Bayesian Mafia - Game Over: Mafia Wins!

For your simulated organized crime needs.

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Adam H
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Bayesian Mafia - Game Over: Mafia Wins!

Postby Adam H » Wed Mar 12, 2014 9:03 pm UTC

Bayesian Mafia


Adam’s Standard RulesTM:
Spoiler:
  1. You cannot post in this thread unless you are alive and included in the player list.
  2. You cannot talk about this game outside of this thread, unless in an appropriately titled spoiler in the discussion thread, or unless it was specifically sanctioned by the mod.
  3. You cannot edit your posts.
  4. You cannot quote private messages from the mod.
  5. You cannot lurk.
  6. You cannot ruin the game for other players.
  7. You cannot say, imply, or pretend that a hammer vote has been cast unless it is obvious from counting the public votes in the thread.
  8. If you break any of these rules, you will lose, be removed from the game, and shame will be heaped on you.
Game Specific Rules:
Spoiler:
Deadline and Voting:
  1. Edit (April 3): Post votes and unvotes in bold and on a new line with whitespace above and below.
  2. You can unvote before changing votes, but you don’t have to. Only your most recent vote will count.
  3. Once a player has received the majority of votes (“hammer”), that player is dead. The day ends immediately and players cannot talk or change votes.
  4. Every player has a single vote and there are no vote-rigging mechanics of any kind.
  5. Votes will reset if there is a modkill or daykill. A deadline extension would be given as needed.
  6. The mod will give the players a deadline for the end of each day. Once the deadline has been reached, players may still post and change votes (unless hammer has been reached). However, once the mod announces the end of day, all votes are finalized and players may not post.
  7. If votals are tied at the deadline, the lynchee will be decided randomly. The exception is if every player is voting for one of the players tied for the most votes – in that case there will be no lynch.
Setup and Roles:
  1. There are 3 mafia and 8 town.
  2. Town wins if mafia is eliminated from the game.
  3. Mafia wins if they eliminate town and have one member survive to the end of the game.
  4. Once victory is assured for either team, the game will end immediately.
  5. There are no players with independent win conditions.
  6. LYLO and MYLO will not be announced.
  7. All players are sane unless told in their role PM that there is a possibility that they are insane. "Sane" means your powers do exactly what your role PM says they do, and "insane" means your powers don't do exactly what your role PM says they do.
  8. Your win condition will not change over the course of the game.
  9. There may be duplicate town roles.
  10. The mafia was given some, most, or all of the town roles in the game. They were NOT told which players received those roles.
  11. At the conclusion of every night, players may receive the results of night actions, which are called "Experiments". The results of the Experiments can originate from your power or another player's power, and are given without context (you will not be told why you received the experiment results). and are generally in the form "There is a X% chance that [Player] is scum". This information is mathematically accurate assuming you have no other data. However, there is a chance that those results have been tampered with or are otherwise inaccurate. See below for details (in the spoiler "Probability Details").
  12. Other than the Experiment results, you will not receive confirmation that any of your night actions are successful.
  13. Dead players will have their faction revealed on the morning after death. However, there is a mechanic that may result in some reveals being of the form "There is an X% chance that [Player] is scum". Roles and powers will not be revealed upon death.
Probability Details:
Spoiler:
As stated above, many players will publicly or privately be given information in the form "There is an X% chance that [Player] is scum". The probability will be determined as follows:

If the player is scum, X=Sqrt(rand())
If the player is town, X=1-Sqrt(rand())
where rand() is a random number between 0 and 1

Any time I ever refer to a probability, I will have calculated it with the above algorithm.

If you initially know nothing about how likely the player is scum, then X% becomes the absolute best estimate for the player's probability of being scum. For example, if I told you 100 times in 100 parallel universes that there is a 33% chance that Adam is scum, one should expect that he is scum in 33 of those universes.

However, if you previously thought that Adam had a 3 in 11 chance of being scum just because there's only 3 scum out of 11 players, then it gets tricky, doesn't it… :twisted:

See this thread for a bit more information. I also briefly explained it in the meta thread if you need a third way of hearing it.

Players:
1. wam - MAFIA
2. Suzaku (replaced Vytron D2) - Killed N5
3. Madge - Killed N4
4. New User - Killed N5
5. Lawrencelot
6. mpolo - Lynched D3 - MAFIA
7. just_me - Lynched D1
8. moody7277 - Lynched D2
9. cemper93 - Lynched D6
10. kalira - Lynched D4 - MAFIA
11. BigNose - Lynched D5

Role PMs will be sent out ASAP. Hold tight! Please PM me if you do not see your role PM.

