A pokemon trainer is walking randomly in a one dimensional field which we represent as following graph. The trainer just started their journey and only has a Charmander. Each time the trainer visits the left end of the field (the vertex 0), a wild Caterpie attacks and Charmander beats it. If the trainer is at the right end of the field (at vertex 7), their rival attacks them with a Squirtle. To beat Squirtle, Charmander needs to train on Caterpies: it beats Squirtle if and only if it has beaten 3 Caterpies before. What is the probability that Charmander beats Squirtle if the trainer starts at 2