Newcomb's Box is Empty

If we accept the premises of the Newcomb Problem, then it's not possible to receive $1,001,000 from playing this game. But you have the choice to take both boxes, and therefore the mystery-box is empty.

Once you approach the boxes to make your decision, the boxes have been determined. From this point, we know that:

(A) You cannot end this game with $1,001,000.

We know this because it's a stipulation of the problem: nobody walks out of here with both boxes full of cash. We can't violate this rule, or we are negating the premise of the paradox.

Another stipulation is the choice:

(B) You may choose to take both boxes.

If the mystery-box contains $1,000,000 and you have the option to take both boxes, then you can walk out of here with $1,001,000. But since you cannot leave with this money, and you may take both boxes, we can conclude that the mystery box is empty.

Suppose the opposite:

(C) The mystery box contains $1,000,000.

More formally:

C ∧ B -> ¬ A

A -> ¬ (C ∧ B)

¬C ∨ ¬B

So if we accept B (another stipulation of the puzzle itself) then we must accept that C is false.