The basic assumption of the idea of equal opportunities is based on the assertion that all individuals competing for an advantaged social position should have equal opportunities, i.e., that each and every one of them should have fair opportunities to achieve a particular goal. Despite the fact that equal opportunities is one of the basic mechanisms for a just distribution of advantageous social positions, the idea of fair equality of opportunity remains divided between different competing political projects, e.g., egalitarian liberalism, libertarian political theory, multiculturalism, etc. This paper examines two basic dimensions of equal opportunities to which existing conceptions fail to offer a unanimous answer, i.e., a) the issue of fairness and b) the issue of the currency of fairness. The concluding part of this paper presents two basic paradoxes that determine both the direction of the discussion as well as the possible solutions to the achievement of fair equal opportunities as part of any process for competing for advantegous social positions.