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James_Ernest comments on Jokes Thread - Less Wrong Discussion
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Um.
Probability of a head = 0.5 necessarily means that the expected number of heads in 1000 tosses is 500.
Probability of a head = 0.6 necessarily means that the expected number of heads in 1000 tosses is 600.
I don't think so. None of the available potential coin-states would generate an expected value of 600 heads.
p = 0.6 -> 600 expected heads is the many-trials (where each trial is 1000 flips) expected value given the prior and the result of the first flip, but this is different from the expectation of this trial, which is bimodally distributed at [1000]x0.2 and [central limit around 500]x0.8