We apply the exploitation/exploration dichotomy faced by organizations in business strategy to the decisions of individual executives as to whether to continue in their current organization and exploit career opportunities there or explore new ones through the avenue of job search. Specifically, we observe whether executives pursue offers from an executive search firm to be considered for positions at other organizations. Insights from the multi-armed bandit problem help explain who searches and who does not, focusing on the structural attributes of each individual’s situation. Individuals are more likely to search where their current roles are less certain and where broader career experience makes search more useful because the array of possible opportunities is greater. The results also shed light on the operations of executive search firms, who are central actors in executive careers.