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There is the link catte pointed to originally

[url=https://wiki.mafiascum.net/index.php?title=Category:Vanilla_(Open_Setup]https://wiki.mafiascum.net/index.php?title=Category:Vanilla_(Open_Setup[/url])
Pookina: Unsure how to read ZFR's alignment from his proposed no-lynch solution; sounds like something he'd come up with as Town or Mafia, so I'll reserve my judgement. The rest of y'all are GRASS ON THE GROUND.
If betting was allowed I would have bet you the new PS5 that he is 100% Town or Mafia based on what he wrote so far.
dedoporno: If betting was allowed I would have bet you the new PS5 that he is 100% Town or Mafia based on what he wrote so far.
HMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM

that's 100% probable, he is technically 100% (Town or Mafia).
nmillar: I don't understand how an odd or even number of players makes a difference, as a no lynch would still result in m/(n-1) regardless of the number of players.
ZFR: In case of odd number of players players, an NL+NK brings the Mafia 1 step closer to victory as it reduces the number of players they have to NK.

Consider 4T vs 1M (odd number of players).
The Mafioso has to NK 2 players to win. If they decide on No-lynching, then Mafioso only needs to NK once.

Now consider 5T vs 1M (even)
Mafioso has to NK 2 players to win. If they decide to NL one Night, the Mafioso still has to NK twice.

For the most basic situation consider LYLO (odd), vs MYLO(even). In this case the Mafiosi have to NK once to win. In case of odd (LYLO), an NL reduces this to 0 and it's game over. In case of MYLO, an NL means they still have 1 Day.
I thought I understood more before your explanation.
Or maybe you made a mistake. When you say "Consider 4T vs 1M (odd number of players).
The Mafioso has to NK 2 players to win. If they decide on No-lynching, then Mafioso only needs to NK once."
I'm sorry, but... in that scenario wouldn't that NL lead to a next Day 3vs1? Thus needing a mislynch and another NK for a Mafia victory?
(Unless you're considering the game ends with the mislynch because the Night+1's NK and thus the Mafia victory is a foregone conclusion)

Either way I parse your statement it looks like you're saying that a NL leads to less people the scum has to kill. I really don't get it, unless you wrote NL but actually meant to say mislynch.
joppo: I'm sorry, but... in that scenario wouldn't that NL lead to a next Day 3vs1? Thus needing a mislynch and another NK for a Mafia victory?
Yes, that's the point. At that stage Mafia need a single another NK for victory. So on D1 they needed 2 NKs to win, and after the NL (and N1 NK) they need only 1 more.

Contrast with a starting 5 vs 1. At this stage Mafia need 2 NK to win. Now, if on D1 we do NL (and N1 NK), then on D2 they still need 2 NKs to win.

With an odd number of players, by doing an NL we're essentially giving Mafia a free NK. With an even number of players we're also giving them a free NK, but that "free" NK is meaningless, since it doesn't drop the "minimum Nights left for Mafia to win" requirements.
OK, I think this might be easier to understand if I write about it in a completely different way.

Forget about the number of NKs.

Town can win only if they kill all Mafia. They can only kill Mafia by Lynching. They have a limited number of Lynches.

Let n be the number of "chances" that Town have to Lynch Mafia. Note that NL doesn't count towards n since Town can't kill Mafia by NL. Lynch here means actually someone dying by lynching - an action that can kill Mafia.

so e.g.

2 vs 1 : Townies have only one chance to Lynch Mafia. They mislynch it, they lose. n = 1.
3 vs 1 : Townies have only one chance to Lynch Mafia. They mislynch it, they lose. n = 1. (Remember NLs don't count)

4 vs 1 : Townies have two chances to Lynch Mafia. They mislynch one, they have one more. n = 2.
5 vs 1 : n = 2

... etc

3 vs 2 : n = 1
8 vs 3 : n = 3

Obviously, the higher n, the bigger the chances for Town to win, right?

Now:

_ For an odd number of players, doing NL decreases n by 1.
_ For an even number of players, doing NL doesn't change n.

ergo:
For an odd number of players, NL decreases Town's chances of winning
For an even number of players, NL doesn't decrease Town's chances of winning, and actually does increase them by a bit since the probability of hitting Mafia blindly increase by a small amount.
Sorry I am still a bit late. SL Pre Event is letting time forget.
Anyway with Zephyr mathematical proven that for now we best do nothing
VOTE NO LYNCH
Votecount the Second

No Lunch 1 - korotan (#37)

Not voting 11 - Engerek01, trentonlf, Lifthrasil, bucktoothgamer, ZFR, JaiSpohpere, GymHenson, dedoporno, joppo, pookina, Nmillar

Post edited November 24, 2020 by my name is sadde catte
ZFR: 3 vs 1 : Townies have only one chance to Lynch Mafia. They mislynch it, they lose. n = 1. (Remember NLs don't count)
Always skip on 4!

ZFR: For an odd number of players, NL decreases Town's chances of winning
For an even number of players, NL doesn't decrease Town's chances of winning, and actually does increase them by a bit since the probability of hitting Mafia blindly increase by a small amount.
TL;DR - It either changes nothing mathematically (but we don't risk mislynching so there's that) or changes it in a negative way but our current setup is the neutral outcome? Does that mean that without "knowing" we are better off doing NL every other day until we do know or have a good enough reason to try?
ZFR: 3 vs 1 : Townies have only one chance to Lynch Mafia. They mislynch it, they lose. n = 1. (Remember NLs don't count)
dedoporno: Always skip on 4!

ZFR: For an odd number of players, NL decreases Town's chances of winning
For an even number of players, NL doesn't decrease Town's chances of winning, and actually does increase them by a bit since the probability of hitting Mafia blindly increase by a small amount.
dedoporno: TL;DR - It either changes nothing mathematically (but we don't risk mislynching so there's that) or changes it in a negative way but our current setup is the neutral outcome? Does that mean that without "knowing" we are better off doing NL every other day until we do know or have a good enough reason to try?
Yeah so I understood the game.
ZFR: For an odd number of players, NL decreases Town's chances of winning
For an even number of players, NL doesn't decrease Town's chances of winning, and actually does increase them by a bit since the probability of hitting Mafia blindly increase by a small amount.
dedoporno: TL;DR - It either changes nothing mathematically (but we don't risk mislynching so there's that) or changes it in a negative way but our current setup is the neutral outcome? Does that mean that without "knowing" we are better off doing NL every other day until we do know or have a good enough reason to try?
No. We can only NL once. Once we do it, number of players becomes odd and NLing becomes bad.
Ok, I'm setting a deadline for this Day:

19:00 UTC 28/11/2020

This is open to extension if needed. I'm aware that US Thanksgiving falls in this week so let me know if this causes any conflicts for you.
Post edited November 21, 2020 by my name is sadde catte
Pookina: Hi. I am myself.
Quite a bold claim. Wonder if someone can counter it...
ZFR: No. We can only NL once. Once we do it, number of players becomes odd and NLing becomes bad.
That's why I said every other day. Or maybe I'm not following the pattern correctly.
dedoporno: That's why I said every other day. Or maybe I'm not following the pattern correctly.
Never mind, I'm dumb. I forgot that the NK also happens and along with the lynch will always keep the number odd.