Kangaroos, monopoly and discrete logarithms

The kangaroo method computes a discrete logarithm in an arbitrary cyclic group, given that the value is known to lie in a certain interval. A parallel version has been given by van Oorschot and Wiener with "linear speed-up". We improve the analysis of the running time, both for serial and parallel computers. We explore the variation of the running time with the set of "jumps" of the kangaroos, and confirm that powers of two are a good choice (we do not claim they are the best choice). We illustrate the theory with some calculations of interest to Monopoly players, and the method itself with a card trick due to Kruskal.