Instead of choosing a box, submit the source code of a program that decides whether or not to open a box. Then, the predictor reads the source code, puts money in boxes, and only then does your source code run and open boxes.

Now, imagine that there was a computer program that makes the same choices you do in the same situations, and the Predictor can read that source code before filling the boxes.

That's the intuition pump I use for thinking about Newcomb-like problems.