Most decisions we make in daily life require to take into account a large number of different factors. It is generally believed that we select some of them, use only those for the decision process, and disregard the others. In many experimental studies of decision making, this process is dramatically simplified and only very few factors are included. One typical paradigm is choosing between two alternatives (gambles) where each of which allows to win a certain amount with a certain probability. In this study, we juxtapose such a simple situation with a more complex one, with more alternatives and more factors. We also measure which of these factors the decision makers actually are interested in (i.e. which they are looking at). We then impplement a dozen computational models, each designed to predict the decision a human makes based on which factors each individual looked at. We find two models that predict the choices significantly better than all others. The two models have in common that they, first, use explicitly the order in which they collect the information about the different choices and second, keep this information in memory.