Generally luck egalitarianism requires that persons should be responsibilities for all inequalities caused by their choices, while society should eliminate all inequalities due to luck. This demanding position has triggered many criticisms. Luck egalitarianism, however, can hold a moderate position, that is, it does not permit all inequalities resulting from choices, nor does it require to eliminate all inequalities due to luck. Although people often make imprudent choices, and they have to make frequent choices in their lives, choice is the thing that shows their subjectivity and their being equal moral subjects. Under some extreme circumstances, luck egalitarianism has to accept that society should compensate severe inequalities caused by bad option luck. We cannot make a clear-cut distinction between choice and luck, but it is this imprecise distinction that can provide a reasonable basis for Rawls's difference principle, and is a necessary device in the construction of theories of egalitarian distributive justice and their application.