I was reading this interesting article on hot hands and streaks in sports. The article revolves around the 16 possible sequences of 4 coin flips (H = heads, T = tails):
HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT
The article states the following:
[I]n the sixteen length-four sequences, there are only eight that have any occurrence of HH, but there are eleven that have an occurrence of HT. That is, the distribution of HH and HT is not uniform in the fourteen sequences.
And then there is a footnote:
At first, this may seem paradoxical since the two counts might be expected to be equal by “symmetry”. But, the two occurrences are not symmetric, which I leave you to ponder.
Since then I try to think of an explanation on why this is the case? Why are there more sequences in which at least one
HT occurs than there are sequences where at least one
Of course, by simply looking at each sequence, I can see (and count) the
HT occurrences, but I would like to know why exactly (which property of the sequences) leads to this fact.