It's probably a good idea to PM me any questions you have instead of writing them in thread.
Last edited by Adam H on Thu May 08, 2014 2:19 pm UTC, edited 14 times in total.
-Adam

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Adam H
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Re: Bayesian Mafia - Night 0

Postby Adam H » Wed Mar 12, 2014 9:24 pm UTC

XKCD Pharmaceuticals is in crunch time! Its eleven employees are busy working on improving their drugs and collecting research data. Yet underneath the surface, something weird has been going on. Everyone can feel it. It's as if a few of these employees are purposefully obscuring data and misusing statistics! How dare they! But you'll figure it all out after tonight.

It is now Night 0. No night actions should be submitted tonight. Please confirm that you have received your role PM, and we'll start Day 1 in 24-48 hours.
-Adam

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Vytron
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Re: Bayesian Mafia - Night 0

Postby Vytron » Wed Mar 12, 2014 9:27 pm UTC

Confirming (I just got my Role PM). Also:

Adam H wrote:For example, if I told you 100 times in 100 parallel universes that there is a 33% chance that Adam is scum, one should expect that he is scum in 33 of those universes.


Well, this is damning, with 11 players in the game, 33% chance of the mod being scum seems better than average, let's lynch him.

Vote Adam

Because his sig says so :P
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Re: Bayesian Mafia - Night 0

Postby New User » Wed Mar 12, 2014 9:29 pm UTC

Confirm

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moody7277
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Re: Bayesian Mafia - Night 0

Postby moody7277 » Wed Mar 12, 2014 9:46 pm UTC

There is a 91% chance I am confirming.
The story of my life in xkcdmafia:

Tigerlion wrote:Well, I imagine as the game progresses, various people will be getting moody.


BoomFrog wrote:I still have no idea what town moody really looks like.

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Re: Bayesian Mafia - Night 0

Postby Madge » Wed Mar 12, 2014 10:32 pm UTC

Of the infinite number of parallel universes out there, I only confirmed in 27 of them. Fortunately, this universe is one of those 27.
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cemper93
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Re: Bayesian Mafia - Night 0

Postby cemper93 » Thu Mar 13, 2014 1:07 am UTC

I might have gotten a PM.

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kalira
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Re: Bayesian Mafia - Night 0

Postby kalira » Thu Mar 13, 2014 2:45 am UTC

Chances are, 'cause I wear a silly ring (28% of the time)
79 out of 100 moments you come into view,
Chances are 81% likely I got a role PM from a random member of the mods assigned to this game.
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Lawrencelot
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Re: Bayesian Mafia - Night 0

Postby Lawrencelot » Thu Mar 13, 2014 9:02 am UTC

Confirm with probability 1

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mpolo
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Re: Bayesian Mafia - Night 0

Postby mpolo » Thu Mar 13, 2014 9:21 am UTC

There is a 57% chance that I am pretty confused right now, but a 73% chance that I have read something in my inbox to cause that.
Image <-- Evil experiment

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BigNose
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Re: Bayesian Mafia - Night 0

Postby BigNose » Thu Mar 13, 2014 9:47 am UTC

Whatever
Adacore wrote:In all honesty, BigNose has been pinging me slightly with almost every post since the start of the game. But he always does - I was utterly convinced he was anti-town for most of Wizardry2 and he was the High Wizard. I just can't read him.

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Adam H
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Re: Bayesian Mafia - Night 0

Postby Adam H » Thu Mar 13, 2014 6:23 pm UTC

It has come to my attention that some of the role PMs are not exactly clear...

If you don't know whether you are mafia or town, then you are Town.

*cough cough* that is all.
-Adam

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Re: Bayesian Mafia - Night 0

Postby just_me » Thu Mar 13, 2014 11:31 pm UTC

conf

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Re: Bayesian Mafia - Night 0

Postby wam » Fri Mar 14, 2014 9:50 am UTC

There is a 99% chance I thought I had already confirmed.
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Adam H
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Re: Bayesian Mafia - Night 0

Postby Adam H » Mon Mar 17, 2014 3:18 pm UTC

The boss calls you all in for a meeting. "There has been some sloppy work recently. I believe some of you may be purposefully sabotaging us! If any of you see anything suspicious, you are authorized to use whatever force necessary to stop the offending party. OK, now back to work!"

