Primary Objectives (Phase I Portion): 1). To determine the safety and tolerability of eltrombopag in elderly subjects with AML 2). To determine the maximally tolerated initial starting dose of eltrombopag for elderly subjects with AML Primary Objectives (Phase II portion): 1). To better define the safety and tolerability of eltrombopag in elderly patients with AML at the maximally tolerated starting dose Page 9 of 18 determined in Phase I portion of study. 2). To determine the incidence of peripheral platelet count improvement (using baseline and response parameters as defined below) for subjects with disease related thrombocytopenia. Secondary Objectives (Phase I and II): 1). To preliminarily determine the efficacy (using AML response criteria as defined below) of eltrombopag in elderly subjects with AML.