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Plasmon comments on Anthropics in a Tegmark Multiverse - Less Wrong Discussion
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Does your point remain valid if you take a realistic distribution over coin imperfections into account?
Possibly irrelevant calculation follows (do we have hide tags? Apparently not)
Suppose we have the simplest sort of deviation possible: let alpha be a small number
P(10 heads) = (1/2+alpha)^10
P(HTTHTHHHTH) = (1/2+alpha)^6*(1/2-alpha)^4
Remarkably (?)
dP(10 heads) /dalpha = 5/256 at alpha=0
dP(HTTHTHHHTH) /dalpha = 1/256 at alpha=0
It seems that simple coin deviations (which are by hypothesis the most probable) have a stronger influence on simple predictions such as P(10 heads) than on complicated predictions such as P(HTTHTHHHTH)