I would like to bring the Montmercy v Pizza debate to a close because they are screaming over each other and drowning out all other debate. First of all I'm going to ask both Pizza and Montmercy to refrain from responding in a wall of posts to this.

I am not much of a behavior analyst but I am pretty good with facts and statistics. I will start by summarizing both theories.

Montmercy's Theory:
When town use shirt it shows correct investigation results.
When scum use shirt it reverses the investigation results.
ATPG, Populus Romanus, Johhog, and Memnon are mafia.
Mafia can kill one of their own.
They set up a chain to clear themselves, then ATPG sacrificed himself to clear the first link of the chain.
Mafia is not killing Confirmed Innocents because they aren't innocent

ATPG's Theory:
When town use shirt it shows correct investigation results.
When scum use shirt we don't know what happens.
ATPG - Memnon are innocent
Johnhugthom is scum
Remaining mafia can be found among B-Ray, Believer, Ishmael, Seamus, Tratorix, Yaropolk, Warman
Scan chain has not been compromised.
Mafia are not killing Confirmed Innocents for WIFOM reasons

I calculated the probability of the ATPG chain scanning 3 innocents in a row without ever hitting the same target as mafia. The formula that I used is:

P of hitting innocent = (#Alive - #Confirmed Innocents (as you wouldn't scan them) - Self (1) - Mafia Kill (1 except when ATPG died) - #of Mafia (3 or 4)) / #Alive

Total P = product of each night's P's.

Night Alive C.I. Self Killed 3 Mafia 4 Mafia
1.........16.....0......1.......1........0.69.......0.63
2.........15.....1......1.......1........0.60.......0.53
3.........14.....2......1.......0........0.57.......0.50
TOTAL:...................................0.24.......0.17
There is a 17% or 24% chance for ATGP chain scan to occur naturally. It's pretty low but not beyond impossibility.


Conclusion:

At the end of today's day we will have 10 people alive (assuming JH is lynched)
If we started with 4 mafia, 1 will be dead under either theory (ATPG or JH)
That means that once we are down to 6 players we're toast (unless we lynch some more scum).
If we refrain from further lynching except when mafia is located we have 4 rounds remaining.
Each incorrect lynch cuts the number of remaining rounds by 1.

To validate Montmercy's theory will take 1 night scan - someone outside the chain must scan Memnon.
To validate ATPG's theory we'll have to keep scanning half of the remaining 8, essentially a 50/50% chance of finding scum.


Proposal
1) We lynch JH in case ATPG is correct
2) We spend the 1 day scanning Memnon to put that theory to rest. I would prefer this would not be done by someone nominated by Pizza. I nominate myself. Believer - if you prevail over me, I would ask you to investigate Memnon regardless.

I am note convinced of either theory yet, however here are my non-statistical reasons for giving Montmercy's theory a chance
  • For pizza to sacrifice himself was not necessary - they could have just trailed the chain off into innocents, but this would be an awesome move if they're mafia and ATPG goes for bold moves all the time.
    Making investigation results public without a twist would be too overpowering.
    Confirmed innocents are not being killed.


Vote: Johnhugthom
Vote: Yaropolk