TM 2023 | Open: PYP S_TM | Endgame

[Lady Lambdadelta]

In a 3 vs. 10, the probability of an arbitrary group of three players containing at least one scum is 58% (I suspect imaginality had the right calculation and just forgot to subtract from 1).

I'd be interested in hearing from everyone on why you picked the number you picked, if anyone hasn't already answered that. For myself, I briefly glanced at a couple of the previous PYP S_S games to get a feel for it but didn't rely on it all that much (since the rule here is different, there's less incentive to stick to lower numbers; in fact, I suspected the median would be closer to matching the number of players). I did consider submitting some absurdly high number that isn't special to mathematics (like, on the order of TREE(3) or some insane function like that, but not specifically a number people might know) to guarantee no clashing, and hey, that would've turned out exactly the same.

i agree with that as the base calculation, live evidence from past games suggests the number is higher in triplicate number choices, as would a cursory glance at scum selection choices and the kind of logic that is put in by scum to their choices.

Not sure I really agree that median over lowest number changes the outcomes of this in any way besides where the optimal target numbers end up. Some people will do your thinking and aim to be solo feeling people will pair, some people will go low thinking median will drive people away, in a similar strategy, it's... not that different to "some people will pick 9, thinking it will beat anyone who goes omega high but no one will flock to that higher single digit number".

it's a fractional edge over picking 3 names at random from a strictly maths standpoint but that edge is increased IMO by the psychology of how the game is played and further redoubled in usefulness by not revealing town power structure via claims overmuch, especially when Scum chose Multitasking over informed, so they are decently in the dark, some info assuredly but a good chance they're missing a few different high power info roles they have to play around as a result.

[Lady Lambdadelta]

also I managed another 4 hours of sleep, which has helped me slightly but i can already feel the edges of my mind tearing at themselves so i might take a break for a day or two and come back to this when i'm not actually losing my mind?

[Lady Lambdadelta]

reads wise Ceph feels funky to me, I'm upgrading Rad to a bit more town, and I remain very confident Ythan is town.

I have some other reads but I'm a little worried about them because I can't tell what is a good read and what is brainburn.

[Lady Lambdadelta]

my team reads right now include

a complete Ythan agreement, a dissonance on Bella (some of them think leaning on Klick is scummy, some of them think it's in character for Bella) a lot of null reads on Rad that I think I'm slightly higher town on then they are and an observation that Maru's slow start is typical for them and I should be cautious to scumread them for just a bad string of opening posts.

[Bellaphant]

The other issue is, if people are impressionable, like me, the only take away they are gonna have is that the 'reasonable' responses (me, imag, alissy, gimli) are town, and those aren't even particularly good takes!

nah, dont think thats town indicative

pretty much all i got from this whole thing was a town lean on ythan

This post isn't town, or the reasonable people aren't town?

[Lady Lambdadelta]

okay, that's about all i think i can manage for the moment without diving off the deep end again, apologies for the mess my brain is in, life isn't easy right now, i spent like an hour this morning staring at food before remembering i was meant to do something with it

i'll probably check in periodically without posting to keep reading and stay current with the thread so if people end up with specific questions i'll probably answer them? i'm not good at not posting, so this is the compromise to keep myself out a bit.

[Bellaphant]

Klick basically agrees with you, is still telling me that lld is scum (dv says he sees it, rr says they just finished a game where lld did similar-ish but was town, so nully), klick says datisi is scum . He's really confident his tr-s are town, although I'm less sure on people like rad.

[Datisi]

bella slot might be town for that lmao

[Cephrir]

The other issue is, if people are impressionable, like me, the only take away they are gonna have is that the 'reasonable' responses (me, imag, alissy, gimli) are town, and those aren't even particularly good takes!

nah, dont think thats town indicative

pretty much all i got from this whole thing was a town lean on ythan

This post isn't town, or the reasonable people aren't town?

