The World Health Organization (WHO) recently established a global stockpile of oral cholera vaccine (OCV) to be preferentially used in epidemic response (reactive campaigns) with any vaccine remaining after 1 year allocated to endemic settings. Hence, the number of cholera cases or deaths prevented in an endemic setting represents the minimum utility of these doses, and the optimal risk-averse response to any reactive vaccination request (i.e. the minimax strategy) is one that allocates the remaining doses between the requested epidemic response and endemic use in order to ensure that at least this minimum utility is achieved. Using mathematical models, we find that the best minimax strategy is to allocate the majority of doses to reactive campaigns, unless the request came late in the targeted epidemic. As vaccine supplies dwindle, the case for reactive use of the remaining doses grows stronger. Our analysis provides a lower bound for the amount of OCV to keep in reserve when responding to any request. These results provide a strategic context for the fulfilment of requests to the stockpile, and define allocation strategies that minimize the number of OCV doses that are allocated to suboptimal situations.