In many choice situations in real life, we are initially uncertain about the properties of choice options, such as the possible outcomes and their probabilities. Making a decision then not only requires a procedure for comparing the options, but also a procedure for searching for information and stopping search. We develop a formal framework for specifying sampling strategies in terms of a search rule, a comparison rule, and a stopping rule to study how these three building blocks together shape risky choice. In a series of simulations, we demonstrate how different combinations of the building blocks and in particular their interaction give rise to qualitatively different cognitive processing mechanisms and systematically different choice patterns. For instance, we show how the same variations in the search rule can lead to diametrically opposed effects on reward maximization, depending on the comparison rule. Moreover, in line with previous research showing that cognitive strategies often interact with the task environment, we show how the behavior that a particular sampling strategy gives rise to also critically depends on the structure of the choice problems. Finally, underscoring the idea of bounded rationality and the merit of its cognitive-ecological perspective, we demonstrate how different sampling strategies can be used to balance the expected reward in a given environment against the efforts spend on sampling and computation to obtain this reward.