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Written by Garrett Wollman on 2024-12-12 at 22:54

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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Written by Garrett Wollman on 2024-12-12 at 22:57

(I don't know the answer to this, but I probably could have figured it out in college, when the idea of shuffling a music library was not really credible since the biggest CD changer you could buy only held like 6 discs.)

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Written by Kevin Boyd (he/him) 🇨🇦 on 2024-12-13 at 00:20

@wollman I wonder if it fits into the same problem area as the birthday paradox?

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Written by Garrett Wollman on 2024-12-13 at 00:52

@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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