Live Action Mafia

A game of sneakiness and paranoia
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PostPosted: Wed Oct 11, 2017 10:47 pm 
In case you missed the proxy thread, he was not-returned-innocent by 3 splitter pair investigations in a row.

PostPosted: Wed Oct 11, 2017 11:00 pm 
Besides like easily two of those being mafia faked

PostPosted: Wed Oct 11, 2017 11:04 pm 
Python just tased me. (Reasonable thing to do.)

I don't know whether I'm framed, unlucky, or being slandered by jamb. There must be at least 6 other splitter investigations out there if jamb got 3, which could narrow it down.

PostPosted: Wed Oct 11, 2017 11:07 pm 
Pesto has been tased. Adam did it in front of me. Adam now has a used taser with Pesto's name on the handle.

For the record: I was privately communicating with Jackie about her splitter investigations. After the 3rd result, I took Adam aside and brought up the idea of tasing Pesto. I also brought up the idea to Jackie in our chat, and she said, "absolutely." So we sat in Cave, waited for it to charge, and then went up and tased Pesto in Left Front.

PostPosted: Wed Oct 11, 2017 11:20 pm 
I believe that we now have a shovel handle and a taser handle to distribute among people.

If we tase/shovel different people, we get items that are distinguishable, and can thus distinguish yet more people.

PostPosted: Wed Oct 11, 2017 11:21 pm 
Chiller wrote:
Besides like easily two of those being mafia faked

Huh? I mean, I could be mafia, but I vouch that I personally performed all 3 investigations, so I'm at least willing to put my neck on the line for this and not just "easily faking" something.

Also, Mendel where you at? I wanna give you this shovel handle.

PostPosted: Thu Oct 12, 2017 1:00 am 
Now, probability isn't my strong suit. But if I understand correctly, Bayesian stuff gives.

Probability of Jackie isn't mafia = probability of getting 3 negatives with a town jackie* probability jackie isn't mafia/probability of getting this result.

I estimate Jackie has .8 chance of being town, since I got sketch vibes. And I'm assuming that the probability of getting this result is .5 jackie is mafia + .0625 if jackie is town.

This gives Jackie a (.125*.8)/.5625=1/6 chance of being town. So yeah.

If I'm a bit wrong then I think the correct math might be plugging in .3(=.2+.8/8) for the denominator, which still only gives 1/3, which are pretty good lynching odds.

If I'm very wrong (I'm starting to think this is the case) then the denominator should be like .165, which still gives .6 at best, which is still bad.

Ergo Jackie is bad. QED><>:;'

PostPosted: Thu Oct 12, 2017 1:03 am 
I feel like the probability that Pesto is bad also ought to be involved somehow? Because if he is, the probability of getting these results with a town Jackie is significantly different (ie close to 1).

PostPosted: Thu Oct 12, 2017 2:09 am 
I realized my numbers need some editing, as I wasn't considering the fact that there are multiple baddies. I'm assuming 6/24 players are bad (we have like 24, right?)

I'm assuming SK Jackie is in contact with mafia.

The best numbers for Jackie are prior probability of .75 being town, .125 chance of result while being town, and .25+.75/8 overall chance of result.

This yields .27 chance of Jackie being town. I'm pretty confident that's a hard upper bound. I wouldn't be that generous, and think the probability of town Jackie is <.2

If my result is true, which I claim it is, Jackie is baddd.

#lynchJackie #freeTown #noMoreMurders #mafiaJackieIsMafia #numbersDontLie #JackieLies

I should sleep. Plz lynch Jackie.

PostPosted: Thu Oct 12, 2017 3:13 am 
Some comments about the calculation of Jackie badness:
- The probability of Jackie getting a result "like this" in terms of investigations if Jackie is town is 1/4, not 1/8. Specifically, there would have been a 1/8 chance of Jackie investigating Jakob not-innocent 3 times, in addition to the 1/8 chance of investigating Pesto not-innocent 3 times. Basically, Jackie gets *some* person as not innocent in the first investigation, and after that she has a 1/4 chance of getting them not-innocent in subsequent investigations. Though Jackie told me she had "a very mild gut feeling pesto is scum," which she wouldn't have had with Jakob, so I would say the probability of getting a full result "like this" as town is very slightly below 1/4, maybe like 1/5.

