I thought of a (perhaps silly) way to check if Ama is rogue: We can set a trap on her as either rogue or vigilante. This has the disadvantage of possibly losing us a set a trap, but it's one way to be absolutely certain of it without one of us sticking their neck out to contact her.
If we set a trap on her as rogue and she is actually rogue, then we get the charge back when she dies (if she ever gets lynched, e.g.). It just ties it up so that we can't use one of our charges again until she's dead.
If we set a trap on her as rogue and she is actually vigilante, then we lose the charge and we're very sad. But at least we know her role and can kill her eventually, perhaps using the other set a trap charge.
If we set a trap on her as vigilante and she actually is rogue, then we lose the charge and we're very sad, but we gain a rogue.
If we set a trap on her as vigilante and she is actually vigilante, then we get a free kill on her.
If we take a maximin approach to this payoff matrix, I think we'd rather set a trap on her as vigilante. But I think she's more likely to be a rogue than a vigilante, so maybe the expected value is better if we set a trap on her as rogue. I'm not sure how bad it is to have one of our set-a-traps tied up until our rogue dies...
What do you guys think?
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