Paradox poll

Be sure to also check out Riddle #5, which has stalled for a lack of wild guessing.

Today's post is a paradox poll. While I favor one way to resolve the problem, I'm curious what other people think, so please comment below. There really are no wrong answers to this.

Here's the paradox. There are two boxes before you—call them A and B—and you have a choice either to (1) open both boxes or (2) open only box B. You keep whatever is in a box you open, so if you choose to open both boxes then you keep what's in both boxes and if you choose to open only box B then you keep what's in box B but forgo whatever is in box A. Also, you have to make your choice all at once; you can't open box B and then later decide to open A, too. If it helps, imagine you have write down your choice on a piece of paper and that someone else opens the box(es) for you based on what you wrote down. Good so far?

So what's in the boxes? Money or nothing. No matter what happens, box A will contain $1,000. As for what box B contains, that depends on another person who we'll call Bob. Bob will try to predict whether you'll open both boxes or only box B. If he predicts you'll open only box B then he'll add $1,000,000 to box B. If Bob predicts you'll open both boxes then he'll add nothing to box B. Below is the table.

	A & B	B only
A & B	$1,000	$1,001,000
B only	$0	$1,000,000

In the table above, you choose the row, and Bob, based on his prediction, will choose the column. You want Bob to predict that you'll open only box B. All else held equal, you would prefer to open both boxes.

Here's the twist. Suppose you've played this game many times already—though presumably for much smaller sums—and Bob has correctly predicted your choice every time.

What do you choose to open?