Given that human memory is fallible, it is likely adaptive for people to preferentially encode, retain, and retrieve important items better than insignificant ones. Using a dynamic decision-making paradigm with a response deadline, we find that humans demonstrate a bias to better remember 1) items with positive rather than negative value, and 2) items with high-magnitude values. Performance was greater when participants were shown all item-value pairs simultaneously, and were thus able to selectively attend to high-magnitude values. The same magnitude bias is observed for sequentially studied positive items, but not for negative items. Decision trajectories show participants sometimes change their minds during the course of a trial, choosing an item after first moving toward the other. Changes of heart occurred more often for trials with negative items. These findings suggest that memory is sensitive to value, and that real-time game paradigms can be used to reveal dynamic memory processes.