Abstract Decision under risk and uncertainty (probabilistic choice) has been attracting attention in econophysics and neuroeconomics. This paper proposes a probabilistic choice model based on a mathematical equivalence of delay and uncertainty in decision-making, and the deformed algebra developed in the Tsallis’ non-extensive thermodynamics. Furthermore, it is shown that this model can be utilized to quantify the degree of consistency in probabilistic choice in humans and animals. Future directions in the application of the model to studies in econophysics, neurofinance, neuroeconomics, and social physics are discussed.