Open 842: Diffusion of Power [Postgame]

[catboi]

Vote Count 1.04

GuiltyLion (1):

fua

Tejate Raichu (1):

northsidegal

implosion (1):

Amazonian Legends

Cephrir (1):

numberQ

morph the cat (1):

implosion

redtea (1):

GuiltyLion

numberQ (1):

Cephrir

Not Voting (6):

imaginality, morph the cat, redtea, Tejate Raichu, Ydrasse, Shirou

With 13 alive, it's 7 to eliminate.

Deadline for Day 1 is January 22 at 2:00 PM EST.

Deadline Timer:

(expired on 2022-01-22 15:00:00)

[fua]

VOTE: Tejate Raichu

[implosion]

Implosion's interactions with us are giving me dedede vibes, but I haven't (yet) gone back to look at his iso in that game. Insomnia struck so it might be tomorrow before I do that review.

I'm quite confident that if I had drawn scum here, 2017 meta would be not among the best indicators of how I'd play.

Assuming a 5-5 split, we have on average 97% chance of at least one pair of Town cops (i.e. cops who have the same action on the same night), and 78% chance of two pairs (or one triplet). Even if it's a 4-6 split, the 4 town players have 81% chance of at least one pair.
The same analysis applies to docs, of course.
So objectively, for the town as a whole, we can't really tell a lot from the existence of any particular pair.

However, subjectively it's a little different. Subjectively, there's 1-80%^4 = 60% chance of you being paired with a town player if you're part of five town players with that role (and 50% if there are four of you, 70% if there are six of you). So someone claiming the same role and night as you gives you at least a slight reason to suspect them over baseline suspicion (3/12 = 25%).

Hello; it is Me, Math, here to say This Wrong. There are two ways to explain why it's wrong: one, each town player's night is independently chosen, so me being, say, night 4 doesn't make the existence of another night 4 player be any more or less likely. The more poignant way to explain it is that if you know that as soon as someone claims the same role and night as you, it increases the probability that someone has the exact same role as you above the 60% baseline because, well, they might be telling the truth. The 60% probability that someone shares a role with you is the probability before any claims happen - if nobody else claimed the same role as you, then that probability would drop to 0%. So it stands to reason that if someone *does* claim the same role as you, it'll increase *above* 60%. And because the nights are independently chosen that increase will be by exactly the right amount to cancel out this idea of thinking about who does or doesn't have the same night.

Spoiler: Much, much more detailed calculations that I'm not 100% sure are all correct but I dare you to find an issue

Let's say Veronica is a Night 4 Doctor and sees Guillermo claim Night 4 Doctor. What are her before and after probabilities of Guillermo being scum?

Before, Guillermo had a 25% chance of being scum; this is simple as there are 12 other players and 3 of them are scum. After, we can calculate with Bayes' rule. If G is the event that Guillermo is scum and D is the event that Guillermo will claim night 4 doctor, all the while assuming that Veronica knows her own role, we have:

P(G | D) = P(D | G) P(G) / P(D)

If we assume that scum will pick a roleclaim at random (which is safe to assume here, because the effect we're trying to isolate is that of Veronica knowing her own role, not that of scum being more likely to claim cop vs doctor or an early vs a late night), then P(D | G) = 0.1. That is, the probability that Guillermo will claim Night 4 Doctor if he is scum is exactly 0.1.

