Opportunities in society are commonly interpreted as chances of success . Within this interpretation, should opportunities be equalised? We show that a liberal principle of justice and a limited principle of social rationality imply that opportunity pro les should be evaluated by means of a Nash criterion. The interpretation is new: the social objective should be to maximise the chance that everybody in society succeeds. In particular, the failure of even only one individual must be considered maximally detrimental. We also study a re nement of this criterion and its extension to problems of intergenerational justice.