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No, that is not correct. Have a look at my list of 16 length-4 sequences. Exactly half of all flips-after-heads are heads, and the other half tails. Exactly half of all flips-after-tails are heads, and the other half tails.

The result of Miller and Sanjuro is very specifically about "averages of averages". Here's a key quotation:

"The relative frequency [average #1] is expected [average #2] to be ...". M&S are

notsaying that in finite sequences of trials successes are actually rarer after streaks of success. They're saying that if you compute their frequency separately for each of your finite sequences then the average frequency you'll get will be lower. These are not the same thing. If, e.g., you run a large number of those finite sequences andaggregatethe counts of streaks and successes-after-streaks, the effect disappears.