Recent experimental and theoretical work on reinforcement learning has shed light on the neural bases of learning from rewards and punishments. One fundamental problem in reinforcement learning is the credit assignment problem, or how to properly assign credit to actions that lead to reward or punishment following a delay. Temporal difference learning solves this problem, but its efficiency can be significantly improved by the addition of eligibility traces (ET). In essence, ETs function as decaying memories of previous choices that are used to scale synaptic weight changes. It has been shown in theoretical studies that ETs spanning a number of actions may improve the performance of reinforcement learning. However, it remains an open question whether including ETs that persist over sequences of actions allows reinforcement learning models to better fit empirical data regarding the behaviors of humans and other animals. Here, we report an experiment in which human subjects performed a sequential economic decision game in which the long-term optimal strategy differed from the strategy that lead to the greatest short-term return. We demonstrate that human subjects' performance in the task is significantly affected by the time between choices in a surprising and seemingly counterintuitive way. However, this behavior is naturally explained by a temporal difference learning model which includes ETs persisting across actions. Furthermore, we review recent findings that suggest short-term synaptic plasticity in dopamine neurons may provide a realistic biophysical mechanism for producing ETs that persist on a timescale consistent with behavioural observations.