I enumerated the sequences that the article mentioned, and counted how often a tail filled a head, and vice versa, and got 12 instances where a head follows a head, and 10 where a tail followed a head. So there is a difference for just counting up all the possible 4 flip sequences where at least one of the first three is a head. However, doing a randomised test where I generated a random 4 length sequence, rejecting it if none of the first three was a head, then doing the same test showed no real difference.

Code here https://github.com/gregryork/Flips/tree/master/src/flips