Elements Mafia 25 - Hosted by Mesaprotector

[Cheesy111]

Root continues to have a point. 
Rootranger - 4 - ddevans96, regen2k9, UTL, Shantu
Mort - 1 - majofa
bogtro - 1 - Annele
PlayerOa - 1 - Legit
OTL- 7 - Onizuka, RootRanger, 1world24, Mort, Jocko, PlayerOa, Cheesy111
Onizuka- 1 - qwerter
helston - 1 - blarp
blarp - 1 - McSod

[bogtro]

I'm not following this argument. I think that it's relatively clear that either OTL is a townie or an extremely smart mafia - more likely town. If this is the case, then we are killing 1 town for the killing of 1 unknown. Lynching anyone else gives us 2 unknowns.

If we lynch OTL, the mafia will kill somebody else resulting in 4 deaths. If we don't lynch OTL and the mafia decides to kill OTL (as Root seems to think), the result will be 4 deaths. Therefore, not lynching OTL gives us at least as much information as lynching OTL.

I really don't care so much whether or not we lynch OTL. My point is that option is always available to us, and if that option is taken away from us by the mafia killing him, all the better for us.

[Laxadarap]

I'm not following this argument. I think that it's relatively clear that either OTL is a townie or an extremely smart mafia - more likely town. If this is the case, then we are killing 1 town for the killing of 1 unknown. Lynching anyone else gives us 2 unknowns.

If we lynch OTL, the mafia will kill somebody else resulting in 4 deaths. If we don't lynch OTL and the mafia decides to kill OTL (as Root seems to think), the result will be 4 deaths. Therefore, not lynching OTL gives us at least as much information as lynching OTL.

I really don't care so much whether or not we lynch OTL. My point is that option is always available to us, and if that option is taken away from us by the mafia killing him, all the better for us.

Roots point is that IF the mafia aren't linked to OTL, then its a free double civy kill with no risk to them.  I feel like the argument here, is that whether the chance that OTL and his partner are both civy is worth possibly learning something.

[bogtro]

EBWOP:
If we lynch OTL, and the mafia is not a fire element (probability 22/23*21/22*20/21*19/20=19/23=about 82.6%), the mafia has a chance of killing their own, based on:
a) All 4 mafia have different elements - probability 22/22*20/21*18/20*16/19, which is about 72.18%
b) 2 mafia have the same element, 2 other mafia have different elements - probability 6*22/22*1/21*20/20*18/19, which is about 27.06%
c) 2 mafia have 1 element, 2 mafia have another element - probability 6*22/22*1/21*20/20*1/19, which is about 1.5%

In case a, their probability of killing a mafia is 4/20=1/5=20%
In case b, their probability of killing a mafia is 2/22=1/11=about 9.1%
In case c, their probability of killing a mafia is 0%

Therefore, the expected probability of killing a mafia is about 16.88% (note that this includes the probability of lynching a mafia immediately by the mafia being the other fire element).

If we don't lynch OTL, the probability of killing a mafia is based on:
a) Mafia is the other fire element (about 17.4% chance)
a1) Two mafia have the same element, one has fire, one has something else. Probability 12*1/23*22/22*1/21*20/20=about 2.48%
a2) All mafia have different elements - probability 1/23*22/22*20/21*18/20=about 3.72%
b) Mafia is not a fire element (about 82.6% chance)
b1) All 4 mafia have different elements - probability 1*20/21*18/20*16/19=about 72.18%
b2) 2 Mafia have the same element, the other 2 are different - probability 6*1*1/21*1*18/19=about 27.06%
b3) 2 Mafia have 1 element, 2 mafia have the other - probability 6*1*1/21*1*1/19=about 1.5%

Killing mafia by lynching probabilities:
a1) 3/21=about 14.3%
a2) 7/23=about 30.4%
b1) 8/23=about 35.8%
b2) 6/23=about 26.1%
b3) 4/23=about 17.4%

Weighting these gives a mafia killing probability *just by lynching* (this does not take into account the possibility of the mafia deciding to not kill OTL) of 34.6%

Although I am not too sure in my math at the moment, and any mistakes should be pointed out, the number of 34.6% without killing OTL vs. 16.88% with killing OTL makes the decision clear to me.

The main point here is that we have a better chance by killing 2 unknowns than the mafia do of killing one unknown.

