How long until you first see HTH?
Asked at Jane Street
A fair coin is flipped repeatedly until the pattern HTH first appears.
What is the expected number of flips? Compare it with the wait for HTT.
Show a hint
Set up states for how much of HTH you have matched. The subtle case is what happens after you match "HT" and then flip an H.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.