Value-Weighted Retention Targeting Can Concentrate Harm: Diagnostics and Safeguards for Online Gambling

Retention incentives in online gambling are often allocated by ranking players on estimated treatment effect times lifetime value. Under a fixed budget this value-weighted rule maximises operator value, but operator value and player harm can rise together. We show that the harm exposure of any budget-exhausting rule exceeds the population mean by the covariance between treatment and harm divided by the budget, and give sufficient conditions for value-weighted ranking to make it non-negative. In a simulation where harm rises with value, the estimated value-weighted rule raises mean harm among treated players from 0.421 to 0.476 at a 30% budget, and further at a 10% budget. Harm tracking value is not enough: in one design an accurate value-weighted rule falls below the population mean despite a strong harm-value correlation. A harm weight on the score lowers exposure to about what effect-only ranking reaches with no harm input. With estimated components the weight also raises operator value, but not through harm information: the gain turns into a cost with accurate components and is small or absent unless harm rises with value, consistent with trimming the noisy upper tail of the product score. A hard cap beats the harm weight only with accurate components, and its ceiling holds only for the measure it is given. In this design, with estimated effects, ranking on the effect alone beats value weighting for every learner at budgets up to 30%, significantly in all but one cell; removing effect-churn moderation reverses this. All parameters are illustrative.