Mini Theme 2007: Police Academy 1 - Game Over

[Ankamius]

Keep in mind that there's a cop that was randomly assigned any of the five sanities, so technically it's possible for all five of us to be sane/naive.

[OnTheMark]

Bah my formulas are off again.

It's more the point is that you can determine which half is likely to have accurate results and lynch in the other half. Then mass check and trap scum.

Pedit It's possible but the odds are infintesimally small to have 4 randoms die in the first two days, and that paragraph was assuming A50 was sane/naive.

[OnTheMark]

Not for the chart but for the players of sanity listing it dropped Nos...Apparently my excel wants to erase Nos.

[OnTheMark]

Breaking down the options
If A50 is Sane:
OnTheMark ,Ankamius (replaced PenguinPower),Jingle,eddie (Eddie Cane and schadd_) (replaced schadd_), are the remaining alive possible sane cops.
If A50 is Naive:
OnTheMark,Ankamius (replaced PenguinPower),Jingle,eddie (Eddie Cane and schadd_) (replaced schadd_), are the remaining alive possible naive cops.

Notice the overlap? How they are exactly the same?
In this game there is a combined total of 4 sane/naive cop roles combined. There are 4 possibilities.
This means there is 0 forced randoms among these possibilities.

I left Porkens alive LOL Ghost PORKENS! Fixed

[OnTheMark]

Gorkington,Titus,Nosferatu,EspeciallyTheLies,Punreader (replaced CheekyTeeky) insane/paranoid list

[OnTheMark]

More than likely at least 1 random in Gorkington,Titus, Nos, ETL,Punreader

Now if everyone checks the same person they did on D2. We can sus out a majority of the randoms. And then from that form impenetrable town blocks.

I find that is the better way to go and not the parity cop because the instant we figure out who is actually a true cop they are deader than a doornail.

[OnTheMark]

I'm going to bed now but generally sorting people's sanities is more important than the info from the check.

[Punreader]

Mod: I need a 48 hour V/LA.

More like 40, actually, but I can't post tomorrow or half of the day after.
I'll return when able to.

[Jingle]

Assume mass target of Player A, night one. Player A checks player B.
50% chance random hooray.

Repeat step two except Player A targets Player B again.
All players with same result are 75% chance to be not random.
All players with different result are guaranteed random.

This demonstrates a fundamental misunderstanding of probability.

Again, a demonstration with only one player to simplify things, but the math expands.

Scum Result
Scum Result<
Town Result
Scum Result N1 < Scum Result
Town Result<
Player A < Town Result
Scum Result
Scum Result<
Town Result N1 < Town Result
Scum Result
Town Result<
Town Result

Look at that chart. D2 you have 0 information. D3 you have a 50 percent chance (2/4 results) that each individual is revealed as random. D4 you have a 25% (2/8 results) that each individual is random. D5 is a 12.5% chance. This expands to the function (2/(2^n-1)) where n is the day number, resulting in a bell curve that maxes out at a 3.125% chance of a random cop not having been revealed in 3p LYLO.


So... On D4 (LYLO, FYI) the odds are that you haven't revealed all of the random cops IN THE CASE THAT THE 13th COP ISN'T RANDOM. Also, this doesn't take into account any of the deaths (Lynching and Killing are both mandatory in this setup.) You have 0 usable results. You have succeeded in turning the game into mountainous, but with an added layer of WIFOM scum can use to manipulate people, and town loses.

Trust me on this. I've shown where your math is clearly flawed (using a flowchart, no less) and have pages of math about this setup somewhere in my for fun math binders. This setup has 20 possible combinations from before the playerlist is randomized, all with different probability weights. There are then 8 different possible outcomes from the D1 lynch for each of those, again, all with different probability weights. Then, depending on that lynch either 4 or 5 unique options for the nightkill. Bear in mind, we haven't even taken cop actions or random results into account, and you have literally 796 individual gamestates, all with a different associated probability. That's not a made up number either. If you discount the ability of scum to shoot themselves, you have exactly 796 possible gamestates taking into account everything before the cop targets on the first night, and that's before you get into the ugly math.

Months ago, when smith first talked to me about this setup in the Dead Thread of Team Mafia (which is open and available for anyone to peruse for confirmation) I became interested. What I have been spoonfeeding town is OBJECTIVELY the optimal play for town. I decided optimal play was slightly townsided but well within acceptable limits (particularly for an open) and that I didn't particularly care about playing in the game. I only really /inned cause I felt bad that smith's game was having trouble filling despite being so interesting.

So call me scum if you want, but respect the thought and ability that went into my analysis of this setup.

And that is why I've been handwaving the math since D1. Because there's a lot of it, and not all of it is pretty.

And... I've stayed up an hour later than I intended to because I got off on a probability tangent. Good job, Jingle.

[Jingle]

________________________________________Scum Result
_____________________________ Scum Result<
_________________________________________Town Result
_______Scum Result N1 <___________________Scum Result
_____________________________Town Result<
Player A <________________________________Town Result
________________________________________Scum Result
____________________________Scum Result<
__________Town Result N1 <_________________ Town Result
_________________________________________ Scum Result
____________________________Town Result<
__________________________________________Town Result

Stupid forum ate my formatting.

[Ankamius]

It just randomly hit me how Jingle reasoned me being obvtown.

