Right back!

[rhinoceros]
It seems to me that the *transparent* boxes make lots of a fifference. You (the Chooser) stand in front of them and look:

If you see the million dollars in the second box, then you know that the Predictor predicted that you would choose only this box, and this is why he put the million there, according to the rules. You decide to take both boxes. You end up with $1,001,000 and you have proven the Predictor wrong!

[hell-kite]
My guess is your premise is wrong: Of course it is sensible and well-nigh "determined" that the Chooser, seeing both boxes filled, will take both. But, given his clairvoyant abilities, the Predictor WILL KNOW how the Chooser will behave. If under the circumstance of both boxes filled, the Chooser will always choose both, THEN THE PREDICTOR WILL NEVER FILL BOTH BOXES.

He foresees that IF he DOES, THEN the Chooser will take both, so he DOES NOT. He cannot, as a matter of fact, or else we had a logical inconsistency: You CANNOT prove the Predictor wrong, because the Predictor is, by definition of 100%-TRUE-PREDICTION, ALWAYS RIGHT!

[This was my initial answer, but things got more complicated as I considered your second possibility]

[rhinoceros]
If you see the second box empty, then you know that the Predictor predicted that you would choose *both* boxes, and this is why he left the second one empty, according to the rules. You decide to take only the second box (the empty one), forfeiting $1,000 (it is possible if you are rich enough) but proving the Predictor wrong again!

[hell-kite]
It occured to me that the transparent box-game is flawed regarding an imbalance of the Predictors and the Choosers options. In the closed box-game, both have only two choices: The Predictor can put the million in the box or not. The Chooser can take only one box or two. In the transparent version, the Predictor still has only two options, but the Chooser has his two basic options, plus the option to defect or cooperate, thus, he has 4 options. Thus, the Predictor cannot adequately react according to his prediction. Thus, the rules of the game do not fit anymore.

BUT, note that the Predictor still can predict correctly: He knows how the Chooser will behave, even though he only has two suboptimal choices. Thus, this is, imho, not at all an argument for free will. In the closed box-case, the Predictor never was the cause of the Chooser's behaviour (except in the sense that his existence constitutes one aspect of the game). In the transparent box-game, he becomes a causal force because the decision of the Chooser becomes dependent on his actions.

Again, I believe the transparent box-game is not valid for deterministic or anti-deterministic argumentation.

Hopefully coherent,
Björn