You're right, I didn't word that very clearly. I meant "more strings contain this substring", not "this substring occurs more times total" (which, as you say, w

You're right, I didn't word that very clearly. I meant "more strings contain this substring", not "this substring occurs more times total" (which, as you say, would be the usual meaning of "matches happen more frequently"). Why care about strings containing a particular substring versus total number of occurrences? The article referenced this PDF: https://www.cs.cornell.edu/~ginsparg/physics/INFO295/mh.pdf https://www.cs.cornell.edu/~ginsparg/physics/INFO295/mh.pdf, which is about how many coin flips it takes to see a run of N heads. That's really what the argument in the second half of my post is about, but it applies to the "how many strings contain this substring" problem too, and that one seemed simpler to draw a table for.