It is now Day 1. 11 players alive, 6 to hammer. Deadline in 7 days.
-Adam

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BigNose
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Re: Bayesian Mafia - D1: Sabotage?

Postby BigNose » Mon Mar 17, 2014 3:38 pm UTC

I'm 99% sure it wasn't me!
Adacore wrote:In all honesty, BigNose has been pinging me slightly with almost every post since the start of the game. But he always does - I was utterly convinced he was anti-town for most of Wizardry2 and he was the High Wizard. I just can't read him.

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Re: Bayesian Mafia - D1: Sabotage?

Postby Vytron » Mon Mar 17, 2014 5:31 pm UTC

Vote BigNose

As I'm 100% sure it wasn't me, I see no reason BigNose wouldn't be sure like me, unless Adam sent him some "there's 1% chance you're scum" message to account for his uncertainty. Maybe scum aren't sure if they're town.

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Lawrencelot
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Re: Bayesian Mafia - D1: Sabotage?

Postby Lawrencelot » Mon Mar 17, 2014 7:10 pm UTC

Vote: New_User

As a new user, he must either be scum or town, so 50/50% chance. Since there are only 3 scum out of 11, and 50% is more than 3/11*100%, this should be the best vote.

Only two more to go, we got dis

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Re: Bayesian Mafia - D1: Sabotage?

Postby moody7277 » Mon Mar 17, 2014 7:22 pm UTC

Lawrencelot wrote:he must either be scum or town, so 50/50% chance.


I don't think probability works that way. :P
The story of my life in xkcdmafia:

Tigerlion wrote:Well, I imagine as the game progresses, various people will be getting moody.


BoomFrog wrote:I still have no idea what town moody really looks like.

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Re: Bayesian Mafia - D1: Sabotage?

Postby mpolo » Mon Mar 17, 2014 7:34 pm UTC

The results here are going to be harder than usual to interpret.

If a player is scum and is investigated by someone with an X%, the result will be less than 50% about 25% of the time and greater 75% of the time. High numbers are very indicative of scumminess, though not guaranteed, and low numbers are somewhat weaker in clearing someone. I have a feeling that I'm going to be really confused for this whole game…
Image <-- Evil experiment

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Re: Bayesian Mafia - D1: Sabotage?

Postby wam » Mon Mar 17, 2014 7:59 pm UTC

I'm here, trying to get my head round this game more tomorrow.
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New User
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Re: Bayesian Mafia - D1: Sabotage?

Postby New User » Mon Mar 17, 2014 8:31 pm UTC

Hello everyone. I don't think I fully get the mathematical probability formula concept, but I feel that I'll have a better grasp once we start getting some results from some experiments.

The rules imply that mafia has some way to interfere with experiment results. I expect redirection, godfather, or something like inverse the probability (change a 1 to a -1 for example).

The game's signups and confirmation took so long that I forgot some of the rules and such. Wasn't it said that everyone has some sort of power role (no vanilla roles), and that power roles are not revealed when we die? And I think we should go with the worst case scenario, assuming the mafia knows all of the town power roles (but it was explicitly said that they don't know who has those roles).

Also the forum isn't performing well so I don't know if I'll be able to send this post.

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Madge
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Re: Bayesian Mafia - D1: Sabotage?

Postby Madge » Tue Mar 18, 2014 2:25 am UTC

Yeah, the slow start has thrown me through a loop, just have to go re-read my role PM to make sure I'm operating from a point of maximal information.

Now, at the moment the prior probability of any one of us being scum is 27% - so obviously any results that seem to indicate someone is scum with a probability higher than that are useful. (This prior probability will change every time someone is lynched or NK'd - assuming a mislynch and a night kill tonight [most likely situation if experience is anything to go by], we have a 3/9 or 33% chance of each player being scum tomorrow)

But I'm wondering how we go about claiming - obviously if one has a power that gives a >90% chance that someone's scum, then it should be claimed - but what's the cutoff for probability?

I know little about probability so my "gut" feeling is perhaps that we should assume a result to be "reliable" if the probability it gives is twice chance (so, D2, a cop should claim if they have over 66% probablity of scum target). But I don't know how reliable my intuition is on this - should we be looking for more robust results than that?
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Re: Bayesian Mafia - D1: Sabotage?

Postby Lawrencelot » Tue Mar 18, 2014 9:21 am UTC

but what's the cutoff for probability?

