Invoking nondeterminism doesn't make the thought experiment easier, just more complicated. From http://www.scottaaronson.com/blog/?p=30 http://www.scottaaronson

Invoking nondeterminism doesn't make the thought experiment easier, just more complicated. From http://www.scottaaronson.com/blog/?p=30 http://www.scottaaronson.com/blog/?p=30 : >(Incidentally, don’t imagine you can wiggle out of this by basing your decision on a coin flip! For suppose the Predictor predicts you’ll open only the first box with probability p. Then he’ll put the $1,000,000 in that box with the same probability p. So your expected payoff is 1,000,000p2 + 1,001,000p(1-p) + 1,000(1-p)2 = 1,000,000p + 1,000(1-p), and you’re stuck with the same paradox as before.) Even if you have "free will" and your actions are semi-random, that's not different than flipping a coin to make your decisions.