Sneaky: OK, here's my updated envelope-analogy and the reason why it fails.To restate the idea: suppose we have 6 playing cards: a red ace and a black ace, a red king and a black king, a red queen and a black queen. We have two envelopes with special three-way pouches, labelled "A Q K", so that each three-way envelope contains an ace, a king, and a queen. Randomly and without looking, I put an ace into the A-pouch on both envelopes, the queens into the Q-pouches, and a king into the K-pouches.
Furthermore, we have to accept the proposition that it's impossible to open one of the pouches without destroying the other two cards. It's booby trapped with incendiaries or something.
Now I mail one of the envelopes to my friend 5000 miles away, and at agree to peek at our ace-pouches at exactly the same time. Obviously, if he sees a red ace I will see a black one, and vice versa. Nothing mysterious is going on there. No reason to invoke "spooky action at a distance."
But here's the big wrinkle:
I look in any of three pouches at random, I have a 50/50 chance of getting a red card, right?
What if my confederate opened his A-pouch before I even received my package, and saw a black ace? Surely then it would be logical to assume that the odds of my finding a red card are more than 50/50, right? He knows that one of my choices must be red, and the other two could be anything, so it must be more than 50%. (If my mental math is right, the odds of getting a red card should be 2/3.)
But that's where my metaphor breaks down with reality. If these envelopes truly behaved in a quantum mechanical way, my chances of getting a red card would *still* be 50/50 even when my friend has discovered I am holding a red ace. This occurs because the odds of my finding a red card in the non-ace slots mysteriously goes down, so that the overall odds are still 50/50.
Could this be because there is some principle that makes a red ace imply less likeliness of a red queen or king? Perhaps the deck isn't very well shuffled, or like-colored cards repel one another, or some weird principle like that is in play?
But that doesn't make any sense, because it was entirely arbitrary which pouch my friend peeked into. He might have said, at the very last moment, "Forget this plan to look at our ace pouches. I'm going to look at my queen pouch on a whim." In that case the color of the queen would be known and the probability of the colors in the other two pouches would shift.