Basically we have a four way POE between RT, Mikal, Shining, and Thoth at this point. There are nine players left. Assuming two scum, this is the worst case scenario:
DP 2: XOOOOXOOO 25% chance to hit scum in POE
DP 3: XOOOXOO 33% chance to hit scum in POE
DP 4: XOOXO 50% chance to hit scum in POE
Gameover if we guess incorrectly
Scum will likely NK the town players outside of the POE up until we hit scum, at which point they will target town players within it. We have a 25% chance to not hit scum within the POE before the end of the game, a 50% chance to not hit them before the last DP. Keep this in mind when determining who to protect and who to investigate. Also keep in mind that if we hit scum early we will town confirm several players.
If we hit scum today (0ML in POE):
DP 3: XOOOOOO 20% chance to hit scum
DP 4: XOOOO 25% chance to hit scum
DP 5: XOO 33% chance to hit scum
Gameover if incorrect - 40% chance to win
If we hit scum DP 3 (1ML in POE):
DP 4: XOOOO 33% chance to hit scum
DP 5: XOO 50% chance to hit scum
Gameover if incorrect - 67% chance to win
If we hit scum DP 4 (2 ML in POE):
DP 5: XOO 50% chance to hit scum
Game over if incorrect - 50% chance to win
Oddly enough, the math works out when you factor out scum incentives when nking that the longer we take to lynch scum in the POE the more town confirmed players we take into the late game when there are less places for scum to hide and our chances to hit them actually become quite high. The middle option is actually best, but really the takeaway is that we shouldn't worry too much about hitting scum today and just gather info so we can solve the late game.