Five years ago, your rich uncle secretly commissioned the construction of a supercomputer! The purpose of this binary behemoth (the "Very Good Predictor") was to predict, as accurately as possible, every action you would take over the course of these five years. It has managed to do so with 100% accuracy for its entire run time. Now, your uncle has approached you with this information, and an offer to participate in a game involving the supercomputer's final prediction.
He has placed two envelopes in a room: Envelope A and Envelope B. As your action within the game, you're allowed to open and then keep the contents of either just Envelope A, or both Envelopes. Envelope B contains a check for $1,000, says your uncle. He also tells you that the monetary content of Envelope A is contingent upon the prediction of the Very Good Predictor. If it predicted that you would only open Envelope A, then Envelope A contains a check for $1,000,000. However, if it predicted you would open both envelopes, then Envelope A only contains a check-sized piece of paper which reads, "Sorry, Champ, you're out of your league."
Please note that you cannot change your mind based on the contents of an envelope: reaching for Envelope B after opening Envelope A will result in your uncle's other computer, the Very Good Destroyer, melting your brain.
Do you only open Envelope A, or do you open both Envelopes?
If the former, can you justify not taking an Envelope which definitely contains $1,000?
If the latter, do you object to being called "Champ?"
Bonus: If you chose to only open Envelope A, what if the Very Good Predictor only had 99% accuracy, or, for that matter, 51% accuracy?