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The main takeaway:

For an effect of human psychology to be real, it cannot be rigorously replicated using random noise. If the human brain was predisposed to choose heads when a coin is flipped, you could compare this to random predictions (heads or tails) made by a computer and see the bias. A human would call more heads than the computer would because the computer is making random bets whereas the human is biased toward heads. With the Dunning-Kruger effect, this is not the case. Random data actually mimics the effect really well.