Nothing is as it Seems Mafia: The Game

[Ole' Dude With the Face]

Originally Posted by Sithdarth

The difference comes in that IF information comes to light about one of the three random selections

But, we don't have any information currently, so you kind of jumped the gun. I don't think you're any more scummy than any one else, yet. You just did what you do.

[Death by Stabbing]

Originally Posted by Cephrir

Unfortunately, this bandwagon is growing far too quickly for my liking. Quicklynches are bad.

Look there are 50 of us playing this game in 2 days we've already gotten to 11 pages...I'm surprised we've even agreed this much on one person...we'll be at this until next year if we don't get a few rounds of quicklynchings in...I'm not sure if Sithdarth is innocent or mafia...but we need to lynch someone and the first few days are usually bandwagony...

[Inbred Chocobo]

Wait wait wait... what?

Okay am I the only one that is following the course of logic that SithDarth just posted? Let me break it down to what I see Sith doing.

Instead of picking a random person out of the whole list, he picks three people. The odds of one of those peeps being mafia is higher than the odds of just picking a person off the list. Maybe only by a bit, but its a higher chance. Now he picks one of those peeps, and votes for them, since at least one person out of the three being mafia is a real high chance, he might as well start going for one and seeing what crops out of it.

Now, if you are arguing the size of the mafia is incorrect, you were implying that there were more. If you factor that into Sith's equation, that means that there is even a higher chance of you being mafia.

Then again I could be misreading everything. Ah well I'm just going to vote: Giever cuz he is last on the list, and while I do like Sith's theory, its just a fancy way of random voting to me.

[Bailey]

Okay, some of this is making sense to me.

Ignoring any roles which we do not specifically know the numbers of, we have three mafias of five and two cult leaders.

Five times three equals fifteen. Fifteen plus two equals seventeen. Seventeen times three is fifty-one, and fifty-one is roughly equal to fifty. So chances are about one in three that any particular person is either a mafiate or the cult leader, since that adds up to seventeen and seventeen is a bit more than a third of fifty.

You then chose three people at random under the assumption that, since one in three people are either a mafiate or a cult leader, any three randomly chosen people will include one person who has one of those roles.

The problem here is the same one which strikes when you rely on coin flips; if you flip a coin and it comes up heads, that does not mean it WILL be tails the next time you flip it. It continues to be a fifty percent chance. Granted, we only have fifty people, so eventually we MUST reach scum, whereas with a coin, it is possible, no matter how imbrobable, to get like five-hundred heads in a row.

So we kill the person and they turn out to be innocent. This does, in fact, raise the chances of each of the remaining people of being scum, but it raises it from (still ignoring self aligned stuff) 17/50 to 17/49, not from 1/3 to 1/2.

Still ignoring self-aligned nonsense, the chances that you picked two innocents and a scum, as is your assumption, has chances of 187/1225, or around fifteen percent.

So, if one of them dies and turns out to be innocent, then there is around a fifteen percent chance that each of them have a fifty percent chance of being scum.

This sounds crappy overall, but considering that a 7.5% chance is higher than 34.7%... wait... Maybe we should just ignore those numbers?

EDIT: Whoops. Did my math wrong. 15 is the chances that he chose one scum and then two innocents, not the chances that one of the people he chose was scum and the other two innocent. It was actually more like 45.7% chance for that, making the chances that one of those two people were scum around 68.55%

This seems impressive... up until you realize that that is pretty close to twice the chances that any one person is scum. In short, this actually does nothing, but it looks fancy.

[Ape Boy]

See, that's all well and good, except it doesn't leave any room for acting upon evidence we find during nights or general suspicion created during days.

No formula can compete with good 'ol fashioned rampant paranoia.

[Professor Smarmiarty]

People, Sith makes sense. His maths work. It will also help our day 2 and 3 votes if we get no further information.
Vote: ODWTF
In favour of Sith's plan.

[P-Sleazy]

Lay off Sith guys. or atleast, lay off his math. It makes PERFECT sense to me.

Also, I'm gonna be a non-committer (exams) until Monday next.

[Professor Smarmiarty]

Originally Posted by B_real_shadows

Lay off Sith guys. or atleast, lay off his math. It makes PERFECT sense to me.

That would be because it makes perfect sense.

[Sithdarth]

This works because I'm choosing people without replacement. That is if I had a bag of 15 red marbles and 35 blue marbles and I pulled out 3 marbles. Then I looked at just two of them. If I saw that the two of the marbles I pulled out where blue it changes the chances that the last marble is red because the probability of each event is not independent. That's because removing a marble and placing it aside before I chose a second marble changes the probabilities.

The problem here is the same one which strikes when you rely on coin flips; if you flip a coin and it comes up heads, that does not mean it WILL be tails the next time you flip it. It continues to be a fifty percent chance. Granted, we only have fifty people, so eventually we MUST reach scum, whereas with a coin, it is possible, no matter how imbrobable, to get like five-hundred heads in a row.

That only works if you allow your random selection method to choose the same person twice. I did not and therefore each probability depends on the one before it. Further I'm unable to actually look at what my choices are so all I can do is use the Hypergeometric probability density function to give probabilities that at least one of the 3 happens to be a mafiate. This gives me 4 possible situations each with their own probability of happening. Once I get to look at one or two of the choices and see what they are I can exclude some of the possibilities. That exclusion increases the probabilities of the possibilities remaining because everything still has to add to one.

Whoops. Did my math wrong. 15 is the chances that he chose one scum and then two innocents, not the chances that one of the people he chose was scum and the other two innocent. It was actually more like 45.7% chance for that, making the chances that one of those two people were scum around 68.55%

You really have to apply Bayes theorem here because the probabilities aren't independent and that does strange things to conditional probabilities.

I would like to point out though that the 80% chance of one of the remaining two being mafiate that I calculated before seems better than it is. That's because I still have a 50/50 chance of getting it right by choosing between them. So my actual chances of picking one of them and coming up with a mafiate are .8 * .5 or about 40%. Still better than the standard 30%.

[Bailey]

Oh, by the way, you listed four people, not three.

Originally Posted by Sithdarth

34. has a 30% chance of being assigned to a mafia
39. has a 43% chance
30. has a 46% chance
27. has a 7% chance

Well, since I don't know any part of Bayerian theory, I'm just going to keep going with the math that I DO know which is this: Any time somebody in mafia presents a list of people "one of which is a mafiate, I dont know which" there is an 87% chance that they are themselves a mafiate who is trying to buy time by saying "well it must be the next guy". You mentioned 27 because your original math included that number, but you glossed over 27 as soon as you could. It therefor follows, in my mind, that Cephrir, number 27, is aligned with you.

Unvote: Nikose
Vote: Cephrir, whose name I am spelling correctly