Rock, paper, scissors!

Person A and person B play a game of rock paper scissors with the following rules:

1)Rock beats scissors, scissors beats paper, paper beats rock

2) Person A is forbidden to use paper or scissors for the first game. If he uses paper or scissors and beats person B, he will draw. Otherwise, he will lose. (i.e. if person A uses paper and person B uses rock, person A will draw.)

3) If person A and person B draw with each other, they play another game, this time, the other person is forbidden to use paper or scissors. (i.e. if person A draws with person B in the first game, person B will be forbidden to use paper or scissors in the second game.)

If person A and person B are unintelligent and choose rock paper scissors at random and the probability that person A wins is $\frac { a }{ b }$ , find $a+b$