Intuitively (subjectively) why this argument doesn't work: if you switch to the path in the lower bunk, you can switch to the upper bunk "at any moment", regard

Intuitively (subjectively) why this argument doesn't work: if you switch to the path in the lower bunk, you can switch to the upper bunk "at any moment", regardless of if there is a path which exists on the lower bunk. In this example, a1 is connected to both c1 and c2: a1 b1 -- c1 | | | a2 -- b2 -- c2 If, instead of deleting edges, we assigned a distance d = 1/p, then you'd expect (and probably easily prove) that the distance to the target vertex is at most the distance to its partner in the other bunk. The fact that this intuitive "problem translation" doesn't actually translate to probabilities is quite surprising (to me)!