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A comment on 40k coin tosses yield ambiguous evidence for dynamical bias.
"sum (20000 choose x)/2^20000 for x from 10231 to 20000",
which Wolfram Alpha evaluates to 0.00056.
The probability of getting a number of flips that differs from 10000 by at least 231 is twice that, so about 0.001.
So, in fact, the probability of this happening by dumb luck is about 1/1000. That's pretty strong evidence.
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"sum (20000 choose x)/2^20000 for x from 10231 to 20000",
which Wolfram Alpha evaluates to 0.00056.
The probability of getting a number of flips that differs from 10000 by at least 231 is twice that, so about 0.001.
So, in fact, the probability of this happening by dumb luck is about 1/1000. That's pretty strong evidence.