Oh, please. Unless ATPG is killed or 2 kills show up you can't determine anything based on what happens. It's Mafia 101 to leave a detective alive for a short period of time to make the town lynch him. I would agree with lynching ATPG next if we were near the end-game, but we're not close to that if there's only 1 kill per night. Under the circumstances, I see no pressing need to lynch ATPG unless we get evidence to show he's a mafioso. If he is lying, he'll be lynched eventually. It's kind of hard to forget about someone who has publicly claimed to be a detective.
I see no possible benefit to killing ATPG next round. If he is mafioso, he'll have to limit his kills to pretend he's the detective. That alone works well for the town and gives us enough time to judge him. If he's the detective, lynching him is clearly a bad idea.
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