Classic Mafia - Conclusion!

[TheNave]

somebody didn't pay attention at stochastic classes... the probability of three mafias to be next to each other (f.e. jernemies, luti, mfc) is exactly the same as the one for three mafias to be at any other given three positions (f.e. Bamboori, mfc, Simoneon)
it's the same as, if I roll a dice and got a six three times in a row, is it more likely for me to get a fourth six than getting a three? no, it's not, the probability of both is 1/6th.

following that logic alone does not fit you at all Apoc and makes you even more suspicious now, it's like you're desperately trying to find reasons to kill of citizens, even with zero regard for the actions and statements they made in this game so far... for Amadis it was "a hunch" this time it's "probability" but not the good one, the stupid bullsh*t one, this is just not like you when you're usually on town side

you just moved even higher on my list and made me change my vote to Apocalypsis... at this point I wouldn't care who of my three top suspects to lynch today, but seeing bullsh*t logic like that from you just sealed the deal for me

[LutiChris]

somebody didn't pay attention at stochastic classes... the probability of three mafias to be next to each other (f.e. jernemies, luti, mfc) is exactly the same as the one for three mafias to be at any other given three positions (f.e. Bamboori, mfc, Simoneon)
it's the same as, if I roll a dice and got a six three times in a row, is it more likely for me to get a fourth six than getting a three? no, it's not, the probability of both is 1/6th.

I don't really want to defend apoc but i sympathize with his line of reasoning in the sense that if STM didn't use a random generator to make his lists and simply typed this by hand then you will have to consider the human mind which is bound to have patterns that we can identify and what would be the likeliness for them to do such an action. I often contemplated when making such lists if i should put them far apart of maybe make two connect next to each other and the other far away. but having a human put all 3 of them next to each other doesn't seem likely. I would agree if it was purely random but nothing is purely ramond. random** (wow brain fart)

[TheNave]

well I advised him to use a random number generator when distributing roles at the begining of the game for reasons like this, and I asume he did take my advice and could possibly confirm it here

STM1993 edited this post 03-02-2016 01:29 AM because:

Yes, I used a RNG.

[LutiChris]

Lets wait and see if this is correct. If he did use a generator then i'm with you.

[Ramond]

somebody didn't pay attention at stochastic classes... the probability of three mafias to be next to each other (f.e. jernemies, luti, mfc) is exactly the same as the one for three mafias to be at any other given three positions (f.e. Bamboori, mfc, Simoneon)
it's the same as, if I roll a dice and got a six three times in a row, is it more likely for me to get a fourth six than getting a three? no, it's not, the probability of both is 1/6th.

Actually, that's not quite right. Assuming the distribution of roles was uniform, then the percentage is simply the quotient of the favorable cases and the possible cases. I only see 10 ways to distribute 3 'neighboring' Mafias between 12 players, but far more to distribute them not-neighboring. Your die rolling example doesn't fit this case, it's something different since a result can be repeated.

But given the nature of the game and how we don't know how STM distributed the roles (the names are ordered alphabetically, which may have happened after the distribution), I wouldn't really take heed to stochastics anyway. It's a red herring.

EDIT: Right, the total possible amount is 12!/(9!3!) which is 220. Meaning 210 ways to distribute 3 Mafias without all three being next to each other.

EDIT2: Did some editing due to false Maths, but it should be right now.

[Apocalipsis]

Why do you use 12? There were 14 players at the start of the game.

Edit:
With 14 players, the probabilities of 3 mafias next to each other is 12/364, right?

Edit 2:
In any case, I was asking if that was correct. Your reaction was unnecessary Nave.

[STM1993]

Just to confirm:
Yes, I used a random number generator to distribute the roles.

Votes for now, day 3 is still ongoing:
1. AmadisLFE
2. Apocalipsis - #5/11: no vote for now(retracted Luti)
3. Bamboori
4. CosmicSarasa
5. Darl
6. empirefantasy - #10: Bamboori
7. Jernemies
8. LutiChris - #8: LutiChris
9. mfc
10. Ramond - #1/7/9: Apocalipsis
11. Rhino.Freak
12. Simoneon - #3: TheNave
13. TheNave - #2/4/6/12: Apocalipsis
14. T.O.R.N.A.D.O

Vote Tally:
Apoc - 2
TheNave - 1
LutiChris - 1
Bamboori - 1

[Apocalipsis]

Right now I'm torn between voting Bamboori or Nave (mostly because of his reaction).

Before voting, I want to see if Nave's still voting against me, and his response to this:

Actually, that's not quite right. Assuming the distribution of roles was uniform, then the percentage is simply the quotient of the favorable cases and the possible cases. I only see 10 ways to distribute 3 'neighboring' Mafias between 12 players, but far more to distribute them not-neighboring. Your die rolling example doesn't fit this case, it's something different since a result can be repeated.

[A-Man]

I hope I am not becoming too much of a meddler, but I can't stand seeing people use maths this way!

Actually, that's not quite right. Assuming the distribution of roles was uniform, then the percentage is simply the quotient of the favorable cases and the possible cases. I only see 10 ways to distribute 3 'neighboring' Mafias between 12 players, but far more to distribute them not-neighboring. Your die rolling example doesn't fit this case, it's something different since a result can be repeated.

I think what TheNave was trying to clarify with that example is that Apocalipsis's use of probability would've only been valid at the beginning of the game. So you say the probability there exists a mafia in every set of 5 players (from 15 for simplicity) is 1/5 since there are 3 mafia players in total. It stands that 3 mafia players can be in the same set, though less likely at first (since # of ways they can be like that is less as you explained). However, as nature makes her choices, whether they were the more expected ones or the less expected ones, these become current and the probability resets.

What is the probability 2 coin flips yield tails? 0.5 * 0.5. But if you've already tossed the first coin, and it landed as tails, then the probability shrinks to becoming "the probability 1 lands tails", which is 0.5. If you've already scored 3 sixes with a dice, the probability you score a 4th 6 is 1/6. The probability there is 1 mafia in every set of 5 players is great, but as the game progresses and things become determined, all of this resets to match the new numbers.

[Apocalipsis]

I was actually waiting for your answer xD

I think what TheNave was trying to clarify with that example is that Apocalipsis's use of probability would've only been valid at the beginning of the game. So you say the probability there exists a mafia in every set of 5 players (from 15 for simplicity) is 1/5 since there are 3 mafia players in total. It stands that 3 mafia players can be in the same set, though less likely at first (since # of ways they can be like that is less as you explained). However, as nature makes her choices, whether they were the more expected ones or the less expected ones, these become current and the probability resets.

What is the probability 2 coin flips yield tails? 0.5 * 0.5. But if you've already tossed the first coin, and it landed as tails, then the probability shrinks to becoming "the probability 1 lands tails", which is 0.5. If you've already scored 3 sixes with a dice, the probability you score a 4th 6 is 1/6. The probability there is 1 mafia in every set of 5 players is great, but as the game progresses and things become determined, all of this resets to match the new numbers.

Just to clarify what I posted in the previous page: If we assume that each one of the 364 possible distributions of 11-citizen-3-mafia tags on the 14 'slots' of the list have the same probability of happening, then that means that there are 84 favorable cases in which (at least) the first five slots have the citizen tag. That means that each time we start a new game with this specs, there are 23.08% chances of having at least 5 citizens in the first five slots.

While it would be correct to use the information from the current experience like you said, there are 2/7 chances of getting a Mafia in Bamboori's slot, or any other place for that matter, and that wouldn't help me decide whom to kill (which is what I'm trying to do now). Is it that bad to decide using the a priori probability of having a mafia there at the start of the game?