Okay, we're on the same page now, with me feeling a bit less not dumb.

[OnTheMark]

You’re missing a fundamental flaw.

Yes I agree with the 2 power chart you said.

However you’re not understanding that we are going for perfect information.

We’d go for enough to sort.

The law of repeated trials (I forget the exact name) comes into play.

Yes it is possible that a random cop may not reveal itself until lylo.

However a majority of the random cops will end up revealing themselves and that is what we need.

Once we know a majority we have an impenetrable town block in or outside the random cops. Which breaks the setup.

[Ankamius]

UNVOTE: jjh927
VOTE: eddie

Slight change here, I think this is still better today

[OnTheMark]

We aren’t looking for the exact sanities at first.

We are merely looking for random or NOT random.

If the claims aren’t within the realm of the expected setup of random /not random claims we have a statistical requirement of having scum in the pool that is too big, even IF scum lie.

For example if 8 people’s claims change between d1-d2 we know a max of 5 random cops. Then we know that the others are confirmed town and three people lied.

Conversely if only three peoples change we know that either a random cop hasn’t spawned or scum are lying. Run it one more time but only with the people not yet proven random. At least one will end up changing more than likely.

Therefore you have your four random cops in that scenario a majority of which certainly are town.

Scum also can’t lie at any point until the block is determined.

Once said block is determined then parity test.

A confirmed town block is always better than a check on one player.

[OnTheMark]

Hell I can build a chart with all the possibilities on Sunday

But going for a town block is always better.

The only reason we are doing your plan is we have already gone down it and can’t reboot for mine.

It is inferior.

[eddie]

Police Academy Mafia Sane? Insane? Paranoid? Naive? Random? N1 Target N1 Result N2 Target N2 Flip
OTM M X X M M SGBA Town Titus Town
WotC X M M X M Jingle Scum - -
Ank M X X M M SGBA Town Titus Town
Porkens M M M M M - - - -
Jingle M X X M M SGBA Town Titus Town
JJ X M M X M SGBA Scum Ank Scum
Titus X M M X M SGBA Scum ETL Scum
Nos X M M X M SGBA Scum Pun Scum
Ginngie M M M M M - - - -
Almost50 M M M M M SGBA Town - -
ESL M M M M M SGBA Scum Titus Scum
Eddie M M M M M SGBA Town Titus Town
Pun X M M X M SGBA Scum Titus Scum

Sorry, missed the title column the first time.

so wait

literally everyone got the same result twice?

doesn't that essentially confirm Titus as town?

[eddie]

Ankamius- Obvtown - TPool

Where was this explained Ank?

[eddie]

Ankamius (replaced PenguinPower)
Jingle
Gorkington
Nosferatu (replaced KidAmn)
Punreader (replaced CheekyTeeky)

{Eddie, Titus, OTM, ETL}
Literally 1 more town and its game

Scum pool of Nos, Ank, Gork, Pun, Jingle

VOTE: Pun

Flip this and then dig into the third it is

[Ankamius]

Because it's nonsensical for me to drive home a wagon on scum-A50 like I did unless Titus or Nosferatu were my other partner, Titus being basically impossible and Nosferatu being another really weird choice of partner for me otherwise.

Basically, you have to be thinking I'm pulling a really weird gambit or just not playing to my win condition in order for me to be scum, which... well, is what I've been arguing today anyways.

[eddie]

If Ank could run down why Gork is scum

and Jingle could run down why Nos isscum

that would be swell

[Ankamius]

I can probably go look in my notes for why I was scumreading Gorkington but odds are it'll come down to "his posting looks gross"

[eddie]

Because it's nonsensical for me to drive home a wagon on scum-A50 like I did unless Titus or Nosferatu were my other partner, Titus being basically impossible and Nosferatu being another really weird choice of partner for me otherwise.

Basically, you have to be thinking I'm pulling a really weird gambit or just not playing to my win condition in order for me to be scum, which... well, is what I've been arguing today anyways.

I don't think you're scum. I haven't voted you once this game.

I think you're the closest to town in the scum pool. ETL is Jingle cleared, Math is Jingle cleared and A50 spewed town, Titus is cop cleared. This is the town core. Scum goofed by killing SGBA.

However,

you did unvote A50. I know you can say that means nothing, and its not a huge deal, but it is a thing that's relevantish. You also spent a lot of time pushing myself and got shot down, and d2 is a pretty standard bus day. I town lean you, but last game your paranoia with my slot never went to you actually trying to lynch me and your tunnelling on Gork and myself when I didn't really scumread Gork skeeves me out.

So lynch Pun, she can flip red, and we can go from there.

[Ankamius]

Gorkington is making a much bigger deal out of this hydra than it deserves, and he's doing so in such a way that appears to be an attempt to obtain a tactical advantage rather than legitimate annoyance. Cheeky got pissed at us and asked for us to be replaced out then replaced out, that was legitimate. Gorkington's annoyance seems more fake.

-Desperado

I saw this while going through them and I just want to point out how beautiful it is.

[eddie]

Ank, cheeky's in your sig. How well do you know him?

[Ankamius]

eddie, I unvoted A50 because the wagon was very close to going through and Jingle had just restarted an engagement with me, then OTM and SGBA lolhammered the wagon before that engagement finished.

My vote being off the wagon is irrelevant.