This paper introduces the Learner's Tau framework, a discrete probabilistic model designed to characterize the timing of first success in adaptive learning environments. Unlike traditional memoryless models (such as the geometric distribution) that assume a constant probability of success, the Learner's Tau utilizes a discrete Hill-type hazard function to capture the dynamic nature of skill acquisition, specifically the nonlinear transition from repeated failure to mastery. Governed by two interpretable parameters, steepness () and midpoint (), the model provides a mathematical basis for quantifying diverse learning trajectories, from gradual improvement to sudden "aha" moments. The work derives key summary metrics, including a Difficulty Ratio and Mean Time to Mastery, and presents empirical validation using Cognitive Tutor data to demonstrate superior model fit over baseline methods for non-trivial tasks.