How the fuck is this 4/9?

No.11940552 ViewReplyOriginalReport
I can't figure it out? What does this mean?
Possible initial states:
1. (G, G), (S), (S, S)
2. (G), (G, S), (S, S)
P[States]:
1. 1/3
2. 2/3
P[Gold | State]:
1. 1/3
2. 1/3 + (1/3)*(1/2) = 1/2

P[Gold] = (1/3)*(1/3) + (2/3)*(1/2) = 4/9