Suppose we play Rock-Paper-Scissors with the strategy of throwing rock, paper, or scissors randomly with probabilities determined by what we have just thrown in the previous round of the game...

Extracted text: Suppose we play Rock-Paper-Scissors with the strategy of throwing rock, paper, or scissors randomly with probabilities determined by what we have just thrown in the previous round of the game according to the following transition matrix (the states are in order R-P-S): 1/3 2/3 P : 1/2 1/2 1 If we have just thrown paper, what is the mean time until we will throw rock? (Enter your answer as a reduced fraction.)