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Message: <blockquote data-quote="Octangula" data-source="post: 5984721" data-attributes="member: 6691124">Slight, necro, but:Assuming that the odds are equal to move in each direction, there's a very simple rule for the average duration of random walks. You multiply together the distances in both directions. Here, it's 3 each way, so 3*3=9.This does assume that one side wins the roll each time. In reality, there is a 5% chance that the result will be tied, which will lengthen it slightly. This is probably a shortcut that's mathematically incorrect, but my mind wants to say 9.45I'm not sure how the walk is affected by p not being 0.5; I'm looking into this now, mostly to satisfy my own curiousity.Edit: My gut feeling is that with p being something other than 0.5, then it makes it more likely that the walk (and therefore, in your case, the chase) will end faster. If you understand why birthdays not being equally distributed across the year make the birthday paradox more likely to happen, then my thinking is that this applies here as well.</blockquote>