Most subjects maximized own chances to win a lottery in previous experimental studies. Scholars have explained the result by a weak concern for ex ante equality. Rawls (1971/1999) provides a psychological motive for the weak preference. He argues that distributing income according to the outcome of a lottery is "arbitrary" and unfair. Moreover, he believes that treated by the unjust institution, people could possess "excusable envy" towards potential winners, which leads them to deal with others unfairly by maximizing own chances. This study tests experimentally whether subjects practice excusable selfishness. Our results support Rawlsian thought, since many exhibited a weak preference for an equal expected payoff and deviated their baseline social preferences. The finding provides the first psychological explanation for why most people maximize their winning probabilities and casts doubts on the equally lucky view of equality of opportunity.