The latter

[Gimli]

I can feel klick's townyness through bella its so glorious

[Cephrir]

I learned my lesson about assuming LLD emotions = town so I will not be doing that this game

[Gimli]

Klick basically agrees with you, is still telling me that lld is scum (dv says he sees it, rr says they just finished a game where lld did similar-ish but was town, so nully), klick says datisi is scum . He's really confident his tr-s are town, although I'm less sure on people like rad.

bella/klick can you elaborate on datisi scumread? I had the opposite impression off his posts, I think they're quite nuanced for early game reads even if I disagreed with parts of it

[Gimli]

my team reads right now include

a complete Ythan agreement, a dissonance on Bella (some of them think leaning on Klick is scummy, some of them think it's in character for Bella) a lot of null reads on Rad that I think I'm slightly higher town on then they are and an observation that Maru's slow start is typical for them and I should be cautious to scumread them for just a bad string of opening posts.

klick is towntelling I think. when he hydra'd with alisae in demon slayer he disappeared and let alisae wolf alone (pending source), while I think caring about this game enough to start throwing reads and they're not comfortable reads they're spicy, I think that makes him someone who is particularly interested in this game because he randed town and wants to solve

[Gimli]

I learned my lesson about assuming LLD emotions = town so I will not be doing that this game

because of election game?

[Bellaphant]

I'm much happier playing scum than klick is, yes.

[Bellaphant]

I can feel klick's townyness through bella its so glorious

My purpose as a wife is now fulfilled.

@ceph, I know, I do say that to lld.

[Bellaphant]

Re: datisi, mostly meta, cf white flag

Clarifying again that we are both more confident finding town than scum

[implosion]

The letters "G" and "5!" don't actually spell anything on their own. However, if we interpret "G" as the initial letter of a word or a name, and "5!" as the mathematical expression for the factorial of 5, then we can use them to spell out various words and phrases.

For example:

1. G5! could stand for "Google factorial of 5," which equals 120.
   
2. G5! could also stand for "Gina factorial of 5," if Gina is someone's name.
   
3. Alternatively, you could interpret the "!" as an exclamation mark, in which case G5! could stand for "Great five!" or "Good job on five!".

Ultimately, the interpretation of the letters and numbers depends on the context and the intent of the person using them.

Vote Count 1.3

Marashu (4): Alisae, Lady Lambdadelta, Gimli, Staeg
Rad (2): Datisi, Marashu
mith (1): imaginality
Lady Lambdadelta (1): Ythan

Not Voting (5): Bellaphant, Cephrir, Menalque, mith, Rad

With 13 alive, it takes 7 votes to eliminate.

Deadline is April 27 at 10:00 PM PST, in (expired on 2023-04-28 01:00:00).

[Lady Lambdadelta]

I learned my lesson about assuming LLD emotions = town so I will not be doing that this game

this is a weird statement, i'm pretty sure you learned this lesson many moons ago. what new version of this lesson prompted this?

[mith]

I'll just respond to this directly rather than making a massive wall picking apart previous posts.

i agree with that as the base calculation, live evidence from past games suggests the number is higher in triplicate number choices, as would a cursory glance at scum selection choices and the kind of logic that is put in by scum to their choices.

Apologies if I missed this, but have you actually provided statistics on this evidence? I saw you reference a couple of specific games, which is not compelling (could be cherry-picking, deliberately or not).

it's a fractional edge over picking 3 names at random from a strictly maths standpoint but that edge is increased IMO by the psychology of how the game is played and further redoubled in usefulness by not revealing town power structure via claims overmuch, especially when Scum chose Multitasking over informed, so they are decently in the dark, some info assuredly but a good chance they're missing a few different high power info roles they have to play around as a result.

1. I agree with you on the point about not revealing town powers this early. This is a good reason to not go after the singletons day 1.

2. Regarding the maths, there could be a small edge over picking 3 names at random, but there is a

larger

edge in picking scum from the singletons*.

