Before revision:  We additionally show }  it is possible to asymptotically achieve an exact \beta approximation ratio for several natural classes of problem instances, including small prophets (where each distribution is concentrated near zero) and frequent prophets (where each distribution occurs at least some number of times) .
After revision:  We additionally show } frequent instances of prophet inequalities (where each distribution reoccurs some number of times), it is possible to asymptotically achieve an exact \beta approximation ratio for several natural classes of problem instances, including small prophets (where each distribution is concentrated near zero) and frequent prophets (where each distribution occurs at least some number of times) .