After three contests, Hillary Clinton leads Bernie Sanders by the slimmest of margins in the Democratic primary, 51 to 50 in delegates.

But she hasn’t yet tapped into what is probably her greatest strength: black voters.

Mrs. Clinton leads among African-American voters by as much as a 50-percentage-point margin, according to national surveys. They give her all, or nearly all, of her advantage over Mr. Sanders. The virtual deadlock in the Democratic delegate count reflects in large part the fact that black voters have been underrepresented in the contests so far.

That changes Saturday in South Carolina, which has one of the largest black populations by percentage in the country. Fifty-six percent of the South Carolina Democratic primary electorate was nonwhite in 2008, according to the state election commission.