 where \(A \gt S_i\) stands for the conditional that if \(A\) were performed then \(S_i\) would obtain. Thus, instead of using the probability of a prediction of one-boxing given one-boxing, one should use the probability of the conditional that if the agent were to pick just one box, then the prediction would have been one-boxing. Because the agent’s act does not cause the prediction, the probability of the conditional equals the probability that the prediction is one-boxing. Also, consider the conditional that if the agent were to pick both boxes, then the prediction would have been one-boxing. Its probability similarly equals the probability that the prediction is one-boxing. The act the agent performs does not affect any prediction’s probability because the prediction occurs prior to the act. Consequently, using probabilities of conditionals to compute expected utility, two-boxing’s expected utility exceeds one-boxing’s expected utility. Therefore, the principle of expected-utility maximization makes the same recommendation as does the principle of dominance.