You're trapped in a maze. There is a way out. Path junctions are all 3-way.
If you use the strategy of always taking the path going right, what will happen?
(Note: This problem is deliberarely vague.)
(In reply to
re(2): About the by Cheradenine)
It goes back to my original complaint: nothing is known about probability distributions. What constitutes a "random" topology? What affinity do any two nodes have toward being connected? The solution you propose makes assumptions not justified by the problem.