Ment
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The bite is only partially fatal.
So, here's a great idea. We can save the bitten person from death by taking advantage of the fact that the Mafia controls their vote. We execute the Neutral Neutral Villain (NNV), but we don't add the final vote. The Mafia won't be able to resist and, in order to hang the NNV, they'll add the vote from the bitten person. We'll find out who the bitten person is, and we'll heal them during the night! Profit! Yes, I have nothing better to do than come up with idiotic plans, I know.