Does a society that embraces and fulfills equality of opportunity (rightly interpreted) necessarily provide social mobility? In a word, No. To illustrate the point, consider a society whose population is divided into deciles by household income (the income of adult partners combined and of each adult living alone and as sole head of household). Identify social mobility in this society with the chance that any given individual will as an adult live in a household that places in a higher decile of household income than the one in which he was placed as a child, along with the chance that he will end up in a lower decile. Social mobility in the society is high to the degree that knowing an individual's decile of family origin is not predictive of his own decile and low to the degree that this information is predictive.