Waiting for HTH
A fair coin is flipped repeatedly until the three most recent flips are, in order, heads, tails, heads. What is the expected number of flips, counting the final one? Give an exact number.
Related problems & prerequisites
Worth solving first
- First Heads Wins 3.0/10
- Waiting for Double Heads 2.0/10
- Seven Before Eight 2.0/10
Source: Classic pattern waiting-time exercise; the overlap method is due to John Conway. Statement written for AxiomIQ.