Avi has managed to demonstrate that this is probably the correct ANSWER but we still don't have a good derivation, just simulations. I have self-nerd-sniped in a serious way.https://twitter.com/avibryant/status/986057928317648896 …
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Yep, that's the same intuition that led me to that series (but better explained). I'm still worried this is modeling something *slightly* different from your original problem; that is, this is "any roll where you get at least one 100, remove exactly one die".
So the true expectation should, I think, be *slightly* lower than this. (Which does seem like it might be true in the simulation results, but that could also just be noise.)
Yeah, that's an interesting question.
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