Okay, so I have done some calculating. For this post it will be assumed the of the remaining players that two are mafia, two are town and Crazy is SK. A summary will be included at the end.
A red number indicates a scenario in which the mafia win, green for town and indigo for Crazy. A black number indicates a scenario that does not end the game and leads to more options.
DAY THREE:
(1)
Town lynch, scum kill the last of the townies and have a 2:1 majority and win. Mafia victory.
(2)
If we lynch Crazy, scum still kill one of the townies and have a 2:1 majority and win. Mafia victory.
(3) Scum lynch allows the game to go on. So lets see what outcomes arise from optimal play if we hit mafia with the lynch today....
NIGHT THREE:
(1)
Mafia night kill one of the town. That leaves the next day with 1:1:1. On Day Four, Crazy kills someone and wins. Not good for mafia or town, both lose.
(2) Mafia try to kill Crazy and he can be killed, then Crazy loses and the next day is a 2:1 with a chance for town and mafia to win.
(3) Mafia try to kill Crazy and he is not night killable or if mafia choose to submit a no-kill, then we are left with 2:1:1. This next day scenario will be under DAY FOUR.
DAY FOUR (A)
, If Crazy chooses not to day kill anyone:
(1)
Town lynch. Scum can kill town at night, and lose to Crazy's kill the next day, try to kill Crazy again in case night immunity was only one use, or not kill anyone leaving the 1:1:1 scenario as listed above (both town and mafia lose). Either way town loses. Mafia have a slim shot at victory here and Crazy has a good shot at winning.
(2)
A Crazy lynch here leads to a scum victory as they kill one of the townies the following night.
(3)
A scum lynch will lead to a night without a kill and 2 townies versus Crazy. Crazy kills someone the next day before he can be lynched and wins. Or in the unlikely event both town get into the thread and vote crazy the town wins (as long as any other chance for town to win remains, I am not shooting for this option; it is a last resort).
DAY FOUR (B)
, If Crazy day kills town:
(1)
The last two players lynch Crazy and mafia win.
(2)
Mafia and Crazy lynch town and Crazy wins.
(3)
Town and Crazy lynch mafia and Crazy wins.
(4)
No lynch leads to Mafia killing the last town and then Crazy wins the next day. Or Mafia attempt to kill Crazy and either win by killing him or send us into 1:1:1 scenario listed above that town cannot win.
DAY FOUR(C)
, Crazy day kills mafia:
(1)
The last two town lynch Crazy and win.
SUMMARY/THOUGHTS:
If Crazy is able to be killed at night he cannot win, as optimal play for scum is to shoot at Crazy (unless by shooting at town they win, and thus Crazy cannot win regardless). Therefore I believe that Crazy would not have claimed unless he thought it would not decrease his chances of survival. Therefore I am going to largely discount Night 3-2 as a possibility.
If we get a mafia lynch today, Crazy wins in all scenarios where he does not day kill a player tomorrow and is not lynched. Day killing a player does not prevent his lynch as it would take every other player in the game voting him to lynch him at this point, killing someone would therefore not make a difference.
This makes it in Crazy's best interest not to shoot anyone tomorrow. Town can't win if Crazy doesn't shoot tomorrow (except for rare lucky circumstance in Day 4a-3). As long as he doesn't shoot anyone Crazy cannot lose if we lynch mafia today unless Crazy is lynched. Since shooting anyone will never prevent his own lynch if it were to happen, Crazy has no motivation to shoot anyone.
If scum want to win they have to avoid being lynched today or ensure Crazy's lynch on a future day.
Optimal play dictates that town will not win if the setup has left us with two mafia, two town and a serial killer.
My next post will include a complete scenario chart if there were only two mafia players at the beginning of the game.
I'm such a good lover because I practice a lot on my own.