The Iowa Gambling Task (IGT) is one of the most common paradigms used to assess decision-making and executive functioning in neurological and psychiatric disorders. Several reinforcement-learning (RL) models were recently proposed to refine the qualitative and quantitative inferences that can be made about these processes based on IGT data. Yet, these models do not account for the complex exploratory patterns which characterize participants behavior in the task. Using a dataset of more than 500 subjects, we demonstrate the existence of sequential exploration in the IGT and we describe a new computational architecture disentangling exploitation, random exploration and sequential exploration in this large population of participants. The new Value plus Sequential Exploration (VSE) architecture provided a better fit than previous models. Parameter recovery, model recovery and simulation analyses confirmed the superiority of the VSE scheme. Furthermore, using the VSE model, we confirmed the existence of a significant reduction in directed exploration across lifespan in the IGT, as previously reported with other paradigms. Finally, we provide a user-friendly toolbox enabling researchers to easily and flexibly fit computational models on the IGT data, hence promoting reanalysis of the numerous datasets acquired in various populations of patients and contributing to the development of computational psychiatry.