In all cases, DO NOT LYNCH FBI agent or Mafia claim. Lynch 1st Mafia claim the Day after claim.
Lynch Townie on Day 1, total 50% chance. On Day 2:
If Townie Night Killed (50%) 2+1v2v1, FBI Agent immediately claims. No SK CC will occur, as this would be suicide. Mafia may, but it is unlikely, as they ultimately gain no benefit. Investigation is NOT reflected in the percents, since there is an equal chance it will be mafia as it is to be town [As I said, we actually get better Day odds if we lynch a townie on Day 2 if two townies die on D1/N1. This is because it forces the SK to kill mafia on N2, which means that he cannot kill our FBI Agent]
---->Townie (40%) 1+1v2v1. SK must kill investigation. If mafia, that leaves us at 1+1v1v1. 16.67% odds.
---->Mafia (40%) 2+1v1v1. SK will kill FBI Agent. Leaves us at 2v1v1. 8.33% odds
---->SK (20%) 2+1v2.
If Mafia Night Killed (33.33%), 3+1v1v1. [optimal SK scenario] FBI Agent claims, with investigation if available. No CC will occur.
---->Townie (60%) 2+1v1v1. SK will kill Agent. Investigate is useless against mafia. 11.11% odds.
---->Mafia (20%) 3+1v0v1. SK will kill Agent. Effectively 2+1v0v1. 33.33% odds.
---->SK (20%) 3+1v1v0. 75% odds.
If FBI Agent Night Killed (16.67%) 3v2v1
---->Townie (50%) 2v2v1. SK must kill mafia to survive.
-------->Town NK(50%) Town/SK loss.
-------->Scum NK(50%) Leaves us at 2v1v1. 8.33% town odds
---->Mafia (33.33%) Death is 2v1v1 (Mafia win 12.5%), so Mafia will claim. Retry.
-------->2nd attempt
------------>Townie(60%) 2v2v1. SK must kill mafia (50% maf win). 2v1v1. 8.33% odds (total mafia odds 62.5%)
------------>Mafia(20%) Must lynch both claimants. Town/Mafia loss.
------------>SK(20%) Must lynch, followed by mafia claimant. 3v1, 75% chance of victory (25% mafia)
---->SK (16.67%)3v2. 12.75% odds.
-------->If mafia claim, outs self to mafia. Dead in any case, essentially odds-swinger.
------------>2nd attempt
---------------->Town(60%) 2v2v1
------------------->Town NKed(50%), 1v2v1 Mafia win
------------------->Mafia NKed(50%), 2v1v1, lynch claimed "mafia", 2v1, 33% odds.
---------------->Mafia(40%) 3v1v1
------------------->Town NKed, 2v1v1, lynch claimed "mafia", 2v1, 33% odds.
------------------->Mafia NKed, lynch claimed "mafia", Town victory.
-------->If no claim. 3v2. 12.75% odds.
Choose Mafia for Day 1 lynch, total 25% chance. Branching path:
If mafia claims mafia, try again. (total mafia odds: 16.14%)
-->2nd attempt
---->Townie(57.14%) 3+1v2v1. Assuming that SK does NOT target claimant to maximize his own odds.
------>Townie NKed(60%) 2+1v2v1, Lynch claimant. 2+1v1v1.
-------->Townie NKed(75%) 2v1v1. 8.33% odds.
-------->Mafia NKed(25%) 3v0v1. 25% odds.
-------->FBI Agent NKed(75%) 2v1v1. 8.33% odds.
------>Mafia NKed(20%) 3+1v1v1, Lynch claimant. Everyone "claims" an FBI target. 2+1+"1"v0v1.
-------->Townie NKed(50%) 1+"2"v1. All target "claim", before claim (may out liar). 50% odds.
-------->FBI Agent Clear NKed(25%) 1+1+"1"v1. Regardless of CC, 50% odds.
-------->FBI Agent NKed(25%) Clear's identity known. 2+1v1. 33% odds.
------>FBI Agent NKed(20%) 3v2v1, Lynch claimant. 3v1v1
-------->Townie NKed(75%) 2v1v1. 8.33% odds.
-------->Mafia NKed(25%) 3v0v1. 25% odds.
---->FBI Agent(14.29% - If uncountered, try again. If countered, lynch (no one will).
------>3rd attempt
-------->Townie(66.67%) 3+1v2v1
---------->FBI Agent NK(100%) - 3v2v1.
------------->Mafia (33.33%) Death is 2v1v1 (Mafia win 12.5%), so Mafia will claim. Retry.
