If A and B play a game with a fair coin such that A wins by getting consecutive TT for the first time, while B wins by getting a consecutive TH. Who has higher probability of winning the game?
I tried the following method but not sure:
For A to win,
TT, HTT, HHTT ... that is, 2-k for each game length k
For B to win,
TH, HTH, HHTH ... that is, 2-k for each game length k
So ultimately I am getting same probability of each to win.