Suppose you find yourself in a situation in which you can either save both A and B or save only C. A, B and C are relevantly similar – all are strangers to you, none is more deserving of life than any other, none is responsible for being in a life-threatening situation, and so on. John Taurek argued that when deciding what to do in such a situation, you should flip a coin, thereby giving each of A, B and C a 50% chance of survival (Taurek 1977: 303). Only by doing this can we treat each person with the appropriate degree of respect. Taurek seemed to be employing the “Equal Greatest Chance” principle (EGC), according to which, when deciding whom to save, one must give each person the greatest possible chance of survival consistent with everyone else having the same chance. An obvious alternative is the “Save the Greater Number” principle (SGN). I describe an example that shows that EGC is false. I show that the example also demonstrates the falsity of other related views, including Jens Timmermann’s “Individualist Lottery Principle.” I conclude that SGN is true. And I extend the argument to other kinds of cases, showing that which person should be saved may depend on whether some additional well-being may be gained for someone in the process.