Demographic Propensity and Tail Risk in Online Sports Betting

Online sports betting losses are not evenly distributed: average losses look modest, while a small group of bettors absorbs most of the harm. This paper builds a demographic Markov-chain Monte Carlo model to study how age, income, and gender shape annual sports-betting losses. Each simulated person's demographics are compressed into a single propensity score θ, which drives their probability of betting at all, their movement between non-, moderate, and heavy betting states over the year, their wager sizes, and their tendency to chase losses. Wagers face a house edge and an affordability cap tied to disposable income, and the model is calibrated to published aggregate anchors: overall participation, participation among men aged 18–49, and handle per bettor. The simulations show losses concentrating among younger, higher-income men, with the most severe outcomes in the lower tail rather than at the mean, while most of the simulated population loses little or nothing. A decomposition separates income's behavioural effect from its budget effect, a descriptive regression ranks the demographic drivers, and robustness checks show the gender gap is a consequence of the calibrated young-male participation boost rather than an independent empirical finding. Because transitions and loss-chasing are stylised rather than estimated from individual betting histories, results should be read as model-based estimates. The contribution is a transparent, fully reproducible framework — complete source code included — for studying how demographic risk factors translate into concentrated betting-loss distributions.