Coin Flipping Sequences

Problem Statement#

The Question#

Interview question: A fair coin is flipped repeatedly. How many flips do you expect before the sequence HHT appears for the first time? Now suppose I told you HHH takes longer than HHT on average. Does that surprise you? Can you prove it?

This problem shows up at Jane Street, Citadel, DE Shaw, and HRT, typically in a first or second round. It's a standard-difficulty...