The Saucepan Man:
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It could have been different - the Hunter and one Wolf could have cancelled each other out, leaving a Wolf v an innocent (albeit, in that case, the Cursed).
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But wouldn't wolf vs. innocent on the last day be a wolf victory?
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Well, the Hunter can, so why not the Wolves.
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Not necessarily - when I was the Hunter in Alcarillo's game, I had to hunt every Day and every Night.
Fordim:
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If the wolf takes out the innocent, then next day double lynching and wolf loses.
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If wolf vs. hunter were deemed not to constitute a wolf victory
a priori then this would be correct and the wolf would have a one in four chance of winning if he/she killed someone (1/2 chance of getting the hunter times 1/2 chance that the hunter hunted the innocent). And there would be a 1/2 chance of a draw and a 1 in four chance of a villager win.
But if wolf vs. hunter is a wolf win (as I think it ought to be) then it's a 3 in 4 chance of winning for the wolf and 1 in 4 for the villagers, assuming the wolf attacked someone.
But I think you've incorrectly tallied the probabilities for the other scenario (wolf does not attack anyone):
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Hunter gets lynched, wolf wins.
Innocent gets lynched, wolf wins.
wolf gets lynched, wolf loses.
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I would correct as follows:
1. 1/3 chance that the hunter gets lynched, in which case:
a. 1/2 chance he hunts the innocent that day (wolf wins)
b. 1/2 chance he hunts the wolf (villagers win)
2. 1/3 chance the innocent gets lynched (wolf wins
or draw depending on wolf vs. hunter rule)
3. 1/3 chance that the wolf gets lynched (villagers win)
So if hunter vs. wolf is a draw then we have a 1/4 chance of a wolf win if the wolf attacks that night and a 1/6 chance if he does not.
If hunter vs. wolf is a wolf win then we have a 3/4 chance of a wolf victory if the wolf attacks that night and a 1/2 chance if he does not.
Either way, it's better for the wolf to attack.