I have ammo, which charges the "gun" with 1 shot.
It seems like it would be a reasonably elegant mechanic for everyone to start with one unit of ammo, so that when the mafia kill someone, they replenish their ammo by looting the body. Suppose that everyone does in fact start with one unit of ammo. Then here's a scheme that'd force a mafia to out themself with probability 13/16: we choose a provably random person (provable randomness isn't banned!
) right before day end, everyone gives them their ammo, and then everyone watches them until day end. If they don't die by the end of the day, then we execute them.
If the person we chose is mafia, we're happy because we execute a mafia.
If the person we chose is town and a mafia kills them, we're happy because a mafia outed themself to make the kill. (The mafia get a lot of ammo, but they're presumably not kill-limited if we don't do anything.)
If the person we chose is town and the mafia don't kill them, we're happy because we've destroyed all the ammo (or all but a small amount of it that the mafia hide) (we don't have a way to destroy items short of executing people, but it might be worth executing someone to get rid of a bunch of ammo).
This scheme might be optimizable, but before I optimize it, are the assumptions valid? That is, do people start out with about one ammo each? Is the gun even a mafia item, or is it a vigilante item?