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I am researching the two-envelope problem. In particular, I am working with the variant in which the chooser tries to pick the envelope with more money in it with a greater than 50% accuracy, having viewed the contents of only one envelope. The problem is well-described here: https://www.futilitycloset.com/2016/06/28/blackwells-bet/

The problem is, I cannot find this solution to the problem described anywhere in the mathematical literature. Help finding relevant papers, please?

Note: I have a different solution that does not require the generation of an unrelated random variable.

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  • $\begingroup$ I'm curious, what is your different solution? $\endgroup$
    – user479223
    Commented Jul 17, 2023 at 3:52
  • $\begingroup$ 1) Choose an envelope. Let x be the value in the envelope. 2) Choose any function, F, which is strictly monotone decreasing and has range [0, 1]. 3) Swap envelopes with probability F(x). The strategy works because swapping is more likely for low values than for high values, without making any assumptions about the distribution of the amounts in the envelopes. $\endgroup$
    – Mathguy2718
    Commented Jul 17, 2023 at 3:57

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There is an extensive literature. Note that Blackwell did not explicitly consider this problem, the naming is a bit controversial. A recent paper with pointers to earlier literature is

The Two-Envelope Problem for General Distributions, S. Portnoy (2020).

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