform a kill by voting in the PT during the day, the same way lynches are performed in the main thread. They can vote for a Townie or for a PT member. Rebels and Mafia can both only win when the other faction is completely eliminated. Essentially, there is a sort of Mafia-within-Mafia going on in the PT where the mafia are trying to find the rebels.

[the worst]

Interesting, kinda reminds me of Awoo's recursive multiball IV problem

I can't really guess at balance on this but it feels townsided. from a funness POV I'm not sure recursive multiball appeals to me personally but it's definitely an interesting experiment.

[northsidegal]

you think it's townsided? i think it's crazy scumsided.

consider the scumteam strategy of eliminating all town until it's literally just the goons left. for the town, that's essentially 13:5 mountainous (EV of 7%). the potential encouragement for bussing

might

be slightly in town's favor, but it's still a big hurdle to overcome.

it is a pretty interesting setup, but it needs something more for town i think for it to be playable.

[the worst]

Yeah my mind leaped to a scenario where there's mad cross-bussing. You're right that it's highly optimal to just kill all town first. Sorry.

[northsidegal]

nothing to be sorry for!

the setup could be (EV wise, at least) balanced just by making it nightless (i.e. taking away the scum kill). in that scenario you could even afford to

remove

a few townies – 10:5 would still be pretty balanced, maybe even a little townsided.

it gets a little confusing what to do when you get to parity, though. like, say that there's 8 players alive, 4 town and 2 of each mafia team. do the townies get endgamed? in a 5 town 3 mafia 2 rebel scenario i would say that they probably should and the game should immediately go to mafia lylo, but in other scenarios it's almost like town has been kingmade.

i mean, the alternative is that they just get endgamed at parity regardless and the rebel goons win instantly, which i suppose isn't actually that bad of a solution now that i think about it. the fact that that's a threat for the mafia goons might even keep the original vision of the setup (i presume) of crossbussing alive more – as the mafia goons get closer and closer to lylo, if even just one goon has died they have to kill a rebel lest they get endgamed just like town does.


it seems like that would end up making the setup even more townsided such that you could almost remove another few townies – town already outperforms in nightless with 33% EV, the addition of a bussing incentive i imagine would only serve to help. i don't really like that, however – that gets to too high of a ratio of mafia to town for my preferences. i think it would be playable, however.

[callforjudgement]

What about, if the number of goons drops to the number of rebels, the goons instantly lose no matter how many townies are alive (leaving the remaining rebels to try to beat the townies by themselves)? Especially in a Nightless, that would likely promote "lynch via bussing" techniques more and more heavily as scum do better and better, causing a large amount of negative feedback, and if you combine that with "townies die if their numbers equal total scum" then it removes a lot of potential screwy endgame scenarios (not sure whether or not there are any left).

You'd need more Goons for this to work. Somewhere around 9:4:2 or 10:4:2, perhaps.

[northsidegal]

kind of seems really punishing for the mafia goons

i think our ideal win percentage distribution is 33/33/33 and i don't feel like that's the case for that (not that i have anything to support that other than "it feels wrong")

[Awoo]

recursive multiball nightless

... never got around to making a fast script for recursive multiball, ran into some mathematical obstacles. so low numbers only, guys

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)
(4, 1, 1) : (0.3333333333333333, 0.13333333333333333, 0.5333333333333333)
(6, 2, 1) : (0.33333333333333326, 0.2936507936507936, 0.37301587301587297)

(8, 3, 1) : (0.3333333333333333, 0.3818181818181818, 0.2848484848484848)
(10, 4, 1) : (0.3333333333333333, 0.43663003663003663, 0.23003663003663002)

(12, 5, 1) : (0.33333333333333326, 0.4738562091503268, 0.19281045751633985)
(14, 6, 1) : (0.33333333333333326, 0.5007518796992481, 0.16591478696741851)
(16, 7, 1) : (0.33333333333333326, 0.5210803689064557, 0.14558629776021076)

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)
(6, 1, 2) : (0.3333333333333333, 0.07142857142857142, 0.5952380952380951)
(8, 2, 2) : (0.3333333333333333, 0.15218855218855215, 0.5144781144781144)
(10, 3, 2) : (0.33333333333333326, 0.23489843489843487, 0.43176823176823176)
(12, 4, 2) : (0.3333333333333333, 0.2981900452488688, 0.36847662141779786)

(14, 5, 2) : (0.33333333333333326, 0.34631513424083077, 0.3203515324258358)

(16, 6, 2) : (0.3333333333333332, 0.3837096033892371, 0.28295706327742937)
(18, 8, 1) : (0.3333333333333332, 0.5369800569800569, 0.12968660968660967)

Give town/loyalists a lower winrate because town is OP in nightless edition:

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)
(5, 1, 2) : (0.25, 0.05952380952380952, 0.6904761904761904)
(6, 2, 2) : (0.19999999999999998, 0.1222222222222222, 0.6777777777777777)
(8, 3, 2) : (0.23076923076923073, 0.2368298368298368, 0.5324009324009324)

