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Except that simply isn't true. When randomly performing rotations you're much more likely to end up in certain states (as I mentioned in my other comment). Whether you make 10k random rotations or 20 random rotations you're still more likely to end up in a certain state.

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In theory I agree with you, in practice I don’t.

Sum 20 coin flips mod 3 and you can find the bias in the output. It’s hard with a small sample set, but you could do it. Sum 10k coin flips and it’s a different situation.

Eventually you fall through the noise floor for any reasonable sample size.

It's almost certainly less effort (though arguably also less fun) to write a valid state checker than it is to prove that N random cube operations will yield something that's within some tolerance of a uniform distribution across all legal cube states.

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