For P(D), we have P(D) = P(G) P(D | G) + P(-G) P(D | -G); the only term here we haven't calculated is P(D | -G), the probability that Guillermo will claim Night 4 Doctor given that he is town. This is the key term, because it's the only term that depends on Veronica's role, and is implicitly what you are claiming will be lower based on Veronica knowing that she's a Night 4 Doctor. Technically there is going to be a very slight effect here simply because Veronica and Guillermo both are claiming doctors of any kind that will make Guillermo slightly more likely to be scum. But that's not what you were talking about - you were talking specifically about them being doctors of the same night. And that has no effect here. Because the setup was determined with every doctor being given a night independently at random, Guillermo's night and Veronica's night are independent variables. Veronica's night therefore has no impact whatsoever on the analysis. We can finish the calculation just for the hell of it. If there were 5 cops and 5 doctors, if Guillermo is town, he's one of nine players, five cops and four doctors, meaning P(D | -G) = 0.2 * (4 / 9) (the 0.2 is his probability of being Night 4, the 4/9 is probability of being a Doctor). Likewise if the split were 4/6 or 6/4 then P(D | -G) would be 0.2 * (3/9) or 0.2 * (5/9). Now we actually have to make a sort of sub-call to Bayes rule, because Veronica knowing that she is a doctor makes it slightly more likely that there are more doctors in the setup. If (all with the underlying assumption that Veronica is town) V is the event that Veronica is a Night 4 Doctor and 4, 5 and 6 are the events that there are that many doctors, then for each n in {4, 5, 6}, we have:

P(n | V) = P(V | n) P(n) / P(V).

Each P(n) = 1/3. P(V) is fixed and we only care about how relatively likely they are; P(V | n) is either 4/10, 5/10 or 6/10 (it's n/10). So we can say that 4/15, 5/15 and 6/15 of the event space is taken up by there being 4, 5 or 6 doctors. So on the whole, we have

P(D | -G) = (4/15) * 0.2 * (3/9) + (5/15) * 0.2 * (4/9) + (6/15) * 0.2 * (5/9) = 0.0918518519. As expected, this is very slightly under 0.1, as a result of Veronica knowing that she's a doctor making another doctor claim slightly more likely to be scum.

Thus, P(D) = 0.25 * 0.1 + 0.75 * 0.0918518519 = 0.09388888892

so P(G | D) = 0.1 * 0.25 / 0.09388888892 = 0.26627218926. In other words, Guillermo's probability of being scum has gone up from 25% to about 26.6%. And again, to be clear, this analysis should apply completely regardless of whether Guillermo claimed night 4 doctor or night 2 doctor.

I hope this has been edifying.

[implosion]

Also.

I think if anything fua's claim today is slightly +scum rather than +town as fua hinted it's a late-day action so it seems like it could be designed to encourage us to keep fua around, while also making docs likely to target fua which is fua is scum gives scum freer rein to kill whoever they like. Definitely feeling a bit wary about that.

Can we please not? This is like, the equivalent of rolefishing. And I think everyone or at least a lot of the people calling fua town are not calling fua town for the roleclaim (I'm not specifically, though I do think the roleclaim is +town).

[Cephrir]

there's been a few instances of Cephrir commenting negatively on something without following through on it.

I'm sure this won't do anything for you, but for, this is normal behavior for me

[Cephrir]

I guess we are not giving numberQ the votes he asked for

VOTE: northsidegal

[morph the cat]

I'm quite confident that if I had drawn scum here, 2017 meta would be not among the best indicators of how I'd play.

Noted, but I doubt you have a good handle on what I'll be looking for. And that game's a jumping off point for research.

[Shirou]

GuiltyLion (2):

Shirou

, fua

Not Voting (5):

imaginality, morph the cat, redtea, Tejate Raichu, Ydrasse

With 13 alive, it's 7 to eliminate.

I unvoted in 355

[Shirou]

I would be fine with one of numberQ/imaginality/redtea dying I think

the latter two don't have many posts but what they posted hasn't impressed me

[catboi]

GuiltyLion (2):

Shirou

, fua

Not Voting (5):

imaginality, morph the cat, redtea, Tejate Raichu, Ydrasse

With 13 alive, it's 7 to eliminate.

I unvoted in 355

Apologies, fixed.

[Shirou]

I think there's at least one scum active in thread but I don't know who they could be yet so I'm not gonna make random guesses

I don't particularly have confidence of any of the above slots mentioned in my previous post being more than very slightly more likely to flip scum than random though, so I'm still not gonna vote them yet, but if deadline was tomorrow I would be forced to vote one of those.