(10, 4, 2) : (0.24999999999999994, 0.31385281385281383, 0.43614718614718617)
(11, 5, 2) : (0.2222222222222222, 0.37935430582489404, 0.3984234719528838)

(13, 6, 2) : (0.23809523809523808, 0.4208806329549363, 0.3410241289498256)
(15, 7, 2) : (0.24999999999999994, 0.4519046298222499, 0.29809537017775006)

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)
(6, 1, 3) : (0.2, 0.033333333333333326, 0.7666666666666666)
(8, 2, 3) : (0.23076923076923078, 0.08298368298368297, 0.6862470862470862)
(10, 3, 3) : (0.25, 0.14495504495504494, 0.605044955044955)
(11, 4, 3) : (0.2222222222222222, 0.2076204840910723, 0.5701572936867054)
(13, 5, 3) : (0.23809523809523808, 0.26808442675315736, 0.49382033515160456)

(15, 6, 3) : (0.25, 0.3153040704528117, 0.4346959295471881)

[Awoo]

Somewhere around 9:4:2 or

10:4:2

, perhaps.

oh yeah haha look at mr. "i'm just guessing, i didn't do the math" over here haha nice one dude i know you did the math

[Allomancer]

but if we get rid of the special nightkill mechanics it just becomes a regular multiball huh?

[northsidegal]

are those numbers in nightless?

how does it deal with town losing a majority? does it instantly endgame them, or...?

[Allomancer]

i believe with nightless mafia win conditions is control 50% of the town.
Town wins by eliminating all Mafia and Rebels.
Mafia wins by having equal numbers or greater than Town and eliminating all Rebels.
Rebels win by having equal numbers or greater than Town/Mafia combined.

[northsidegal]

right, but what happens to the townies in the situation when you get to like 3 town 4 mafia 2 rebels? do the townies instantly get endgamed?

if you got to 4 townies 2 mafia 2 rebels, would the rebels instantly win?

[Allomancer]

at 3:4:2 and 4:2:2, townies can still scumhunt. Because the mafia are still scumhunting as well (for the Rebels) it would still work out fine.

[Awoo]

Right let me clarify those numbers.

When town <= (goons + rebels), all townies are endgamed and removed from the game, game continues as goons VS rebels nightless.

[northsidegal]

11:5:2 looks like it's very balanced

not sure how interesting people would find playing an 18 player nightless near-vanilla or how much the high scum:town ratio would affect things, but i think it'd be playable

[Awoo]

if you got to 4 townies 2 mafia 2 rebels, would the rebels instantly win? yes, according to the script I used to produce those numbers.

What is the new ruleset you guys are proposing for endgaming? I'm having a hard time getting my head around the specifics of this.

3:3:1, town : loyalists : rebels, nightless

The mafia (loyalists + rebels), who know each other's identity as mafia members, collectively decide that there is no benefit to keeping this third faction in the game (the town), whose win condition is literally to kill both of them, and proceed to chain lynch them unto extinction, then fight it out since it's nightless anyways and keeping the townies in the game doesn't actually help them. as soon as town has minority, they're toast. it's optimal play for mafia + rebels to always keep majority over them, since they don't want the town to have any chance of winning since only one faction can win. So the rebels and loyalists form a temporary alliance to remove a common enemy. Therefore townies should just be endgamed when they have minority. Even if mafia wants to keep town around as a 'pet' to help them scumhunt, they would absolutely never let town have majority or equal numbers from this point on - they would take turns lynching town, mafia, town, mafia, etc. Town's EV in this situation is 0.

4 : 3 : 1, town : loyalists : rebels

the mafia should only want to lynch a townie here. if the rebel votes with town to lynch a loyalist, he outs himself to the town, which is bad since they're trying to kill him too. Even in larger numbers, there will always be that minority of rebels inside the mafia that would end up getting outed by flipping on their mafia family.

So it's a bit of a stalemate at equal numbers. Which is why town should probably just get endgamed here too. Loyalists are trying to look "towny" to their in-group by not turning on one another to try to get majority, and the rebel also needs to look "towny" to survive to endgame.

[northsidegal]

if you got to 4 townies 2 mafia 2 rebels, would the rebels instantly win? yes, according to the script I used to produce those numbers.

i think this is probably just the way it should be

i feel like it makes the most intuitive sense and i also think creates very interesting gamestates as you approach lylo with, say, equal numbers of mafia and rebels alive.

[Awoo]

1 : 1 : 1 -- the rebel should always just endgame the other two. It makes sense in terms of the flavor and saves us a headache.

2 : 1 : 1. There's a conflict of interests. (For clarity sake, I will use the terms Town, Loyalists, and Rebels, with Mafia referring to loyalists + rebels)

should townies be endgamed?

according to the rebel, yes.
according to the loyalist, no.
Therefore imo the townies shouldn't be endgamed, since endgaming is just "the way the game would have gone if we had played it out anyways."

