Okay here we go again.
Again assuming that Volt will not protect anyone.
Firstly assume that Fire will kill Volt Tonight and otherwise both scum will scumhunt.
1 IC, 2 VT, 2 scum
Lynch VT (1/2): LOSE* (total = 1/2)
Lynch scum (1/2): 1 IC, 2 VT, 1 scum => 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 1/2*2/3 = 1/3)
- Lynch scum (1/3): WIN (total = 1/2*1/3 = 1/6)
No-lynch: 1 IC, 2 VT, 2 scum
- Ice kills VT (2/3): 1 VT, 2 scum => no-lynch**
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 2/3*1/2 = 1/3)
- 2 scum die (1/4): WIN (total = 2/3*1/4 = 1/6)
- Nobody dies (1/4): LOSE*** (total = 2/3*1/4 = 1/6)
- Ice kills Fire (1/3): 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 1/3*2/3 = 2/9)
- Lynch scum (1/3): WIN (total = 1/3*1/3 = 1/9)
So if we lynch:
Pr(WIN) = 1/6 ~ 16.7%
Pr(LOSE) = 1/2 + 1/3 = 5/6 ~ 83.3%
If we no-lynch:
Pr(WIN) = 1/6 + 1/9 = (3+2)/18 = 5/18 ~ 27.8%
Pr(LOSE) = 1/3 + 1/6 + 2/9 = (6+3+4)/18 ~ 72.2%
Now assume that both scum will scumhunt ahead of killing Volt.
1 IC, 2 VT, 2 scum
Lynch VT (1/2): 1 IC, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 1/2*1/2 = 1/4)
- 2 scum die (1/4): WIN (total = 1/2*1/4 = 1/8)
- Nobody dies (1/4): 1 IC, 1 KVT, 2 scum => no-lynch => WIN**** (total = 1/2*1/4 = 1/8)
Lynch scum (1/2): 1 IC, 2 VT, 1 scum => 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 1/2*2/3 = 1/3)
- Lynch scum (1/3): WIN (total = 1/2*1/3 = 1/6)
No-lynch: 1 IC, 2 VT, 2 scum
- 2 VTs die (2/9): LOSE*** (total = 2/9)
- 1 VT dies, 1 scum dies (4/9): 1 IC, 1 VT, 1 scum
- Lynch VT (1/2): LOSE (total = 4/9*1/2 = 2/9)
- Lynch scum (1/2): WIN (total = 4/9*1/2 = 2/9)
- 2 scum die (1/9): WIN (total = 1/9)
- Nobody dies (2/9): 1 IC, 1 KVT, 1 VT, 2 scum
- Lynch KVT (1/4): 1 IC, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): LOSE (total = 2/9*1/4*1/2 = 1/36)
- 2 scum die (1/4): WIN (total = 2/9*1/4*1/4 = 1/72)
- Nobody dies (1/4): 1 IC, 1 KVT, 2 scum => no-lynch => WIN**** (total = 2/9*1/4*1/4 = 1/72)
- Lynch VT (1/4): WIN**** (total = 2/9*1/4 = 1/18)
- Lynch scum (1/2): 1 IC, 2 VT, 1 scum => 2 VT, 1 scum
- Lynch VT (2/3): LOSE (total = 2/9*1/2*2/3 = 2/27)
- Lynch scum (1/3): WIN (total = 2/9*1/2*1/3 = 1/27)
- No-lynch: 1 IC, 1 KVT, 1 VT, 2 scum
- 1 VT dies, 1 scum dies (1/2): 1 IC, 1 VT, 1 scum
- Lynch VT (1/2): LOSE (total = 2/9*1/2*1/2 = 1/18)
- Lynch scum (1/2): WIN (total = 2/9*1/2*1/2 = 1/18)
- 2 scum die (1/4): WIN (total = 2/9*1/4 = 1/18)
- Nobody dies (1/4): 1 IC, 2 KVT, 2 scum => no-lynch => WIN**** (total = 2/9*1/4 = 1/18)
So if we lynch:
Pr(WIN) = 1/8 + 1/8 + 1/6 = (3+3+4)/24 = 10/24 = 5/12 ~41.7%
Pr(LOSE) = 1/4 + 1/3 = (3+4)/12 = 7/12 ~ 58.3%
If we no-lynch (and no-lynch again if necessary):
Pr(WIN) = 2/9 + 1/9 + 1/18 + 1/18 + 1/18 = (4+2+1+1+1)/18 = 9/18 = 1/2 = 50%
Pr(LOSE) = 2/9 + 2/9 + 1/18 = (4+4+1)/18 = 9/18 = 1/2 = 50%
*Since there will either be only 2 scum or 1 scum and 1 Town remaining.
**I'm assuming that with 1 VT, 2 scum such that scum still don't know who the other scum is that the no-lynch will be allowed to go through, since they will still want the other to think they are Town.
***I'm counting 1 IC or KVT and 2 scum during Day as a loss. Maybe they could convince one of the scum to no-lynch, but given that both scum know who each other are, they know for sure that a no-lynch is a guaranteed loss. Really this could go either way, I'm not sure.
****I'm counting the situation in which both scum know the other at Night as a win, since we're assuming both are scumhunting.
KVT = Known (to scum) VT ie a VT who has been targeted by both scum at once, and has thus survived, and then will no longer be targeted by scum since we're assuming scum will be scumhunting.
So I'm going to go ahead and
Vote: no-lynch again.
As boring as this is, I think this gives us the best chance of winning. If no one dies Tonight, we no-lynch again tomorrow.
Now obviously this analysis is meant to be a tool, something we use to help us rather than dictate what we do. If we're super confident that we know who both the scum are, then lynching them Today and Tomorrow will win the game for us without leaving anything to chance. Of course, lynching a Townie Today could very well be an instant loss.