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Jun
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comment parting integral into two parts, is this correct?
"Not always" — as in "almost never".
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Apr
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comment Can a coin with an unknown bias be treated as fair?
Your first paragraph may be theoretically true, but it still seems to be possible to define the fairness of a coin objectively, by considering ensembles. There is a configuration space describing the initial conditions of the problem. I can define 'local fairness' in a region as the fraction of configuration space volumes leading to T and to F. Like most dynamical systems, a coin will have a large enough region where initial conditions leading to T/F outcomes are strongly mixed, and 'local fairness' will be approximately constant. The closer it is to 1, the fairer the coin (by definition).