In post 828, GuiltyLion wrote:
I don't really follow 818 or how it contradicts 808
I think you're assuming mime tries to roleblock in the world where we lynch Thor whereas I believe Mime's best play is to not roleblock and assume mafia is killing Eragon
818 addresses why the mime should roleblock.
Assuming the case where the mime doesn't roleblock:
Mafia kills Eragon. We are now at 3v1v1. Mime has either a 1/4 or a 1/3 chance to stop the nightkill, depending on if we lynch. Mafia has the same odds of correctly shooting the mime, which they want to do. That means mime has a 3/16 or a 2/9 chance of outright losing the game (odds mafia hits mime and mime doesn't hit mafia).
Assuming the case that mime DOES roleblock:
Mafia attempts to kill Eragon. Mime attempts to stop mafia. Mafia has a 100% chance of correctly targeting. Eragon has a 1/5 chance of correctly targeting. Mime has a 1/4 chance of correctly targeting. (They know Eragon isn't the mafia.) That means mime has a 1/20 chance of autolose. Note, this is lower than the chance of autolose if they holster their roleblock, it's just an autolose to town instead of whichever faction plays better. If Mime successfully blocks, they allow one shot to hit Eragon the next night and then the game is nightless until either they win or lose. If Mime unsuccessfully blocks, it doesn't matter if Eragon has the same target as them, because then Eragon dies and can't tell us anything anyway. What does matter there is that it changes their 1/4 and 1/3 to 1/3 and 1/2. Which means, for the next day that mime has a 1/12 or a 1/6 chance at autolose. Much lower than the initial chances of 3/16 or 2/9. (Greater than 10% lower in the former case and greater than 5% in the latter.)
Simply put, holstering the shot increases the chance that mime loses to being shot by the mafia by more than the chance town wins off of a hail mary investigation. So mime has literally no reason NOT to take the chance on roleblocking mafia. Thor was just presenting the situation in a way in which the pro mafia choice of actions seemed like the pro mime set of actions when it really wasn't, but when one looks at the math it becomes obvious that that is the case.