The article argues that a global consideration of the luck egalitarianism offers the foundations of both global distributive justice and a policy of open borders or free mobility. The argumentation exposes and criticizes the theory elaborated by Ayelet Shachar, according to which the lottery of birth must be neutralized by means of a Tax on the Privilege of Birthright, and it's maintained in its place that the neutralization of the birth lottery can be make more effective and fair through other institutional mechanisms that include a tax on the enjoyment of citizens' benefits and a policy of free mobility across political borders