Three people, A,B,C play a game. A rolls the die.
Then, in order of "B,C,A,B,C,A..." they each roll the die. They keep going until someone wins. To win, you have to get the same number as the previous number rolled on the die. ( A can't win with his first roll because there was no roll before to compare it too.)
What is the probability that each person will win?
(In reply to solution
An interesting method, cetainly easier than attempting the full series simplification...
It's very impressive that you can solve this so quickly (within 10 minutes of the posting). You must have some sort of alert to new problems being posted!!