A rough idea of judging whether a scramble, perhaps hand scramble, of a Rubik's cube has been done long enough is that "things" have gone through a state that is as far from the solved state as possible.
For example, every cubie has an antipode: during the scramble, every cubie must have passed through its antipode position at least once. Or, every cubie must have passed through its original position, but in an incorrect orientation. Or both of the two conditions, in either order.
Other variations possible, including the very difficult diameter of the full Rubik's cube graph (God's number). Or, always start scrambles from Superflip.
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