The cluster illusion makes us think that random processes are nonrandom and vice versa. When Tversky and Kahneman showed people (including statisticians) the results of real strings of coin flips, like TTHHTHTTTT, which inevitably have runs of consecutive heads or tails, they thought the coin was rigged. They would say a coin looked fair only if it was rigged to prevent the runs, like HTHTTHTHHT, which “looks” random even though it isn’t.64 I witnessed a similar illusion when I worked in an auditory perception lab. The participants had to detect faint tones, which were presented at random
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