Alf is then offered two boxes: one transparent and visibly containing £1000; the other opaque. Alf is told that the opaque box may contain £1000000, or it may be empty. Alf is given the option of taking just the opaque box, or both boxes.
The apparently easy decision for Alf is complicated by Alf knowing that the purpose of his previous testing was to enable the Panel to Predict what he will choose, and that that Prediction has determined whether there is £1000000 or £0 in the opaque box.
Only if the Predictor predicted Alf would take only the opaque box, was £1000000 put into it. Alf is told, and believes having watched previous episodes of the game show, that the Predictor has proven 95% accurate in its predictions (of both choices) to date.
The dominance argument for taking both boxes is causal. The prediction has already been made - the opaque box either contains £1000000 or it doesn't - so Alf may as well take both boxes, with certainty getting £1000 more than if he only takes the opaque box.
The maximised expectation argument for taking just the opaque box is evidential. This strategy delivers £1000000 if the Predictor was correct with probability 95% giving an expected gain of £950000. Taking both boxes gives a lesser expected gain of £1000 + 5% * £1000000 = £51000.
Philosophers are still divided by Newcomb's paradox. 60% of 168 letters following
a 1973 Martin Gardner Scientific American magazine article discussing Newcomb's paradox favoured the maximised
expectation argument for taking just the opaque box.
11% argued that the paradox stems from inconsistancy in the posed problem:
the assumed existance of the Predictor leads to a logical contradiction so is untenable.
Such arguments can lead to notions of Inherant Unpredictability and Free Will;
though questioning how the Predictor might predict the outcome of a Contestent's predicted
coin toss provides a director refutation.
The Two Cheques Paradox