There isn't, there is correlation: both your choice now and the SIP's prediction were based on exactly the same things. The only possibility of you outsmarting the predictor would be if something affected your decision making in a manner unforeseen by the predictor - such as brain injury - between the the time the SIP made its choice and the time you make yours, such that it is basically a different person than the one the SIP made its prediction on. Or if there is some change in the set-up to the game itself. Otherwise the predictor is assumed to be always right, and as such choosing only box B is the optimal solution. They will want me to take both, but in this instance you are no longer assuming that the SIP is always right. I.e. it seems to be a material deviation from the original set-up, and introduces additional information to my decision making that was not available to the SIP. This basically seems to hinge on how strong one thinks the predictor's accuracy is. If it is assumed to always be correct then it will have foreseen everything that could possibly happen and thus choosing both boxes yields just USD 1,000 and choosing just one box yields USD 1,000,000. If it is assumed to be fallible then you introduce expected results. If you change the set-up of the game between when the SIP makes its prediction and when you make yours, then you change the argument, and possibly the outcome, entirely. But I will always choose the one box and be USD 1,000,000 better off. I also think the disparity of the amounts makes this less of a dilemma than it could be. Say it was 10k in box A and another 10k in box B... your only way to get more than 10k is to outsmart the predictor. But assuming the predictor is always right, if taking box B yields any higher amount than is in box A then it would seem that taking just box B is the way to go.