I couldn't help myself and put together a little simulation; it's of course difficult to simulate a problem like this because of the psychology of closest unique to median (or lowest, in the other games), so I've simplified the problem as follows: 3 Mafia, 10 Town, town is picking randomly from a set of 10 numbers (10 is completely arbitrary here), Mafia is picking 0, 1, and 2:

Simulating 60000 games gave the following results:

Code: Select all

#     Mafia    Overall  Percentage       Expected
1     62960    226144	0.278406679	0.230769231
2     69553    150756	0.461361405	0.423076923
3     34894     59043	0.590993005	0.58041958
4     10285     14968	0.687132549	0.706293706
5      1992      2606	0.76438987	0.804195804
6       283       341	0.829912023	0.877622378

In this simulation, the probability of Mafia appearing in a group of 3 is up to 59% vs. 58% for an arbitrary set of 3 players. There's nothing particularly special about the groups of 3 though; overall, Mafia are more likely to avoid grouping (compared to an arbitrary selection of 3) because they are picking unique numbers compared to each other.

Additionally, we have the specific knowledge of how the numbers split. I would expect the likelihood of Mafia in specifically the one triplet

with the knowledge that we have the partition that we do

is actually slightly lower than 58%. (This follows directly from knowing the edge for singletons and pairs in the full simulation is much more significant.) Might write some code for this later just as an interesting math question; I just don't consider it all that relevant to the game.

* All of this depends on the likelihood of a scum gambit being negligible, of course. (Though I would guess that if we were 100% sure of a scum gambit with a singleton and a pair, it would be more likely mathematically for the pair to be on their own rather than as part of a triple?)

3. The "IMO" here seems like a far cry from your earlier rhetoric on this. (That said, I have really only skimmed the earlier argument at this point.)

------

Anyway, that's probably all the maths I will be doing on this (at least for the game, it's an interesting problem!). I'm not likely to base anything on how the numbers happened to fall beyond things like "we know Ythan has a role, we know Staeg likely has a role, etc., forcing a claim out of these slots day 1 would be counterproductive".

Initial reads coming later, I should probably get some work done. But in the meantime,
VOTE: Lady Lambdadelta

[Datisi]

Re: datisi, mostly meta, cf white flag

Clarifying again that we are both more confident finding town than scum

can klick elaborate on what he means by meta, just white flag?

[Lady Lambdadelta]

I'll just respond to this directly rather than making a massive wall picking apart previous posts.

i agree with that as the base calculation, live evidence from past games suggests the number is higher in triplicate number choices, as would a cursory glance at scum selection choices and the kind of logic that is put in by scum to their choices.

Apologies if I missed this, but have you actually provided statistics on this evidence? I saw you reference a couple of specific games, which is not compelling (could be cherry-picking, deliberately or not).

it's a fractional edge over picking 3 names at random from a strictly maths standpoint but that edge is increased IMO by the psychology of how the game is played and further redoubled in usefulness by not revealing town power structure via claims overmuch, especially when Scum chose Multitasking over informed, so they are decently in the dark, some info assuredly but a good chance they're missing a few different high power info roles they have to play around as a result.

1. I agree with you on the point about not revealing town powers this early. This is a good reason to not go after the singletons day 1.

2. Regarding the maths, there could be a small edge over picking 3 names at random, but there is a

larger

edge in picking scum from the singletons*.

I couldn't help myself and put together a little simulation; it's of course difficult to simulate a problem like this because of the psychology of closest unique to median (or lowest, in the other games), so I've simplified the problem as follows: 3 Mafia, 10 Town, town is picking randomly from a set of 10 numbers (10 is completely arbitrary here), Mafia is picking 0, 1, and 2:

Simulating 60000 games gave the following results:

Code: Select all

#     Mafia    Overall  Percentage       Expected
1     62960    226144	0.278406679	0.230769231
2     69553    150756	0.461361405	0.423076923
3     34894     59043	0.590993005	0.58041958
4     10285     14968	0.687132549	0.706293706
5      1992      2606	0.76438987	0.804195804
6       283       341	0.829912023	0.877622378

In this simulation, the probability of Mafia appearing in a group of 3 is up to 59% vs. 58% for an arbitrary set of 3 players. There's nothing particularly special about the groups of 3 though; overall, Mafia are more likely to avoid grouping (compared to an arbitrary selection of 3) because they are picking unique numbers compared to each other.

