If I found myself in this kind of scenario then it would imply that I was very wrong about how I reason about anthropics in an ensemble universe (as with Pascal's mugging or any sort of situation where an agent has enough computing power to take control of that much of my measure such that I find myself in a contrived philosophical experiment). In fact, I would be so surprised to find myself in such a situation that I would question the reasoning that led me to think one boxing was the best course of action in the first place, because somewhere along the way my model became very confused. (I'd still one box, but it would seem less obvious after taking into account the huge amount of previously unexpected structural uncertainty my model of the world suddenly has to deal with.)