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    $\begingroup$ Nice. I teach this in my class. And the intuitive reason that if a pattern matches one of its shifts it has a higher propensity to occur in clusters, delaying the first occurrence, in expectation. $\endgroup$
    – kodlu
    Commented Apr 15, 2020 at 3:40
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    $\begingroup$ And if the letters are not equiprobable, add the reciprocal of the product of probabilities of letters in the $n$ string... $\endgroup$ Commented Nov 15, 2022 at 23:14