This is not even hard. To solve it, just invert the order of events. First you choose, then the alien decides what goes in the closed box. It doesn't really matter which comes first, but it is easier to see. The alien has 99.9 percent chance of knowing your decision accurately. If you are greedy, you have a .1 % chance of fooling him, with expected value of $1K + .001*$1000K = $2K. If you are not greedy, the alien still has a .1% chance of getting it wrong, so the expected value of that decision is .999*$1000K = $999K. $999K > $2K so the greedy thing to do is not be greedy (now there's a real paradox!)