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Here's the scenarios as I see it:
We start with 3 wolves + cole (very unlikely) - The game is basically alreayd over regardless of who is lynched tonight. Villager/Cole goes down, it's 2-2 and game over. Wolf goes down, they convert Lathum and it's 2-2 game over.
We start with 3 wolves, no Cole (very unlikely) - I believed Lathum when he said he's Cole even before hoops swearing he knows Cole is in the game. We lynch a villager/Cole then it's over. We lynch a wolf then we keep playing.
We start with 2 wolves + Cole (very likely) - Obviously if we get the last wolf it's game over we win. If we lynch a villager (3 out of 5 left) then Lathum gets converted and it's 2-2 game over. I think this is where we are, not sure on who is the wolf.
[b]We start with 2 wolves and no Cole (very unlikely) - Even if you ignore logic and hoops vouching for Cole, why does Lathum claim Cole unless he's a wolf? It puts a target on his back.
Lathum coming out - Lathum wants to win the game, I think he thought he'd be safe from the villagers and if he survives the vote, gets converted to win with the wolves.
Based on the above, I think our best play is lynch Lathum today ensuring we're playing another day and go from there. With Cole lynched today, the wolves can't win today/tonight.
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