Math question: If I have N N-sided dice (e.g. 100d100) and I roll them repeatedly, removing any that roll maximum (e.g. 100), what is the expected number of rolls until I have none left, in terms of N?
I simulated it and it's definitely N^2, which is a very neat result. I haven't yet figured out *why* that's true.
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Oooh, neat. Now I'm even more interested.
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I tagged in a couple of my math friends on facebook but no answer yet.
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That kind of makes intuitive sense since at 100 dice it takes expected 1 trial to lose, and at 1 die it takes 100, which sort of hints to at least an O(N^2) solution.
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Wait, I screwed my simulation up, but your tweet here's a good way to think about it. It's the sum for i=1 to N of N/i.
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Urgh am I going to have to simulate this myself....
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My Scala simulation code (fixed to work, I think), fwiwhttps://gist.github.com/avi-stripe/6eb925629e1ae8352552242ef7cf3ede …
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Ooh tail recursion. Fancy.
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