Calculating EV of Cop 9er

[Cook]

7:2 Mountainous is not a horribly balanced matchup in theory. One of the oldest ways in the history of Mafia to balance 7:2 is to give Town a Cop.

Has someone run EV calculations, or figured out a way to calculate, Cop 9er's EV?

[RadiantCowbells]

I don't think you can calculate EV without defining

1) cop behaviour
2) town behavior in response to cop claims

[Cook]

i'd define cop behavior as:
1. investigates a random player they haven't investigated before (a 1/4 chance of finding scum, a 3/4 chance of finding town, to start)
2. if the cop is eliminated, any town they investigated are no longer eligible for elimination by day, and scum will kill them first (killing confirmed townies and also not decreasing the chance of eliminating town each day that goes by)
3. if the cop finds a scum they will claim and get that scum eliminated immediately, guaranteeing that they also die the next night, but stopping all town they investigate from being voted out by day. (if you want to be more realistic, the claim could have a 50/50 chance of being CC'd, at which point there's a 50/50 chance of either the cop being eliminated and then the CC'ing scum, or the scum being eliminated and then the cop getting NK'd)

[Cook]

we also need to consider the possibility of scum claiming cop to draw out the cop, and whether or not that's believed...

some of this feels like quantum computing tbh