I wrote up a pretty detailed analysis of this problem a while back here: https://mindbowling.wordpress.com/2020/09/14/two-envelope-paradox/ https://mindbowling.

I wrote up a pretty detailed analysis of this problem a while back here: https://mindbowling.wordpress.com/2020/09/14/two-envelope-paradox/ https://mindbowling.wordpress.com/2020/09/14/two-envelope-pa... At the end I constructed a super weird example where regardless of what you see in your envelope, you should switch (this seems to go against the symmetry argument, but is sort of saved by a divergence in the expectation value).