Math:
Your no-exile thought relies on Swowl being town, yes? As you say, if we no-exile here and Swowl is scum, Swowl wins.
So in your thought process here, you are town, as is Swowl. That means there are two scum in {Galzria, Didds, Scola}.
First: Why did the Fortress protect against Swowl's attack N2 if there were scum in it? (This is the same question Didds has asked me, and I've answered her in the Fortress).
Second: You are assuming Swowl has a 2-in-4 chance of getting the kill correct at night. But shouldn't you have a 2-in-3 chance of getting right by exiling from your scum pool today? Why would no-exile be your default choice here?
*****
If there are 2 scum and Swowl is town, and we mis-exile today (let's say me):
Night goes: 2 Town (Swowl + 1), 2 Scum
Swowl has a 2-in-3 chance of shooting Scum. He should NOT shoot Didds (Hated). He should shoot Math or Scola. Assuming Scum kills Swowl to remove the Sword from play at that point, the final day is {Math/Scola} vs Didds. Didds is hated, and takes 1 to exile. If Didds is scum, town wins. So this basically results in Swowl having a 1-in-2 chance of hitting scum (between Scola & Math), the same as you're suggesting Swowl has if we no-exile here. It also relies on the fact that both Didds and I are not town - but as we're both hated and take just 2 to exile, I assume if we both WERE town scum would've exiled us already and won the game - therefore we cannot both be town.
Actually - I think town has this at a 50% to win, based purely on Swowl's choice between Math/Scola:
Exile Me/Didds. I'll flip town, Didds will almost certainly flip scum. Literally doesn't matter:
Assume you flip me, and I turn town. Swowl picks between Math & Scola. If he picks wrong, town loses. If he picks correctly, and scum kills him, the final day is: {Math/Scola} vs Didds, and Didds is hated, town wins on Didds exile.
Assume you flip Didds, and she turns scum. Swowl picks between Math & Scola. If he picks correctly, town wins. If he picks wrong, the final day is: {Math/Scola} vs Me, and I'm hated, scum wins on my exile.
Am I missing something here? I guess what I'm missing is that if Didds and I are both town (as is Swowl), then scum wins (Exile one town, Swowl shoots either Math or Scola, both of which would be scum, and the final day would be whichever he didn't shoot against whichever Hated person didn't get exiled. But if Math & Scola are both scum, why haven't they exiled Didds or me yet?)