Equality of opportunity is a principle of social justice, although there are different conceptions of it. We distinguish between liberal and radical (in)equality of opportunity. Both conceptions consider unfair inequalities in life outcomes that result from ascribed characteristics such as social origin, migration background, and sex. However, they differ in that liberal inequality of opportunity considers it fair when natural talents affect life outcomes. Conversely, radical inequality of opportunity places natural talents in the category of morally arbitrary factors that do not provide a fair basis for inequalities in life outcomes. We use polygenic indices (PGIs) to better disentangle the role of natural talents from the roles of ascribed characteristics and individual choices. We compare using PGIs to using measures of skills observed later in life. We apply this approach to two survey datasets, (i) the Wisconsin Longitudinal Study and (ii) the German Socio-Economic Panel Study. According to our results, radical inequality of opportunity is considerably larger than liberal inequality of opportunity, especially for education. Measuring natural talents using PGIs leads to very similar conclusions as using skills measured later in life. However, the differences between liberal and radical inequality of opportunity are smaller using PGIs than using measures of observed skills.