---------------->2nd attempt
------------------>Townie(60%) 2v2v1. SK must kill mafia (50% maf win). 2v1v1. 8.33% odds (total mafia odds 62.5%)
------------------>Mafia(20%) Must lynch both claimants. Town/Mafia loss.
-------->Mafia(16.67%) 4+1v1v1
---------->FBI Agent NK(100%) - 4v1v1. Lynch claimant. 3v1. Go no Lynch, unless triple unanimous decision. 2v1. 33% odds.
-------->SK(16.67%)- No Night Kill means 4+1v2. Lynch claimant. 4+1v1. 80% odds.
---->Mafia(14.29%) - Lynch regardless of claim for consistency with SK false claim. SK will not target claimant.
------>Townie NKed(80%) - Lynch claimant. Everyone "claims" an FBI target. 2+1+"1"v0v1.
-------->Townie NKed(50%) 1+"2"v1. All target "claim", before claim (may out liar). 50% odds.
-------->FBI Agent Clear NKed(25%) 1+1+"1"v1. Regardless of CC, 50% odds.
-------->FBI Agent NKed(25%) Clear's identity known. 2+1v1. 33% odds.
------>FBI Agent NKed(20%) - Lynch claimant. 4v1. NK targets Townie. 3v1. No lynch. 2v1. 33% odds.
---->SK(14.29%) - Cannot false claim to survive. May be conflicting allegience report with known scum; unimportant. Lynch 2nd claimant to prevent time waste. 5+1v1 (87.7%). 5v1(80%).
If mafia does not claim mafia, lynch. 4+1v1v1. (Total mafia odds: 14.35%, better for them to claim)
Lynch SK on Day 1, total chance 12.5%. Branching Path:
If SK claims mafia, try again.
-->2nd attempt
---->Townie(57.14%) 3+1v2v1. SK is claimant.
------>Townie NKed(50%) 2+1v2v1, Lynch claimant. 2+1v2v0. 33.33% odds.
------>Mafia NKed(33.33%) 3+1v1v1, Lynch claimant. All "claims" an FBI target. 2+1+"1"v1v0. Investigation useless. 75% odds.
------>FBI Agent NKed(16.67%) 3v2v1, Lynch claimant. 3v2 25% town odds.
---->FBI Agent(14.29% - If uncountered, try again. If countered, lynch (no one will).
------>3rd attempt
-------->Townie(66.67%) 3+1v2v1
---------->FBI Agent NK(100%) - 3v2v1. Lynch claimant. 3v2 25% town odds.
-------->Mafia(33.33%) 4+1v1v1
---------->FBI Agent NK(100%) - 4v1v1. Lynch claimant. 4v1. 60% odds.
---->Mafia(28.57%) - Lynch regardless of claim for consistency with SK false claim. 4+1v1v1
------>Townie NKed(66.67%) - Lynch claimant. Everyone "claims" an FBI target. 2+1+"1"v1v0. Useless, 75% odds
------>Mafia NKed(16.67%) - Lynch claimant, town wins.
------>FBI Agent NKed(16.67%) - Lynch claimant. 4v1. 60% odds.
If SK simply wilts and dies, 4+1v2. 40% town odds.
Choose FBI Agent for Day 1 lynch, total 12.5% chance. Retry.
-->2nd attempt
---->Townie(57.14%) 3+1v2v1.
------>FBI Agent NKed(100%) 3v2v1
-------->Townie(50%) 2v2v1
---------->Townie NKed(50%) Town/SK loss
---------->Mafia NKed(50%) 2v1v1. Must lynch SK, then mafia, 8.33% odds
-------->Mafia(33.33%) 3v1v1
---------->Townie NKed(75%) 2v1v1. Must lynch SK, then mafia, 8.33% odds
---------->Mafia NKed(25%) 3v1. No Lynch. If No Kill is viable, 25% town odds, otherwise 33.33%
-------->SK(16.67%) 3v2, 25% town odds
---->SK(14.29%) 3+1v2v0 37.5% town odds
---->Mafia(28.57%) 4+1v1v1
------>FBI Agent NKed(100%) 4v1v1
-------->Townie(66.67%) 3v1v1
---------->Townie NKed(75%) 2v1v1. Must lynch SK, then mafia, 8.33% odds
---------->Mafia(25%) 3v1. No Lynch. If No Kill is viable, 25% town odds, otherwise 33.33%
-------->Mafia(16.67%) 4v0v1.
---------->Townie NKed(100%) 3v1. No Lynch. If No Kill is viable, 25% town odds, otherwise 33.33%
-------->SK(16.67%) 4v1, 60% town odds