These are my exact notes (I disregard the risk of mafia/mafia or me being the NK because they don't have an impact on my decision). In both cases, saving thrawn is the best action:
1. Assumption: Scum will always NK thraw if town/town
Both town: 70%
thrawn scum, sharrant town: 25%
thrawn town, sharrant scum: 5%
Save thrawn success: 75%
Save Sharrant success: 25%
2. Assumption: Scum will NK thrawn 67% if town/town, sharrant otherwise
Both town: 70%
thrawn scum, sharrant town: 25%
thrawn town, sharrant scum: 5%
Save thrawn success: 52%
Save Sharrant success: 48%
It's obvious that even under the most optimistic assumptions (case 1), I need to be close to 50% confident thrawn is town for him to be the best JK candidate. I think both the main assumption and me being 50% sure thrawn is town are false. However, I also need to consider how valuable thrawn and Sharrant are later in the game. If thrawn will be a better scum hunter, that gives some more weight behind the idea of JK him.
I think these are more reasonable assumptions, but still pretty optimistic:
3. Assumption: Scum will NK thrawn 70% if town/town, sharrant otherwise
Both town: 45%
thrawn scum, sharrant town: 50%
thrawn town, sharrant scum: 5%
Save thrawn success: 36.5%
Save Sharrant success: 63.5%
As we can see I think a Sharrant JK will be successful almost twice as often. Thrawn needs to be one hell of a scum hunter to make up for that difference.
In the end I decided against a thrawn JK not because I realized my assumptions sucked, but because 1) if I'm able to protect a confirmed townie until late game that'll give additional benefits (for example: limiting our lynching options through process of elimination) and 2) thrawn came under fire late n1, regardless if it was townies or scum attacking him it makes him a less likely NK target because scum can be setting up a later mislynch.
EDIT: Save thrawn success = prob(thrawn = town and NK target)
EPT
