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(12): About the by Cheradenine)
Essentially, what you've just "proven" is that the average random maze, regardless of size, has exactly two loops. I challenge you to draw any maze satisfying the 3-path condition with more than two nodes for which this is true. The problem is that you started at your expected solution (that the probability of finding an exit is 1/2), worked your way back to an initial topology (there are two loops), and then worked your way forward to the solution you wanted again.
Just try sketching a few mazes on paper and following your strategy. I think you'll find that you get caught in small loops more often than you reach the exit.
Incidentally, it is possible to start at a node, follow the right wall, return to the starting node, and then hit the exit. This is a consequence of the three-path condition.
re(13): About the
