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Some of my math. This post is in response to Ong's proposed strategy.
Killing vanilla is optimal I believe because I think I have looked at two vanillas and hope to again tonight.
You think you have looked at two vanillas? Doesn't the seer know the role of the people he scans?
Imagine if we have 9 players left with 4 wolves and 3 specials. That leaves 2 vanillas, who, if both are confirmed, locks the game for us. I want an extra clear because I can't expect people to accept my claim today, which means you can wait for me to be nommed before accepting me as seer.
Imagine if we have 9 players left with 3 wolves and 3 specials. That leaves 3 vanillas, meaning I need four clears to lock the game. The game will be locked from my pov, but I need to die before people start lynching based on my conclusions, which buys the wolves a day, and thus gives them a chance of recovering.
Let's use the numbers from this game. Throughout this analysis I am going to ignore the possibility of an angel blocking a nom and I will assume a special does not get eaten.
scenario 1 - a villager is lynched at the end of day 3
end d3: 7villagers 4wolves, villager lynched
end n3: 6v 4w, villager eaten (43% chance it's a special)
scenario 2 - a wolf is lynched at the end of day 3
end d3: 8v 3w, wolf lynched
end n3: 7v 3w, villager eaten (38% chance it's a special)
day 4 begins. Suppose the specials out themselves, and your scans are all on vanilla villagers.
Ong is the true seer possibility:
scenario 1
start d4: 6vc 4w (3 confirmed specials, 3 scanned villagers). The village wins immediately if the wolves do not counterclaim the seer . Assume the wolves counterclaim all the specials. One wolf will pretend to be the true seer and give his own list of "confirmed" villagers, one will pretend to be the angel, and one will pretend to be the vig. We're back to square 1 and the village doesn't know anything for sure. Therefore, the count is really 6v 4w. The end of day 4 has 2 possibilities...
end d4 1: 5v 4w, villager is lynched.
And its night has 3 possibilities.
night d4 1 1: 4v 4w, villager eaten, vig either shoots a villager that was nommed or holds his fire.
night d4 1 2: 3v 4w, villager eaten, vig shoots a villager.
night d4 1 3: 4v 3w, villager eaten, vig shoots a wolf, probably the fake vigilante.
d4-1-1 and d4-1-2 are immediate losses for the village. d4-1-3 looks very bad for the village and the village still doesn't know if Ong is for real or not.
end d4 2: 6v 3w wolf is lynched.
And its night has 3 possibilities.
night d4 2 1: 5v 3w, villager eaten, vig either shoots a villager that was nommed or holds his fire.
night d4 2 2: 4v 3w, villager eaten, vig shoots a villager.
night d4 2 3: 5v 2w, villager eaten, vig shoots a wolf, probably the fake vigilante.
The village is still in contention to win, and d4-2-3 looks quite good for the village. The village still doesn't know if Ong is for real or not.
The numbers all look better on scenario 2, and the seer has more time to find and confirm villagers and wolves. It should be clear lynching a wolf is always better for the village.
Here is the "Ong is a wolf" possibility where a villager is hung tonight, the angel and the vig come out and they are genuine, and the real seer remains quiet.
start d4: 2v confirmed 4v unconfirmed 4w
Wolf ong gives his list of "3 living villagers" and I call them unconfirmed because all we have is Ong's word. He will include at least 1 wolf, but he may include all the other wolves as part of his list of confirmed villagers. Doing so guarantees that the village hangs a vanilla villager at the end of day 4.
end d4: 2v confirmed 3v unconfirmed 4w, a villager is lynched. This alone is not enough information to tell whether or not Ong is the seer.
And this night has 3 possibilities.
night d4 3 1: 4v 4w, villager eaten, vig either shoots a villager that was nommed or holds his fire.
night d4 3 2: 3v 4w, villager eaten, vig shoots a villager.
night d4 3 3: 4v 3w, villager eaten, vig shoots a wolf.
And we still don't know Ong's true identity after all of this.
Ong, if you are the real seer, you came out way too early.
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