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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 ($h$) and midpoint ($K$), 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.