This study will evaluate the safety and tolerability of eltrombopag in the treatment of low platelet counts in adult subjects with advanced myelodysplastic syndrome (MDS), secondary acute myeloid leukemia after MDS (sAML/MDS), or de novo AML that are relapsed, refractory or ineligible to receive azacitidine, decitabine, intensive chemotherapy or autologous/allogeneic stem cell transplantation. This is a placebo-controlled study in which patients will receive study medication daily for 6 months, during which time the dose of study medication may be adjusted based upon individual platelet counts and bone marrow blast counts. All subjects will receive best standard of care (platelet transfusions, mild chemotherapy, cytokines, valproic acid, all-trans retinoic acid, ESAs or G-CSF) in addition to study medication. Subjects taking placebo may be allowed to crossover to eltrombopag treatment if a clinically and statistically significant improvement in bone marrow blast counts is seen in subjects treated with eltrombopag.