That's it for "scum reads" from me right now. I would also personally give NSG more time before pressuring her.

[Cephrir]

i would like to get content out of her before we go thinking about ending the day, at least

[Shirou]

i would like to get content out of her before we go thinking about ending the day, at least

doesn't feel like we're ending today anytime soon though?

It's only been 48 hours.

[Shirou]

Ah, also I guess unless they're scum together (which wouldn't be that weird considering their openings), I should probably trust Morph read on Amazon for now. Even if they were wrong on it at the moment, as long as they are alive they will likely correctly sort out Amazon correctly. If they die...well, we can cross that bridge when we get there.

[Shirou]

correctly sort out Amazon correctly

correctly sort out Amazon in the end.*

[Cephrir]

i would like to get content out of her before we go thinking about ending the day, at least

doesn't feel like we're ending today anytime soon though?

It's only been 48 hours.

i think i misread the tone of your post

[Cephrir]

morph/amazon are both underwhelming and could both be scum. come at me.

but i have a lot of fish to fry. maybe i should try harder to fry them since morph doesn't seem to be doing that for me.

[morph the cat]

Ah, also I guess unless they're scum together (which wouldn't be that weird considering their openings), I should probably trust Morph read on Amazon for now. Even if they were wrong on it at the moment, as long as they are alive they will likely correctly sort out Amazon correctly. If they die...well, we can cross that bridge when we get there.

For what it's worth, it's a very high confidence read for us. I'll be very surprised if they leave our "Utterly Town, never elim this" pile. We'd love to have 4 more reads of that strength, or even four more in that plus the second tier combined before the day ends.

fua's headed in that direction.

[Cephrir]

town: shirou
town lean: fua, tejate
neutral: ydrasse, amazonian i GUESS but please do more
neutral but i look extra not impressed while talking about them: everyone else
scumlean: guiltylion, nsg

do better

[Cephrir]

actually let's bump fua up to that top tier i think they deserve that

[morph the cat]

morph/amazon are both underwhelming and could both be scum. come at me.

but i have a lot of fish to fry. maybe i should try harder to fry them since morph doesn't seem to be doing that for me.

To quote Cobra Kai, you're a towel.

Maybe you're a town towel, but I have an awful lot of memories of scum-you casting various aspersions on me/my hydrae over the years.

[Shirou]

Ah, also I guess unless they're scum together (which wouldn't be that weird considering their openings), I should probably trust Morph read on Amazon for now. Even if they were wrong on it at the moment, as long as they are alive they will likely correctly sort out Amazon correctly. If they die...well, we can cross that bridge when we get there.

For what it's worth, it's a very high confidence read for us. I'll be very surprised if they leave our "Utterly Town, never elim this" pile. We'd love to have 4 more reads of that strength, or even four more in that plus the second tier combined before the day ends.

fua's headed in that direction.

if you're that confident about it I'm happy there's one less slot to sort, but on hindsight it kinda also means if they are proved to be scum later on, we probably should scum read you for having the complete opposite of a good read on them.

[Cephrir]

morph/amazon are both underwhelming and could both be scum. come at me.

but i have a lot of fish to fry. maybe i should try harder to fry them since morph doesn't seem to be doing that for me.

To quote Cobra Kai, you're a towel.

Maybe you're a town towel, but I have an awful lot of memories of scum-you casting various aspersions on me/my hydrae over the years.

yet you also get leery if i townbin you! my recollection is that i usually townbin you (ffery) as scum. but it's not solely because suspecting you is a waste of time

i've given you time but it's been 30 pages and i'm still decidedly whelmed

[Cephrir]

my recollection is that i usually townbin you (ffery) as scum

but idk i could be wrong about this memories are hard.

[Cephrir]

honestly now that i think about it this is more or less what i'd expect from a morph/amazon scumteam. a cursory dance followed by townlocking each other for inscrutable or too easy reasons, and amazon not doing much to interact with the rest of the game because it's easy for them to look good interacting with morph.

so i reiterate, do better