What's the expected number of 1-runs when tossing a fair coin 100 times;
where 1-run (for heads) is defined as HT or H for the last toss;
for example: THHTHTHTTH has 3 1-runs.
Now I understand the question is about just H or just T single runs -?
The guessed formula isn't correct IMHO.
It can be solved either inductively or deductively. Who do you like more, Newton or Sherlock Holmes?