- I think the probability that Jackie would do this as mafia/SK is less than .5. Declaring a "probabilistic beef" with someone, especially so early in the game, seems risky for mafia. Like, there are ~6 other splitter investigations floating around (though I would be unsurprised if Pravi had 1 or 2), plus any planeswalkers / investigators who didn't investigate yesterday. Would Jackie really expect to not be checked for the investigation? If Pesto got checked as innocent, then (as has happened now) Jackie would end up with people thinking that she is quite sketchy. Probably the probability of doing this as mafia is somewhat greater than the probability of doing this as town. So given a 1/5 chance of doing this as town, I would say maybe a 2/5 chance of doing this as mafia. Notably, your second calculation says there is a .25 + .75/8 overall chance of the result, which seems to suggest that you're assigning a 100% chance that Jackie would do this if she were mafia.

So I would say that given a 1/5 chance of Jackie doing this as town, a 3/4 prior of being town, a 2/5 chance of doing this as mafia, and a 1/4 prior of Jackie being mafia, that gives a (1/5)*(3/4)+(2/5)*(1/4) = 1/4 overall chance of the result. So the probability of Jackie being town (given that chiller is telling the truth) is (1/5)*(3/4) / (1/4) = .6. Which actually matches your "I'm very wrong" case, though I'm pretty sure I arrived at the result in a different way. Of course, from an objective perspective, we can't take "chiller is telling the truth" as a given, so Jackie has an even greater likelihood of being a townie than .6 (I'm not going to try to calculate the probability of "chiller is telling the truth").

Conclusion: I think Jackie is a townie with probability > .6. Chiller should think that Jackie is a townie with probability .6 - [deduction for getting sketch vibes from Jackie]. It probably makes sense for Chiller to vote for Jackie, but I'm not convinced everyone else should, given that sketchier people will likely pop up tomorrow.

PostPosted: Thu Oct 12, 2017 9:34 am 
Things I think I'm legitimately sketchy for:
- as a high kill target and a person who got 3 SPLITTER INVESTIGATIONS, I didn't die. Why? Maybe I pled guilty, which fits the fewer kills? (I know I didn't - sorry mafia if you tried to kill me yesterday, I went to my classes but wasn't otherwise particularly killable - but I'm objectively sketchy for this.)
- getting a result that probabeefed achester, contradicting achester, and perhaps acting too strongly on it (see below).
- God sent me a picture of himself making popcorn, which made me super sketched out by myself.

I think my probabeef last night was too strong, because I realized that no matter what, one of the four people I investigated would've shown up as not-innocent and looked bad for it, so my result should only be as good as my confidence that one of the four people I picked did it. My priors on achester having made that kill were quite high due to a combination of (1) he's one of not-that-many-people I think would be confident making a day 1 kill; (2) the timing of his messages to me about where to find stuff at Star seemed to imply he didn't do it in a slightly too-convenient way that smells like something he'd do if he made the kill; (3) he was on his phone for a bit just before 6 while I was cooking dinner but then asked me at 6:45 whether anything had happened in mafia, which I think was playing dumb. So anyway, I had a gut feeling he did it (as I told Katie), but assigning priors of more than 1:4 or so would be silly. Given this feeling, I proceeded to investigate him, and picked the 3 other people I thought were next-most-likely. I think I updated more than I should've on these investigations; even if I assigned 1:4 priors, an 8:1 update against him should only get me 2:1 odds he did it, which is less confidence than I think I was feeling internally, due to confirmation bias on my theory.

Thoughts coming about updates based on Mendel. I think this is would be a ballsy enough mafia move that I give it at least 2:1 update against achester having made the kill, which brings me to at most 1:1 odds he did it.

Please do check my math on all these things. In particular I'm feeling a bit confused when I think Monty-Hall style about how the probability of the person who wasn't cleared in that set of 4 having done it is equal to the sum of the prior probabilities on those 4 people, and the other 3 were less sketchy imo so it should be only multiplying the probability Pesto did it by 2 or 3? This seems to contradict my earlier computation.

