Suppose that three people A, B, and C are throwing a ball from one to another. Whenever A has the ball, he throws it to B with a probability of 1/3 and to C with a probability of 2/3. Whenever B has the ball, she throws it to A with probability of 3/5 and to C with a probability of 2/5. Whenever C has the ball, he is equally likely to throw to either A or B.
If this game goes on for a long time, what is the mean number of throws between ball possessions for each of the 3 players?