Additionally, we have the specific knowledge of how the numbers split. I would expect the likelihood of Mafia in specifically the one triplet

with the knowledge that we have the partition that we do

is actually slightly lower than 58%. (This follows directly from knowing the edge for singletons and pairs in the full simulation is much more significant.) Might write some code for this later just as an interesting math question; I just don't consider it all that relevant to the game.

* All of this depends on the likelihood of a scum gambit being negligible, of course. (Though I would guess that if we were 100% sure of a scum gambit with a singleton and a pair, it would be more likely mathematically for the pair to be on their own rather than as part of a triple?)

3. The "IMO" here seems like a far cry from your earlier rhetoric on this. (That said, I have really only skimmed the earlier argument at this point.)

------

Anyway, that's probably all the maths I will be doing on this (at least for the game, it's an interesting problem!). I'm not likely to base anything on how the numbers happened to fall beyond things like "we know Ythan has a role, we know Staeg likely has a role, etc., forcing a claim out of these slots day 1 would be counterproductive".

Initial reads coming later, I should probably get some work done. But in the meantime,
VOTE: Lady Lambdadelta

I didn't cherry pick, I actually went to the MS wiki of X/Y PYP and went through the listed games one by one and sought out whether the pattern fit or did not fit in specific games, leaving games where there were no large groupings out, and mentioning examples that didn't fit the pattern

the IMO here is me trying to scale back the insanity going on in my brain right now. I'm pretty confident I'm right in this but if people don't see it then what use is screaming confidently until I lose my mind?

Scum Gambit has happened enough times historically in my review to not be negilgable.

Look, I encourage you to do the review yourself if you think I'm cherry picking or using the argument to obfuscate.

I feel like assertions that the chance there is at least one scum in the triplicate being LESS than the odds of picking 3 scum at random from 13 are provably wrong by the meta review I've done.

Like I feel as if I have people quoting mathematial theory at me that doesn't hold up in practice and I've gone through and done the practical review of all the games I have access to in history of site that I can readily get my hands on.

[Lady Lambdadelta]

like part of the maths people are running is saying "Well how likely is it for scum to make a triplicate" but is ignoring that a triplicate has already been made.

So the percentage isn't "how likely is it for scum to make a triplicate" it's "if a triplicate is made, how likely is it that scum are a part of it?"

That feels like the thing people are overlooking. A large portion of the odds where scum don't end up in a triplicate are already removed. It's did 3 townies select the same number, or did 2 townies select the same number and a spread scum slot into them because scum didn't double up, or did 2 scum slot themselves together and colide with a townie to make a triplicate.

The maths are relevant and suggest a slight edge towards eliminating in the triplicate today but if we're not doing the maths, just going as simple as possible and going "hitting from the bottom group where roles aren't likely to exist and role choices aren't likely to inform scum in anyway is optimal" is already a good reason to be looking to eliminate there if you can find scum there.

If someone ends up looking at the 6s and going "I town read all these slots, I won't kill them" I'm not going to expect that player to then vote there unless it's deadline compromise. But having to outright state "I townread all these slots" as opposed to "I just don't want to do this, so I won't" as a way to ignore those slots is a measurable difference in information for town to use.

[Lady Lambdadelta]

Anyway that's all the stuff that I've been quoted in/referenced by, so I'm out again

[Datisi]

my team reads right now include

a complete Ythan agreement, a dissonance on Bella (some of them think leaning on Klick is scummy, some of them think it's in character for Bella) a lot of null reads on Rad that I think I'm slightly higher town on then they are and an observation that Maru's slow start is typical for them and I should be cautious to scumread them for just a bad string of opening posts.

klick is towntelling I think. when he hydra'd with alisae in demon slayer he disappeared and let alisae wolf alone (pending source), while I think caring about this game enough to start throwing reads and they're not comfortable reads they're spicy, I think that makes him someone who is particularly interested in this game because he randed town and wants to solve

this feels like a meh reason to townread klick. posting in a hydra and having someone else post for you feels very different from each other, but also like, it's team mafia