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How does he or she convey this information to the rest of the innocents without the wolves finding out also?
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The seer would have to step forward and expose his/her identity. But there is a point that, if reached, it won't really matter if the wolves know who the seer is.
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So don't bother with the condescending and infuriating...
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What about my "arrogant healer" role don't you understand?
And now let's look at your math skills...
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Sure it will, math-boy. If we take one innocent out of the pool, then there are less people for the wolves to kill, thereby increasing their chance of randomly selecting someone we want to keep. If you need smaller numbers, here are some.
There are three fish in the pond, a blue fish, a red fish, and an orange fish. The fisherman is guaranteed to catch one. He has a 1:3 chance of catching the blue fish. If we take out the orange fish and leave it on the shore to die or something equally gross, then there are only two fish left. It means that the fisherman now has a 1:2 chance of getting the blue fish. Capiche?
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I can see how this might seem logical to you if you don't think too hard, but there is a huge mistake in your little fish-catching analogy.
You are assuming that it is possible to fish without one of the fish being taken out. That is not the case today. You said-
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If we take one innocent out of the pool, then there are less people for the wolves to kill
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But what you forgot is that someone will be taken out of the pool NO MATTER WHAT, whether my plan is instituted or not! So your little fish thing doesn't apply at all.
Don't try to beat me at math.