Nothing is as it Seems Mafia: The Game - Page 8

Ole' Dude With the Face · 12-10-2007, 05:24 PM

Quote:

Originally Posted by Masked Jedi

Considering this game is going to last forever anyway, does anyone else think that this is a good time to reform the FFF?

You deserve to be voted for just for suggesting that.

Unvote
Vote: Masked Jedi

Truce · 12-10-2007, 05:26 PM

Vote: Sithdarth

Why?

Because there's a 100% chance that he's playing in this game.

Captain Combustible · 12-10-2007, 05:27 PM

7 pages before I see the game has started?!
Anyway I agree with Ole Dude here Vote: Masked Jedi.

Marn of Mayhem · 12-10-2007, 05:57 PM

Vote: BHS

'cos he's a syc... syc... syco.... fancy word !

Zavage · 12-10-2007, 06:14 PM

Eight pages? Wow I'm late. I will

FoS: Sithdarth

because not only did he use math, but he used bad math. Assuming roles were randomly assigned and having no knowledge of any role but your own, ODWTF has a same probability of having a scum role as anyone else.

No, I have nothing better to go on.

Red Fighter 1073 · 12-10-2007, 06:23 PM

Vote: Lunaknight

Do I really need a reason? I mean, really?

Professor Smarmiarty · 12-10-2007, 06:49 PM

Vote: Newb
He's wearing a barrel. I ask Newb, why do you need such a copious amount of leg storage space? Why are pockets not enough? You have a lot of something to store obviously.
Evil perhaps?

Sithdarth · 12-10-2007, 07:11 PM

Quote:

FoS Sithdarth for mathematical deductions that don't actually make sense assuming everything was random.

It makes absolutely prefect sense except for the probability of finding exactly one success in 4 trials cause I messed up when I put it into my calculator. Also, the probabilities don't actually correspond to each of the randomly selected people but rather that exactly one of them has a mafia role. I chose the last of the three simply because I felt like it. (IE: I assumed the first two to be non-mafiate due to lack of information and because it was just as valid as an method of selection. Should information actually come to light about two of my 3 choices the probabilities obviously switch.)

In this case we have P(x) = (15Cx * 35C(n-x))/ 50Cn (those are supposed to be the symbol for combination)

x = number of successes
n = number of trials

If we take 3 trials then n=3 and set x=1 for only one success then we get
P=.45535714285714
setting x=2
P=.1875
setting x=3
P=.02321428571486
setting x=0
P=.33392857142857

Add em all up and you get one. That means there is a roughly 66% chance of one or more mafiates being in a random sample of three. (P at x=1,2,3 added together) In this case I'm more interested in the case of only one mafiate in any random set of 3. This is because we have the possibility of information. That is if we can somehow eliminate 2 out of the 3 random choices as not being mafiates then the remaining person has an approximately 46% chance of being a mafiate.

Now initially with just a straight random choice you have a 15/50 chance of hitting a mafiate or 30%. By choosing 3 at random and eliminating two as non-mafia you can apply conditional probability. That is:

P(B|A) = P(B)*P(A|B)/(P(B)*P(A|B)+P(C)P(A|C))

A = 2 known townies
B = last person is mafia
C = last person isn't mafia

P(B) = .5
P(C) = .5
P(A|B) = .455
P(A|C) = .334

P(B|A) = (.5*.455)/(.5*.455+.5*.334) = .577

Just as a note one random choice gives you about a 15/50 chance (30%) of hitting a mafiate. With a random sample of 3 and information about 2 I've increased my chances of having found a mafiate by 28%.

Now if we only know the role of one of the three:

A = 1 known townie
B = at least one of last two is mafia
C = none of the last two are mafia

P(B) = 2/3
P(C) = 1/3
P(A|B) = .643
P(A|C) = .334

P(B|A) = (2/3*.643)/(2/3*.643+1/3*.334) = .794

That is there is a roughly 80% chance that one of those two is a mafiate. (This is a result I totally didn't expect myself. I love math sometimes.) Though I shouldn't be surprised as this is very close the classic three door scenario where when one door is eliminated you up your chances of winning by changing doors.

