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I don't quite understand your calculations. There are only 13 people in total, 8 of whom are villagers (apparently). Two have already been killed. If another villager is executed, there will be 7 villagers left against 4 mafia and the Maniac. Without a healer, things could get really bad after the next night, right?
There are currently 11 people in total. The Maniac, 4 mafia, and 6 villagers. Let's say the mafia kills two of us, and we use Night Neutral Vote. 1-4-4. A total of 9 people. And Tox wrote that more than a third of the people are needed for an execution, which means 4. Of course, the mafia won't be able to win directly, but if the town isn't united, they can execute whoever they need to. And they can also kill the maniac at night, which would result in 4-6, which is an absolute defeat for the town.
Added 1 minute ago
if the Maniac continues to destroy the town, then yes.
Even if he kills a mafia member, the situation won't become any better. Executing the "bad guy" and/or a successful block by the Inspector will help.