Wait for HH vs HT

The problem
flip a fair coin until you see…Game A:HHGame B:HTwhich game ends sooner on average?

A fair coin is flipped repeatedly.

  • Game A: stop the first time you see HH (two heads in a row).
  • Game B: stop the first time you see HT (heads then tails).

Which game ends sooner on average? Are they the same?