See http://en.wikipedia.org/wiki/Statistical_significance. We could choose a somewhat high alpha value like 10% or 20%. Maybe someone can do some calculations and turn it into an easily comprehensible rule? Like, if a cop gets a result that a player is scum with X% probability, claim it. I study math but I suck at probability and statistics, so such a rule would also benefit me :).

I hope the people who like this (doing calculations) can spend time on this, and help those who just want to play the game so they don't have to spend hours figuring this out.

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Re: Bayesian Mafia - D1: Sabotage?

Postby wam » Tue Mar 18, 2014 11:45 am UTC

Well I'm also rubbish at probabilities.

Also just looked at it and thought oh don't worry adam will explain it all hes good at this stuff....

I agree that once we get a certain probability on someone e.g 90% there should be a claim.
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Re: Bayesian Mafia - D1: Sabotage?

Postby moody7277 » Tue Mar 18, 2014 1:31 pm UTC

My gut feeling is that anything over 75% surety is something we could act on. There's only a 20% chance any investigations will yield a 90% surety, so we may not be able to be that confident.
The story of my life in xkcdmafia:

Tigerlion wrote:Well, I imagine as the game progresses, various people will be getting moody.


BoomFrog wrote:I still have no idea what town moody really looks like.

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Re: Bayesian Mafia - D1: Sabotage?

Postby cemper93 » Tue Mar 18, 2014 2:20 pm UTC

Maybe the question we should ask is: if the cutoff surety we set is X, if we lynch every person with a scum result of >X probability, how high is the chance that we win the game? Or rather: if that chance is Y, how do we have to choose X so that Y is larger than 75%/90%/95%/whatever we can agree on?

The problem is that figuring out the win chance is quite the problem space, and though I think this problem can be solved by a dynamic programming approach (starting with the 2/1 situation and working up from there), I'm a lazy bum and won't do it.

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kalira
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Re: Bayesian Mafia - D1: Sabotage?

Postby kalira » Tue Mar 18, 2014 3:01 pm UTC

Hi, I really am here. Just needed to give my brain a short break after Scooby.

Oh good grief, we've gone from statistics to programming now -- why cemper? WHY? I don't know if my brain will be able to handle this. Basically I've kind of been figuring this game would just end up (for me at least) being something like Unmafia in terms of what we're sure of/not sure of in terms of alignments (i.e. I am assuming nothing). I'm wary of statistics and of the numbers we're going to be given, since the probabilities are all based on random numbers. There is every chance that scum might be randomly helped by numbers, or that we might be randomly screwed over by them.

Vytron, I can't tell if your vote against BigNose is a joke or not... it sure seems more serious than your other vote on the mod, and Lawrencelot's on NU. There's been a lot of apparent joke voting so far; that worries me a bit. In case it was intended as a real vote, though:

Vytron wrote:I see no reason BigNose wouldn't be sure like me, unless Adam sent him some "there's 1% chance you're scum" message to account for his uncertainty. Maybe scum aren't sure if they're town.
(emphasis mine)

Adam H wrote:If you don't know whether you are mafia or town, then you are Town.
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Vytron
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Re: Bayesian Mafia - D1: Sabotage?

Postby Vytron » Tue Mar 18, 2014 3:27 pm UTC

Yeah, there was a reason I did that, I'll probably reveal it if I'm in danger of being lynched.

Unvote

Was fishing for reactions. was pretty much ignored so it was a lose of time.

Anyway, would like the game to start proper, so far it has been pretty much talk about what to do with results. I'm giving kalira townie points for being the first person to actually draw some connections.

Expecting Lawrencelot to remove his vote as well (New User isn't a new user.)

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Re: Bayesian Mafia - D1: Sabotage?

Postby mpolo » Tue Mar 18, 2014 4:53 pm UTC

cemper93 wrote:Maybe the question we should ask is: if the cutoff surety we set is X, if we lynch every person with a scum result of >X probability, how high is the chance that we win the game? Or rather: if that chance is Y, how do we have to choose X so that Y is larger than 75%/90%/95%/whatever we can agree on?

The problem is that figuring out the win chance is quite the problem space, and though I think this problem can be solved by a dynamic programming approach (starting with the 2/1 situation and working up from there), I'm a lazy bum and won't do it.


Also, we don't know how many of these "Experiments" are running around to be played with. Unless you somehow have extra information that I don't have.
Image <-- Evil experiment

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Re: Bayesian Mafia - D1: Sabotage?

