As students’ progress towards achieving their final grade, their learning process shows random characteristics, which make it suitable for modelling as an absorbing Markov chain. This has practical value and offers opportunities for implementation in customizing assessments. Our goal is to develop a stochastic model to estimate and continuously monitor quality and effectiveness indicators within a higher education mathematics course. Specifically, the model is applied to investigate students’ learning process and academic performance patterns in the “Games & Strategic Thinking” course at CUHK. A transition matrix analyses students’ scores over three consecutive academic years from 2021/22 to 2023/24. This transition matrix allows the estimation of students’ progression through the course assessment and the determination of the expected grade at the end of the course based on each learning stage. Additionally, using different grouping strategies for the range of marks, predictions about students’ final grades in current or future academic years are made. The results are interpreted and discussed, providing valuable insights for course designs. Lecturers can use this analysis to plan course structure and arrange assessment methods, ultimately improving students’ learning outcomes.