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There's another version where a stats professor divides people into two groups. One group flips a coin 50 times and writes on a whiteboard the results. The other comes up with 50 results.

They leave the room and when they come back immediately know which is which. Specifically because of the over-alternation that yours mentioned. A string of HHHHHH is exactly as likely as HTHTHT, but people don't intuit that.

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> A string of HHHHHH is exactly as likely as HTHTHT, but people don't intuit that.

this contradicts the comment you're replying to. the premise they are having is that HTHTHT is "less random" than HHHHHH.

The strings are equally likely if they're being purely randomly selected, but not if they're being selected by people with a poor understanding of random. In the latter case, people are more likely to select HTHTHT.

I wonder what thought process led you to believe that even though the strings are equally likely and random, people who don't choose the one you think is more random have somehow inferior understanding of randomness

The issue the anecdote is reflecting is that across the data of 50 naive made-up coin tosses there are too many alternating sequences and probably zero HHHHHH.

and it's different from 50 randomly selected true coin tosses because you think it's impossible for all of them to alternate?

I understand your point, but the context is that repeatedly, experiments have shown that humans inject too much pattern to be good rngs. It turns out that is visible with training after the fact.

Yes, it is possible that any two 50-sequence patterns are actual rng. But some of them are much more likely, and we can tell.

> some of them are much more likely, and we can tell

Yeah if you define randomness as subjective "stuff humans can't predict" then sure...

I'm not sure what your point is. A collection of samples were taken from humans, and they did not form a uniform distribution. Samples from an unbiased RNG are much closer to uniform.

Are you saying we should ignore the distribution we observe from humans and predict them as uniform anyway?

You say yourself "strings are equally likely if they're being purely randomly selected". So you move the goalpost to define "random" as "whatever a human would think is random".

> Samples from an unbiased RNG

you mean a PRNG.

> Are you saying we should ignore the distribution we observe from humans and predict them as uniform anyway?

I'm saying the exercise in general is a little pointless, but that's fine.

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