Postby New User » Tue Mar 18, 2014 5:49 pm UTC

It's going to be up to the discretion of each player to decide when to reveal their own results. I have said this in many games before, and here I'll say it again. I don't think it's realistic to try to impose a set of rules about when or why to disclose such results. The most steadfast advice I have often given is that a doctor should not claim, because if it's a true claim then the doctor would be immediately killed by the mafia (unless there is another doctor or a town redirector, maybe) and since a good doctor can be very helpful to the town then we don't want that to happen. Even if a doctor thinks he has successfully protected against a night kill, it's still probably not a good idea to claim it unless it's near the end of the game. The doctor is better off staying alive to protect against more kills.

If you're a cop, watcher, tracker, lie detector, jailer, roleblocker, or whatever, then it's going to be up to you to decide when to claim your results. I'm not going to support making a "rule" to state when a player should do so, and if such a rule is made then it wouldn't hurt my feelings at all if any player ignores such a rule and just does what they think is best as far as claiming results goes.
cemper93 wrote:Maybe the question we should ask is: if the cutoff surety we set is X, if we lynch every person with a scum result of >X probability, how high is the chance that we win the game? Or rather: if that chance is Y, how do we have to choose X so that Y is larger than 75%/90%/95%/whatever we can agree on?

The problem is that figuring out the win chance is quite the problem space, and though I think this problem can be solved by a dynamic programming approach (starting with the 2/1 situation and working up from there), I'm a lazy bum and won't do it.

I think I can see your reasoning here, but it looks to me like you are thinking something along the lines of us having such a result each day. If there is a cop that gets such a result, and the cop claims that result the next day, then it's very likely that the cop will either be killed or roleblocked. So when you say "if we lynch every person with a scum result of >X" then it should be more like if we lynch the person with that result, because a cop might not get another chance after claiming.

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Re: Bayesian Mafia - D1: Sabotage?

Postby cemper93 » Tue Mar 18, 2014 7:20 pm UTC

mpolo wrote:Also, we don't know how many of these "Experiments" are running around to be played with. Unless you somehow have extra information that I don't have.
I don't think that that matters.

New User wrote:I think I can see your reasoning here, but it looks to me like you are thinking something along the lines of us having such a result each day. If there is a cop that gets such a result, and the cop claims that result the next day, then it's very likely that the cop will either be killed or roleblocked. So when you say "if we lynch every person with a scum result of >X" then it should be more like if we lynch the person with that result, because a cop might not get another chance after claiming.
This is true though. So yeah, glad I was a lazy bum and didn't do the maths. At least I didn't waste my time!

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Re: Bayesian Mafia - D1: Sabotage?

Postby mpolo » Tue Mar 18, 2014 8:03 pm UTC

cemper93 wrote:
mpolo wrote:Also, we don't know how many of these "Experiments" are running around to be played with. Unless you somehow have extra information that I don't have.
I don't think that that matters.


My reasoning was that if we want to set up a threshold of what we need to be able to guarantee a win, that would be affected by the number of experimental results that we have available. But maybe I misunderstood what you were proposing/asking about.
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Adam H
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Re: Bayesian Mafia - D1: Sabotage?

Postby Adam H » Wed Mar 19, 2014 3:22 pm UTC

Votals:
New_User - 1 (Lawrencelot)

Deadline in 5 days.
-Adam

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Re: Bayesian Mafia - D1: Sabotage?

Postby Vytron » Wed Mar 19, 2014 3:35 pm UTC

Okay, now I'm starting to wonder if Lawrencelot's vote was for real.

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Re: Bayesian Mafia - D1: Sabotage?

Postby just_me » Wed Mar 19, 2014 4:37 pm UTC

I don't think NU post is very good.
The main point being that when a standard cop claims he has a pretty good evaluation of how reliable his information is. Now we don't have that.
I also studied maths and the only thing I learned about probabilities is that its really unintuitive and awkward when applied to small n and it needs some serious statistics (like that alpha testing) to evaluate stuff for one trial only.
So even if we don't have fixed rules it would be good to have some discussion (or calculation) about how high a probability needs to be to be related to a meaningful result.
I am not sure whether having a high probability is also that good. Say I get a 80% scum result for sb that means that:
he is scum: sqrt(0,8^2)
he is town: 1-sqrt( 0,2^2)
Now we need to know how high the probability of 0,8^2 and 0,2^2 are and if I understand the thread correctly this should exactly be the number of the probability.
(that is the probability function of the values is linear)
Now what I don't understand is what is the probability distribution of random(0,1)? It needs to be something which has higher probability of returning high values. because else it would be just as likely for that person to be scum as it is to be town.
Okay I don't know.. this is weird.. the sqrt should so some normalising I suppose, but I don't really get it. Now the probabilities for him being scum or town don't add up to 100%.

