Instance-based learning theory (IBLT) is a comprehensive account of how humans make decisions from experience during dynamic tasks. Since it was first proposed almost two decades ago, multiple computational models have been constructed based on IBLT (i.e., IBL models). These models have been demonstrated to be very successful in explaining and predicting human decisions in multiple decision-making contexts. However, as IBLT has evolved, the initial description of the theory has become less precise, and it is unclear how its demonstration can be expanded to more complex, dynamic, and multi-agent environments. This paper presents an updated version of the current theoretical components of IBLT in a comprehensive and precise form. It also provides an advanced implementation of the full set of theoretical mechanisms, SpeedyIBL, to unlock the capabilities of IBLT to handle a diverse taxonomy of individual and multi-agent decision-making problems. SpeedyIBL addresses a practical computational issue in past implementations of IBL models, the curse of exponential growth, that emerges from memory-based tabular computations. When more observations accumulate over time, there is an exponential growth of the memory of instances that leads directly to an exponential slowdown of the computational time. Thus, SpeedyIBL leverages parallel computation with vectorization to speed up the execution time of IBL models. We evaluate the robustness of SpeedyIBL over an existing implementation of IBLT in decision games of increased complexity. The results not only demonstrate the applicability of IBLT through a wide range of decision-making tasks, but also highlight the improvement of SpeedyIBL over its prior implementation as the complexity of decision features the of agents increase. The library is open sourced for the use of the broad research community.