If you need a long-run frequency for ‘fairness’, is it sufficient to have a “fair coin” (rather than a “fair coin flip”)? By a fair coin I mean a coin that has been flipped many times in the past to establish non-predictability. Then the game itself doesn’t need to be repeated for it to be well-defined, but it seems to retain more of the original problem’s tension.
If you need a long-run frequency for ‘fairness’, is it sufficient to have a “fair coin” (rather than a “fair coin flip”)? By a fair coin I mean a coin that has been flipped many times in the past to establish non-predictability. Then the game itself doesn’t need to be repeated for it to be well-defined, but it seems to retain more of the original problem’s tension.