Combinatorics/probability problem: what's the probability that a uniform random shuffle of a music library will place two songs by the same artist consecutively, as a function of the number of songs by each? At what density is this overwhelmingly likely to happen for the most common artist in the library?
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@wollman I wonder if it fits into the same problem area as the birthday paradox?
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@kboyd Quite possibly. The "birthday paradox" setup assumes that birthdays are uniform (which is not the case) or whatever the discrete equivalent is called; this problem is explicitly nonuniform, it has to somehow account for the different densities of various artists in the library, which should make it harder. I'm trying to convince myself it could be simplified to just the first two songs after shuffling without loss of generality (because you can choose to start at an arbitrary point).
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