We show that in infinite worlds, the following three conditions are incompatible: 1) The spatiotemporal ordering of individuals is morally irrelevant. 2) All else being equal, the act of bringing about a good outcome with a high probability is better than the act of bringing about the same outcome with a low probability. 3) One act is better than another only if there is a nonzero probability that it brings about a better outcome. The impossibility of combining these conditions shows that it is more costly to endorse 1) than has been previously acknowledged.