The town needs a mafia lynched.
The the loyalist needs exactly the rebel lynched, followed by a townie.
The rebel needs anyone but himself lynched.

Loyalist is in a tough position, he has the worst of town and scum. he can't out himself because thats playing against wincon, and he can't lynch a townie. hahahaha sucks to be him lmao

[Awoo]

2 : 2 : 2

Town: lynch a mafia
Loyalists: Lynch a rebel
Rebels: lynch anyone

An (mostly) uninformed majority is hunting an informed minority. But does every faction have a path to victory?

lynch a rebel -> 2 : 2 : 1, mafia endgames the town, townies lose, mafia fight it out
lynch a loyalist -> 2 : 1 : 2, same thing but rebels win.

So even though the loyalists could potentially win if the game played out, the townies are just playing kingmaker which is no fun. so they should just die. which means the rebels win. So it's just a more covoluted version of 1 : 1 : 1, which we count as a rebel win anyways.


4 : 2 : 2 - it's kind of like 2 : 1 : 1. it's not broken and any faction can technically win. you know you've created a fucky setup when LYLO is at even numbers


Okay here is my complete philosiphy on endgaming, this is a bit weird, feel free to debate me.

Mafia == 0: Townies win.

Town < Mafia : Townies get endgamed. Game continues.

Town <= Loyalists, Rebels == 0, Loyalists win.

Town == Loyalists == Rebels : Rebels win.

Town == Mafia, Loyalists > Rebels: Townies get endgamed, Game continues

Town == Mafia, Loyalists == Rebels: Game continues.

Town == Mafia, Loyalists < Rebels: Townies get endgamed, followed by loyalists. Rebels win.

I'll be back in the future with a new script to run the numbers on this new ruleset.

[BuJaber]

This might be the wrong thread, but could you explain how you do your calculations or share the script?

Because like I tried to do it manually by calculating odds of town losing to start with (just town losing assuming scum are only town until they are all dead and lynches are random). It takes hours. I got tired after 90 minutes or so and I didn't even come close to finishing all scenarios of town losing.

This setup is even somewhat simple in theory for calculating EV. I shudder to think how to even approach the more complex ones.

[BuJaber]

Manually as in typing the numbers day by day, excel did the math.

[northsidegal]

Okay here is my complete philosiphy on endgaming, this is a bit weird, feel free to debate me.

Mafia == 0: Townies win.

Town < Mafia : Townies get endgamed. Game continues.

Town <= Loyalists, Rebels == 0, Loyalists win.

Town == Loyalists == Rebels : Rebels win.

Town == Mafia, Loyalists > Rebels: Townies get endgamed, Game continues

Town == Mafia, Loyalists == Rebels: Game continues.

Town == Mafia, Loyalists < Rebels: Townies get endgamed, followed by loyalists. Rebels win.

i feel like this probably all makes sense although the town = mafia, loyalists = rebels (i.e. 4:2:2) outcome is i feel unintuitive

This might be the wrong thread, but could you explain how you do your calculations or share the script?

yeah i'd imagine it's some kind of code

[Allomancer]

Here a consideration: 2:1:1 will never become 1:1:1. The loyalist has no incentive to lynch a townie in 2:1:1, because that would cause him to be endgamed by the rebel. Therefore, 2:1:1 will always result in a mafia lynch, and go to 3p LyLo with either a loyalist or a rebel. The only exception is if a plurality lynch were to happen, but by nature of the fact that a townie cannot be lynched, town should never let that happen. If nearing deadline with only 2 votes on a wagon, you can assume that wagon is on town and the person not voting is the loyalist.

[Awoo]

Hey. Phoneposting rn.
That endgame chart I posted is wrong. The last case where town = mafia and rebels >loyalists should not be an instant rebel win.

3 .. 1 .. 2.

Town needs to lynch a mafia.
Loyalist needs to lynch a rebel.
Rebels need to lynch anyone.

Every faction has a path to victory. Town Lynches a rebel followed by the other two mafia in 3 vs 2.
Loyalists lynch rebel rebel then beat town in 3v1.
Rebels lynch loyalist townie.

Also, the "mafia endgame townies when loyalists have majority of the mafia "case works on the logic that 100% of the mafia is co operation with the plan since the rebels are doing it to appear as loyalists. This case doesn't work since the loyalists don't want to appear as rebels cause they would just die. So I'm going to have to go back and rethink some more cases where rebels are majority and townie s are equal or smaller then mafia tonight.

For those wondering, I use some code to calculate the ev. The performance is very slow as the numbers get beyond what you see here. I once waited for 2 hours and it didn't spit out another result in te last thread. Once we can agree on all the endgame scenarios and how the weird cases like 2.1.1 play out I can change things up and rerun it.


Allo's post is super weird and interesting and I don't know what to think of it in terms of how that translates into mathematics.