The rationality of decision making under risk is of central concern in psychology and other behavioral sciences. In real-life, the information relevant to a decision often arrives sequentially or changes over time, implying nontrivial demands on memory. Yet, little is known about how this affects the ability to make rational decisions and a default assumption is rather that information about outcomes and probabilities are simultaneously available at the time of the decision. In 4 experiments, we show that participants receiving probability- and outcome information sequentially report substantially (29 to 83%) higher certainty equivalents than participants with simultaneous presentation. This holds also for monetary-incentivized participants with perfect recall of the information. Participants in the sequential conditions often violate stochastic dominance in the sense that they pay more for a lottery with low probability of an outcome than participants in the simultaneous condition pay for a high probability of the same outcome. Computational modeling demonstrates that Cumulative Prospect Theory (Tversky & Kahneman, 1992) fails to account for the effects of sequential presentation, but a model assuming anchoring-and adjustment constrained by memory can account for the data. By implication, established assumptions of rationality may need to be reconsidered to account for the effects of memory in many real-life tasks. (PsycINFO Database Record (c) 2019 APA, all rights reserved).