Its a perfectly valid application of probability distributions that happens everyday as part of quality control in factories. Its just in this case I've replaced defective parts with mafia members. Just because things are random does not mean you can't use probability and information theory to draw conclusions. In fact, it is because things are random that you can apply these theories. (That is unless Fenris used some non-random method of assigning roles.)

Quote:

because not only did he use math, but he used bad math. Assuming roles were randomly assigned and having no knowledge of any role but your own, ODWTF has a same probability of having a scum role as anyone else.

Read carefully this has nothing to do with his actual individual probability. Its all about the probability that I guessed right by choosing randomly.(Though I didn't really make that clear enough at first and I apologize.) The last part about picking ODWTF was simply my preference for starting at one point over the other. In other words with my current information I have a 30% chance of being right just like everyone else. However, if ODWTF was lynched or killed at night and revealed as a townie I would then have information and would know that one of my other 2 random guesses has a better chance of being a mafiate.

In other words since I have to guess randomly I want to make sure any information gleaned from that guess is as useful as possible.

Ole' Dude With the Face · 12-10-2007, 07:24 PM

Quote:

Originally Posted by Sithdarth's Rambling About Math and Probabilities

Stuff

Yeah, thats all great and all, but it stopped making any sense WAY up there near the top of your post. I wouldn't even respond to all that, except you are accusing me. So yeah, I think its all jibber-jabber (Copyright Mr T.) and nonsense.

Of course I could throw a bunch of wrenches into your math like how do you know exactly how many mafiates there are in each family? After all, who except a mafiate knows exactly how many mafiates are in each family. With a game this size it isn't unreasonable to think there may not be the normal 5 mafiates per family. But then, there might be. Who knows? I don't.

But, yeah what I'm getting to is that I think your math is wrong, and that you state by your own words that it isn't infallible.

Axl · 12-10-2007, 07:31 PM

Vote: Sithdarth

For the tl;dr

12-10-2007, 05:57 PM	#74
Marn of Mayhem Finishing the fight Join Date: Sep 2006 Location: Hellgate: London. Posts: 199	Vote: BHS 'cos he's a syc... syc... syco.... fancy word ! __________________ New signature coming soon.

12-10-2007, 06:23 PM	#76
Red Fighter 1073 Rocky Wrench Join Date: Apr 2005 Posts: 1,351	Vote: Lunaknight Do I really need a reason? I mean, really? __________________ My Sprite Sheet/Mafia Roles

12-10-2007, 05:26 PM	#72
Truce Lakitu Join Date: Nov 2003 Posts: 3,856	Vote: Sithdarth Why? Because there's a 100% chance that he's playing in this game.

12-10-2007, 05:27 PM	#73
Captain Combustible Can't spell.... or count Join Date: Mar 2007 Posts: 27	7 pages before I see the game has started?! Anyway I agree with Ole Dude here Vote: Masked Jedi.

12-10-2007, 06:14 PM	#75
Zavage Behold the Manatee! Join Date: Sep 2007 Posts: 1	Eight pages? Wow I'm late. I will FoS: Sithdarth because not only did he use math, but he used bad math. Assuming roles were randomly assigned and having no knowledge of any role but your own, ODWTF has a same probability of having a scum role as anyone else. No, I have nothing better to go on.

12-10-2007, 06:49 PM	#77
Professor Smarmiarty Sent to the cornfield Join Date: Mar 2007 Location: K-space Posts: 9,758	Vote: Newb He's wearing a barrel. I ask Newb, why do you need such a copious amount of leg storage space? Why are pockets not enough? You have a lot of something to store obviously. Evil perhaps?

12-10-2007, 07:31 PM	#80
Axl Cat Join Date: Feb 2005 Location: No Posts: 428	Vote: Sithdarth For the tl;dr