More head-busting probability

[kirisutogomen]

rifmeister posts a wonderful little problem here, and it reminded me of an entirely different wacko problem posed on the xkcd balrog bolgia blog "blag". I don't particularly recommend slogging through all the comments, as a reasonable number of them are useless or worse, but the link to the Wikipedia article on the "two envelopes problem" is certainly worth a look.

Comments

[fredrickegerman.livejournal.com]

Actually, strike "randomly-chosen" in the above.

[treptoplax.livejournal.com]

Ow, my head. Although... I'm not 100% clear it's equivalent. They did get the first number, which is non-zero information. "Guess the sign or a single real number" is equivalent to "I picked two numbers, is A or B larger", not "I picked [number] and another number, which is larger."

I'm still not entirely satisfied, though.

[fredrickegerman.livejournal.com]

Yeah, I then tried to back-fill by picking two numbers at random from (0,1). But of course that's just like flipping a coin!

Except for one corner case, which also occurs in the original problem: you can pick exactly the number chosen (with probability 0, of course). Which leads me to wonder if we're not in one of these "integrate a function that's everywhere 0 and get 1" kinds of situations.