Three Alike
A fair coin is flipped repeatedly until three consecutive flips are identical (either three heads in a row or three tails in a row). 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: Standard run-waiting-time exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.