More streakless != more random.
This is very true. Randomness is, by nature, lumpy. But we human beings are *terrible* judges of randomness, and we mistakenly equate even distributions with random ones.
I had a friend in gradutate school who did research in this area, and he had an experiment he always liked to do with the undergrad psychology students. He would ask everyone in the class he was TA'ing to write down the outcomes of 200 coin flips, either by actually flipping a coin 200 times, or by faking the results, but without telling him which. The next day, he would collect the papers, and, by the end of the class, he would have sorted them into piles -- real outcomes, fake outcomes -- and he was right the overwhelming majority of the time.
I asked him how he did it. and he told me that he literally did one thing, and one thing only -- he checked each sequence to see if it contained a run of either 7 heads in a row, or 7 tails in a row. If it did, the sequence was probably real. If it didn't, it was probably fake.
Flip a coin 200 times, and you're likely to get at least one run of 7 heads or tails in a row. But, ask a human being to fake 200 "random" coin flips, and they won't make streaks that long, because we think that such streaks look too "non-random."
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@ Grifter -- Your points in response to mine were all totally reasonable, and I'm happy to stand corrected.
With that being said, it still bugs me when people shuffle my deck. I'll concede that I don't have a rational basis for feeling that way, but it does bug me.
That's on me, I guess.