Question:
Someone has a gun. What are the odds of them being Mafia?
Hastily Scribbled Answer:
| Gunsmith |
- Check (EoR): Target a player. You learn whether they carry a weapon. Players with weapons are Whisperers, all investigative roles, Vigilants and Policemen who haven't lost their abilities yet.
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First off, how many roles give you weapons?
The Gunsmith, the Officer, the Agent, the Paranormal Scientist, Vigilante, and Policeman. Six roles.
There are 18 players and 17 roles. Ginyu has told us this mafia's role distribution:
All roles are sent out!
There are 14 Civilians and 4 Whisperers.
There is exactly one Officer who is a Civilian. Any other secondary role might appear once, multiple times, or not at all.
Meaning there are 4 Mafia and 1 armed Civilian guaranteed, making the odds a maximum of 80%. This is the case in the unlikely scenario that there are no other armed roles.
For the other unknown roles, what is the possibility of being an armed role?
The chance of a role being an Armed role is 5/17, or ~30%. (There is exactly one officer.) This means that we can expect to see around 1 armed role for every three roles, or 5-6 armed roles.
Assume there is one other armed role. It can go to the mafia, or to the civilians.
There are 13 unknown civilian roles, and 4 unknown mafia roles.
The chance of this role going to the mafia becomes 4/17, or about 23%. If this happens, the probability of being scum does not decrease. As there are an average of 6ish armed roles, we're looking at likely at least one going to the mafia.
So, in the most
average state, we are looking at 4 whisperers, 1.25ish of which has an armed role. Also an officer, and 4-5 civilian arms.
It hovers around a 50% chance of being mafia. This degenerates into 4/9 - slightly unfavoured - or 4/8 - equal - in an average game.
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