I don't think that's true. I think that the average number of flips before _stopping_ might be 3, but it doesn't become more likely to get HT simply because you're also looking for HH (or vice versa).
It turns out that the average number of flips to get HH and HT is 3 - someone else on the thread described it well - on average, the number of flips to get to a "H" will be 2, and then you will always stop on the next flip - 50% at flip 3 with a HT, and 50% at flip 3 with a HH. Explained that way, it makes sense that the average number of flips is 3.
But, I still find it strange that if you are flipping with one particular scenario in mind, HT or HH, that the average number of flips goes from 3 to 4 or 6, even if I can reason it out with a bit of thinking.
But, I still find it strange that if you are flipping with one particular scenario in mind, HT or HH, that the average number of flips goes from 3 to 4 or 6, even if I can reason it out with a bit of thinking.