This leads to another point. As we don't have any results today we need to rely on non-bayesian scum hunting anyway today.


Also I think NU is scum, because of reasons.

vote NU

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Re: Bayesian Mafia - D1: Sabotage?

Postby moody7277 » Wed Mar 19, 2014 4:59 pm UTC

just_me wrote:I also studied maths and the only thing I learned about probabilities is that its really unintuitive and awkward when applied to small n and it needs some serious statistics (like that alpha testing) to evaluate stuff for one trial only.


I think this was mpolo's concern over how many "experiments" per night we are able to do.

The problem with setting our surety level too high is that the experiment will rarely give that level of surety. Table:

Code: Select all

Surety      Probability of getting
95%         10%
90%         19%
80%         36%
75%         44%
70%         50%
67%         56%


Based on this, I think any surety level above 80% is unrealistic.
The story of my life in xkcdmafia:

Tigerlion wrote:Well, I imagine as the game progresses, various people will be getting moody.


BoomFrog wrote:I still have no idea what town moody really looks like.

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New User
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Re: Bayesian Mafia - D1: Sabotage?

Postby New User » Wed Mar 19, 2014 6:55 pm UTC

@just_me: So you think we should make a steadfast rule that determines when a cop or other useful power role should make a claim? And you think that because I am against that idea, I am scum? I don't agree. I am against making such a rule because it is impossible to enforce, and because I have played enough games of mafia to know that there will be factors in the future of this game that we aren't accounting for now. If we make such a rule now, with the knowledge that we currently have, then that rule won't apply in the future after we get more information. So we'll have to change the rule. We'll end up spending so much time focusing on this rule when it's much simpler to just leave it up to each individual to decide when to claim, since it's their choice anyway and we have absolutely no way to enforce such a rule and make someone claim when they aren't ready, or prevent them from claiming when you aren't ready. We should expect that anyone who has a result to claim is also going to have their own personal judgment of the target (their personal "read" on if they think target is scum or town based on what is in the thread), and also remember that investigations can be skewed by power roles such as godfather. Also, keep in mind that once the cop claims, they can expect to lose much of their usefulness from that point on. Follow The Cop is such a classic town strategy that practically every game is designed for the mafia to be able to prevent it. So a cop would have to make a personal judgment on when to claim based on when they think they might be silenced (by NK) before they have a chance to claim. If I'm a cop, I might get a favorable result in the first night but I might try to stay alive for another night so I can have two results to share instead of just one. Or, if I think it's not worth the risk, I might just go ahead and share my result after the first night.

The point here is, if you're a cop, it's up to you when to share your results. If you want to go along with a rule that other players come up with, fine. If you want to ignore that rule, fine. I'm not going to try to tell someone else how to play the game by making such a rule, and I think we're wasting our time trying to come up with such a rule.

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Adam H
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Re: Bayesian Mafia - D1: Sabotage?

Postby Adam H » Wed Mar 19, 2014 7:10 pm UTC

just_me wrote:Now we need to know how high the probability of 0,8^2 and 0,2^2 are and if I understand the thread correctly this should exactly be the number of the probability.(that is the probability function of the values is linear)Now what I don't understand is what is the probability distribution of random(0,1)? It needs to be something which has higher probability of returning high values. because else it would be just as likely for that person to be scum as it is to be town.
The probability distribution is uniform. Maybe the trick to understanding it is that the probability 80% is rounded, so rather than random(0,1) being either exactly 0.64 (0.8^2) or 0.04 (0.2^2), you know that random(0,1) is either between .632025 (0.795^2) and .648025 (0.805^2), or between .038025 (0.195^2) and .042025 (0.205^2). As luck would have it, there are 80% more numbers in the former compared with the latter. :)
-Adam

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Vytron
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Re: Bayesian Mafia - D1: Sabotage?

Postby Vytron » Wed Mar 19, 2014 7:18 pm UTC

just_me wrote:Also I think NU is scum, because of reasons.

vote NU


Please state those reasons or I'm going to assume "voted because not on my scumteam."


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