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That's not what I was trying to get at. For even a single coin flip, we still need a language to talk about the situation when you and I can't predict it. If I flipped a hypothetical coin that poofs out of existence after a single flip (or more generally single-time events like elections or poker games) the usual probability language applies. No law of large numbers necessary.

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You mean "unpredictable"?

Exactly, yes. We have a language of mathematical unpredictability that applies to many things independently of whether the universe is deterministic. Fundamental unpredictability is irrelevant to practical unpredictability, but when you replace the word "unpredictable" with the word "random" people get weird about it. It's the same damned mathematical theory. Fundamental randomness is irrelevant to practical randomness.

Perhaps that language is time. Literally no research has been done into the analysis of precise time series observer effect data.

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