PostPosted: Thu Oct 12, 2017 9:34 am 
**contradicting Mendel

PostPosted: Thu Oct 12, 2017 10:11 am 
So, about Mendel: A lot of things he has said seem really weird to me, and yet I don't find them *evil* weird. Just weird. Like, I don't feel like mafia Mendel would be this blatant about poorly logicking to throw sketch on me, at least not more so than town him might make the same arguments. I'm sorta reminded of the time I thought dylan was evil because he was making such bad arguments and seemed to be beefing me for not-that-good reasons, and then we got into a townie beef :P

So I'm just gonna evaluate on the probabilities that he's making stuff up for achester versus achester just got unlucky in my investigations. The universe of possibilities is roughly thus.
(1) I'm evil. Your priors are probably about 1:4, mine are 0 or maybe Pr{I misread my role PM really badly}.
(2) achester made the kill, and Mendel's lying for him. My priors were about 1:4 (see previous), and updated to about 1:1 but am up for probability corrections.
(3) achester made the kill, yyao is framed. Priors about 1:4 achester did it, 1:8 he could frame, 1:64 he picked yyao, 1:2 the investigation returned yyao --> 1:2^12 = negligible
(4) yyao made the kill, achester is framed. Priors about 1:32 yyao did it, 1:8 could frame, 1:8 picked achester, 1:2 investigation --> 1:2^12 = negligible
(5) achester is framed, and Mendel's lying for him. This seems dumb unless you consider that SK might jump in to defend someone they perceive to be mafia, which allows them to signal their evilness to mafia. Still about 1:64 on the frame, idk how to compute probability SK mendel would do this.
(6) achester looks not-guilty for the kill (and got unlucky on my investigations), and Mendel's intentionally supporting him, either because they're mafia buddies, or Mendel is SK as described above.
(7) achester looks not-guilty for the kill, and he and I and Mendel are all innocent and just got into a townie probabeef.
(8) achester looks not-guilty for the kill, and he happens to be evil but Mendel and I are townies.

Did I miss any cases? They're not sorted or anything.

Appendix: weird things Mendel has said: the compiled list
(A) Comments that make no sense
"SK's might've both hit baddies" -> on Katie's thread where she'd already acknowledged she was considering SKs individually
"Besides like easily two of those being mafia faked" -> on my thread beefing achester, when I'd declared publicly that I made all 3 investigations; he seemed to be trying to cast doubt on me even before getting the result clearing achester
"Also I somewhat suspect Jackie intended to kill me today/tonight." -> on proxy info; the implication being that I posted publicly on forums asking to find him and give him an item so that I could kill him? That would be a really bad kill plan.

(B) bad logic
poorly done probability in the "I am probabilistically beefing achester" thread, as Katie pointed out
"Jackie is easily SK in contact, which explains only 1 kill today." for no apparent reason other than that I *could* be in contact? it seems more like this was discussion of a possible universe that fit the facts rather than a probable universe
"If my result is true, which I claim it is, Jackie is baddd." -> how did we jump from having a probabilistic beef to an actual one?

PostPosted: Thu Oct 12, 2017 10:41 am 
I thought you were trying to kill me because you were in foo, where I've never seen you before. By this logic I am only alive because I arrived late, and by that point Maya had arrived so the kill didn't work out.

I agree that my thoughts are more all over the place than collected and coherent, I think this has something to do with my not spending enough time on my arguments.

I would still like to push for lynching Jackie, because as I see it Jackie was probability beefing achester, and I thus am probability beefing Jackie. Naively Jackie looks as guilty as achester looked.

For (1) I think you're discounting Pr{Jackie decided not to read role pm and see how things go}

PostPosted: Thu Oct 12, 2017 10:45 am 
Also like it's fairly likely that I am bad and both achester and Jackie are good, and I'm capitalizing on Jackie's beef. Mafia me would try to do this, but my mafia buddies would probably say it's a bad idea.

PostPosted: Thu Oct 12, 2017 10:47 am 
Jackie and I were in foo because Arkadiy had the desk shift and the three of us were planning stuff for our 6.035 project. In particular, we all left pecker lounge at around 3.30 and headed down to desk.

PostPosted: Thu Oct 12, 2017 5:43 pm 
I apparently never actually stated this publicly, but obviously I rescind this beef (though I do think there's a low-but-nonzero probability it's worth remembering if one of {achester, chiller, lukesci} turns out to be evil in the future).

PostPosted: Thu Oct 12, 2017 5:45 pm 
(Also, I realized a thing earlier that's about a 1.2x update against achester being mafia, unrelated to whether he made the past couple days' kills. I don't think he'd want it shared publicly.)

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