I bodged it in #python. Considering that if both numbers are == than it's a loss. https://gist.github.com/MrKimchiBoy/7c13ed442ef11e529cc30b6fb55699f8 …
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I guess the number T you pick is as random as the number on the other slip of paper, so it serves as a surrogate.
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Problems like this all seem to tacitly rely on a uniform probability distribution over an infinite set, here in the setup and step 1. But this distribution doesn't exist. Replace that uniform probability distribution and things generally work out sensibly.
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The linked article actually works for any density function and possibly relies on non-existence of uniform density.
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Would be curious if the proof works with all numbers rational, since otherwise one can't actually draw a real number
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Yes, extends easily.
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Well, Fermats Numerology Games.
https://twitter.com/fermatslibrary/status/1047108698999545856?s=19 …
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Doesn't this naive solution give you better than 50% odds: if the number in your envelope is positive, keep it, if the number is negative, pick the other envelope?
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That's what they said, but with T=0
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How do you choose a number uniformly from an infinite set? Is it the same as fix N choose for -N to N and then take the limit where N goes to inf?
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