One, if it's set up in what I think is the standard way. (Though of course one can devise very similar problems like the Smoking Lesion where the 'right' answer would be two.)

I'm not entirely sure how you're connecting this with the statement you quoted, but I will point out that there is information flow between the Newcomb player's predisposition to one-box or two-box and the predictor's prediction. And that without some kind of information flow there couldn't be a correlation between the two (short of a Cosmic Coincidence.)