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Tiiba comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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If Sleeping Beauty doesn't know what day it is, what could possibly motivate her to say that the probability of heads is something other than 50%? I mean, she knows nothing about the coin except that it's round and shiny, and the metal costs more than the coin does.
Unless I misunderstood, this problem is smoke and mirrors.
If she thinks she will be asked what the coin shows more times if it is tails.