I don't think William Feller is on this list, but according to him, the probability p(n) of first hitting -1 at the nth step is p(n) = bin(n, (n-1)/2) / (n * 2^n) where the binomial coefficient should be taken as 0 for n even -- so p(2k) = 0, which is obvious anyway. The generating function for these probabilities is shown to be G(s) = (1 - sqrt(1-s^2)) / s from which G'(1) = oo. Which shows that as Michael said, the expected time to reach -1 is oo. (I found this to be rather surprising.) --Dan Michael wrote: << Surely many people on this list know more than I do about the distribution of times at which the random walker first hits -1.
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