In 87 years of Academy Awards, there have been 5 African Americans that have won Best Actor (out of 87) and 8 African Americans that have won best supporting actor (out of 68).
It should be noted that Halle Berry (2001 Monster’s Ball) and Denzel Washington (2001 Training Day) won best actress (or actor, respectively) for playing roles that were dehumanizing or did not stray from stereotypes.
Based on these numbers, there should be an African American best actor or actress every 21.75 years and an African American best supporting actor or actress every 8.5 years. However, since the awards are held only once a year, that would turn out to be every 22 or 9 years, respectively.
It also must be said that there are gaps in awards from 1939-63 and 1963-82. Since then there has been an African American to win best actor/actress every 8.5 years or best supporting actor/actress every 4.9 years. All this with very few nominations and no wins in the last 7 years.