[Cheesy111]

Spoiler for Hidden:

EBWOP:
If we lynch OTL, and the mafia is not a fire element (probability 22/23*21/22*20/21*19/20=19/23=about 82.6%), the mafia has a chance of killing their own, based on:
a) All 4 mafia have different elements - probability 22/22*20/21*18/20*16/19, which is about 72.18%
b) 2 mafia have the same element, 2 other mafia have different elements - probability 6*22/22*1/21*20/20*18/19, which is about 27.06%
c) 2 mafia have 1 element, 2 mafia have another element - probability 6*22/22*1/21*20/20*1/19, which is about 1.5%

In case a, their probability of killing a mafia is 4/20=1/5=20%
In case b, their probability of killing a mafia is 2/22=1/11=about 9.1%
In case c, their probability of killing a mafia is 0%

Therefore, the expected probability of killing a mafia is about 16.88% (note that this includes the probability of lynching a mafia immediately by the mafia being the other fire element).

If we don't lynch OTL, the probability of killing a mafia is based on:
a) Mafia is the other fire element (about 17.4% chance)
a1) Two mafia have the same element, one has fire, one has something else. Probability 12*1/23*22/22*1/21*20/20=about 2.48%
a2) All mafia have different elements - probability 1/23*22/22*20/21*18/20=about 3.72%
b) Mafia is not a fire element (about 82.6% chance)
b1) All 4 mafia have different elements - probability 1*20/21*18/20*16/19=about 72.18%
b2) 2 Mafia have the same element, the other 2 are different - probability 6*1*1/21*1*18/19=about 27.06%
b3) 2 Mafia have 1 element, 2 mafia have the other - probability 6*1*1/21*1*1/19=about 1.5%

Killing mafia by lynching probabilities:
a1) 3/21=about 14.3%
a2) 7/23=about 30.4%
b1) 8/23=about 35.8%
b2) 6/23=about 26.1%
b3) 4/23=about 17.4%

Weighting these gives a mafia killing probability *just by lynching* (this does not take into account the possibility of the mafia deciding to not kill OTL) of 34.6%

Although I am not too sure in my math at the moment, and any mistakes should be pointed out, the number of 34.6% without killing OTL vs. 16.88% with killing OTL makes the decision clear to me.

The main point here is that we have a better chance by killing 2 unknowns than the mafia do of killing one unknown.

Sorry to spoil all your math, but aren't there 5 mafia members?

[Mort]

Spoiler for Hidden:

EBWOP:
If we lynch OTL, and the mafia is not a fire element (probability 22/23*21/22*20/21*19/20=19/23=about 82.6%), the mafia has a chance of killing their own, based on:
a) All 4 mafia have different elements - probability 22/22*20/21*18/20*16/19, which is about 72.18%
b) 2 mafia have the same element, 2 other mafia have different elements - probability 6*22/22*1/21*20/20*18/19, which is about 27.06%
c) 2 mafia have 1 element, 2 mafia have another element - probability 6*22/22*1/21*20/20*1/19, which is about 1.5%

In case a, their probability of killing a mafia is 4/20=1/5=20%
In case b, their probability of killing a mafia is 2/22=1/11=about 9.1%
In case c, their probability of killing a mafia is 0%

Therefore, the expected probability of killing a mafia is about 16.88% (note that this includes the probability of lynching a mafia immediately by the mafia being the other fire element).

If we don't lynch OTL, the probability of killing a mafia is based on:
a) Mafia is the other fire element (about 17.4% chance)
a1) Two mafia have the same element, one has fire, one has something else. Probability 12*1/23*22/22*1/21*20/20=about 2.48%
a2) All mafia have different elements - probability 1/23*22/22*20/21*18/20=about 3.72%
b) Mafia is not a fire element (about 82.6% chance)
b1) All 4 mafia have different elements - probability 1*20/21*18/20*16/19=about 72.18%
b2) 2 Mafia have the same element, the other 2 are different - probability 6*1*1/21*1*18/19=about 27.06%
b3) 2 Mafia have 1 element, 2 mafia have the other - probability 6*1*1/21*1*1/19=about 1.5%

Killing mafia by lynching probabilities:
a1) 3/21=about 14.3%
a2) 7/23=about 30.4%
b1) 8/23=about 35.8%
b2) 6/23=about 26.1%
b3) 4/23=about 17.4%

Weighting these gives a mafia killing probability *just by lynching* (this does not take into account the possibility of the mafia deciding to not kill OTL) of 34.6%

Although I am not too sure in my math at the moment, and any mistakes should be pointed out, the number of 34.6% without killing OTL vs. 16.88% with killing OTL makes the decision clear to me.

