  Two-boxing dominates one-boxing: in every state, two-boxing yields a better outcome. Yet on Jeffrey's definition of conditional probability, one-boxing has a higher expected utility than two-boxing. There is a high conditional probability of finding $1 million is in the closed box, given that you one-box, so one-boxing has a high expected utility. Likewise, there is a high conditional probability of finding nothing in the closed box, given that you two-box, so two-boxing has a low expected utility.