Animal behavior should optimize the difference between the energy they gain from prey and the energy they spend searching for prey. This is all the more critical for predators occupying the pelagic environment, as prey is sparse and patchily distributed. We theoretically derive two canonical swimming strategies for pelagic predators, that maximize their energy surplus while foraging. They predict that while searching, a pelagic predator should maintain small dive angles, swim at speeds near those that minimize the cost of transport, and maintain constant speed throughout the dive. Using biologging sensors, we show that oceanic whitetip shark (Carcharhinus longimanus) behavior matches these predictions. We estimate that daily energy requirements of an adult shark can be met by consuming approximately 1-1.5 kg of prey (1.5% body mass) per day; shark-borne video footage shows a shark encountering potential prey numbers exceeding that amount. Oceanic whitetip sharks showed incredible plasticity in their behavioral strategies, ranging from short low-energy bursts on descents, to high-speed vertical surface breaches from considerable depth. Oceanic whitetips live a life of energy speculation with minimization, very different to those of tunas and billfish.