The main point here is that we have a better chance by killing 2 unknowns than the mafia do of killing one unknown.

Sorry to spoil all your math, but aren't there 5 mafia members?

Of which one without an element.
Also, Bogtro, you didn't take the possibility of OTL being maf into account.
I am pretty sure that he isn't, but if you're going pure maths on it you have to.

[bogtro]

Sorry to spoil all your math, but aren't there 5 mafia members?

One of them is a boss without elemental affinity.

Also, Bogtro, you didn't take the possibility of OTL being maf into account.
I am pretty sure that he isn't, but if you're going pure maths on it you have to.

The probability of him being mafia remains the same regardless of who we choose to lynch. We can never be sure of anything, but I feel like it's quite reasonable to assume OTL is innocent.

If he is mafia, then the mafia still need to risk killing one of their own, but we also get a lynch.

[Mort]

(Useless argument because OTL (hereinafter: otl) prolly is town, but stoll fun to do anyway)
Pure number-wise, there is a 20% chance of him being mafia. This would mean that our chances of lynching maf when lynching otl go up by 20%(-ish, don't feel like numbercrunching right now), with the added possibility of lynching two mafs.
Then, the final numbers to 34.6% without killing OTL < 16.88+20=36.88% with killing OTL

But still, you convinced me, so

Rootranger - 5 - ddevans96, regen2k9, UTL, Shantu, Mort
Mort - 1 - majofa
bogtro - 1 - Annele
PlayerOa - 1 - Legit
OTL- 6 - Onizuka, RootRanger, 1world24, Jocko, PlayerOa, Cheesy111
Onizuka- 1 - qwerter
helston - 1 - blarp
blarp - 1 - McSod

[Helston]

I have to agree with bogtro now. I've had a long think about it, and what it boils down to is that if we kill OTL then the mafia get a non-OTL kill tonight, potentially killing one of their own in the process. If we lynch someone else, and assuming OTL is innocent, the mafia may get a free double townie kill, but we get a lynch which may be either a mafia or mafia partner. We can also assume he's not the mafia boss - calling for claims and then being one of three people singled out by it would be incredibly stupid.

What I'm trying to say is that we have a better chance of killing a mafia by lynching someone else than the mafia have of killing one of their own. What's more, Root's attack was a bit tool strong considering OTL had admitted his mistake twice by the time Root posted.

Rootranger - 6 - ddevans96, regen2k9, UTL, Shantu, Helston, Mort
Mort - 1 - majofa
bogtro - 1 - Annele
PlayerOa - 1 - Legit
OTL- 6 - Onizuka, RootRanger, 1world24, Jocko, PlayerOa, Cheesy111
Onizuka- 1 - qwerter
helston - 1 - blarp
blarp - 1 - McSod

[Shantu]

I am starting to lose track of arguments and reasonings, but I would like to point out that even if we leave OTL alive, and his element is a double civy, the mafia will most likely not kill him. This way they will make us think that one of the mafia is a fire elemental, that's why they didn't kill him. They will let us do it, so that in the meanwhile they can go on and kill others. This is all assuming OTL is a civy.

If he isn't, well, we gonna get him sooner or later.

[Laxadarap]

Reissuing my vote on Root

Rootranger - 7 - ddevans96, regen2k9, UTL, Shantu, Helston, Mort, Laxadarap
Mort - 1 - majofa
bogtro - 1 - Annele
PlayerOa - 1 - Legit
OTL- 6 - Onizuka, RootRanger, 1world24, Jocko, PlayerOa, Cheesy111
Onizuka- 1 - qwerter
helston - 1 - blarp
blarp - 1 - McSod

[agentflare]

Rootranger - 7 - ddevans96, regen2k9, UTL, Shantu, Helston, Mort, Laxadarap
Mort - 1 - majofa
bogtro - 1 - Annele
PlayerOa - 1 - Legit
OTL- 7 - Onizuka, RootRanger, 1world24, Jocko, PlayerOa, Cheesy111,  agentflare
Onizuka- 1 - qwerter
helston - 1 - blarp
blarp - 1 - McSod

The main problem with bogtro's statement is that we didn't reach it simultaneously, independantly, as we should have if we logically analyzed as bogtro did. The mafia now knows and can deceive us with it, if they so choose. OTL's value as an indicator is greatly reduced.