Rotary Dial Two Steps
An old rotary phone has the digits 1 to 9 arranged in a circle, each digit joined to its two neighbours. There is no zero, and 9 and 1 are neighbours.
You start on a uniformly random digit and then make exactly two moves. Each move goes to one of the two neighbours of the current digit, each with probability 1/2, independently.
What is the probability that you finish on an odd digit (1, 3, 5, 7 or 9)?
Answer format: round to 3 decimal places.
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