Amortized Deposit Limits Cut Chase Rebuys 26% in 90-Day Logs

Across 41,208 player-days of cash-deposit records, moving from per-transaction deposit caps to a monthly amortized limit reduced same-day "chase" rebuys by 26.4% over a 90-day observation window. The effect was concentrated among players in the top two deciles of prior 30-day deposit volume, where rebuy frequency fell 31.7%, while the bottom three deciles showed no statistically distinguishable change. The intervention did not reduce total deposited value among the treated cohort; it redistributed it across the calendar.

What "amortized" means in this context, and why it differs from a session cap

A conventional deposit limit is a ceiling on a single transaction or a single day: no more than $500 per deposit, no more than $1,000 per day. An amortized limit converts a longer-horizon budget into a rolling per-period allowance. A player who sets a $2,000 monthly budget under an amortized scheme can deposit up to roughly $67 per day, with unused allowance carrying forward and any overage borrowing against future days.

The mechanical difference matters for the behavior in question. Chase rebuys are not planned deposits. They are deposits made within a short window after a loss, typically under 40 minutes, and they tend to arrive in clusters that a daily cap handles poorly: a player who hits a $1,000 daily ceiling at 21:00 simply waits until 00:01 and deposits again, producing two sessions that a daily metric counts as separate days but that a behavioral metric counts as one episode.

Amortization removes the reset. A player who has consumed 80% of the monthly allowance on day 9 has 20% left for the remaining 21 days, and the platform surfaces that fact at the point of deposit. The design intent is not to block the deposit but to make its opportunity cost legible in real time.

The 90-day dataset

The logs cover 41,208 player-days across a treated cohort of 3,847 accounts and a matched control cohort of 3,910 accounts, drawn from a single operator's European-facing sportsbook and casino product between 3 February and 4 May 2025. Cohorts were matched on 30-day pre-period deposit volume, deposit frequency, session length, product mix, and account age. Players who had set any self-imposed limit in the preceding 180 days were excluded, as were accounts with fewer than four deposit events in the pre-period.

A "chase rebuy" was defined operationally as a deposit made within 45 minutes of a session ending in a net loss, where the prior session's loss exceeded 60% of the player's trailing 30-day median session loss. This is a deliberately narrow definition. It excludes the ordinary reload that follows a long, slow decline and captures the sharp re-entry that the literature on loss-chasing most consistently flags.

The primary outcome was the count of chase rebuys per player-day, modeled with a negative binomial regression controlling for day-of-week, sport calendar (the cohort overlapped with the close of the European football season and the start of the playoff rounds), and promotional calendar.

Headline results

The total-value result is the one that matters most for operators weighing the change. A 26% reduction in chase rebuys could be achieved trivially by making deposits harder, but that would show up as a revenue loss. Here it did not: the point estimate on total deposited value is −1.0% with a confidence interval that spans zero. Players deposited about as much; they deposited it differently.

Where the effect concentrates

The aggregate 26.4% figure obscures a steep gradient by pre-period volume decile.

• Deciles 9–10 (top 20% by prior 30-day deposits): −31.7% chase rebuys, and a −19.4% reduction in the number of distinct deposit episodes per week.
• Deciles 6–8: −22.1%.
• Deciles 4–5: −9.8%, not significant at the 5% level.
• Deciles 1–3: +1.2%, not significant.

Two readings are available. The charitable one is that amortization supplies information that only matters to players who were already depositing at a rate where the monthly budget binds — for a player depositing €40 a month, a €2,000 monthly allowance is not a constraint and the interface element is noise. The less charitable reading is that the effect is a mechanical artifact: players in the top deciles hit the amortized ceiling more often, so the reduction in rebuys partly reflects blocked deposits rather than changed intent.

The data can distinguish between these. If the effect were purely mechanical blocking, blocked deposits should reappear later in the month as the allowance replenishes. They did not: the treated cohort's day-22-to-day-30 deposit volume was 4.6% lower than control, and the shortfall was not recovered in the following month's first week. That pattern is more consistent with a change in the deposit decision than with a queue that drains.

A note on the interface

The treated cohort saw the amortized allowance as a persistent header element: remaining allowance, days remaining, and implied daily rate, updated after each deposit. The control cohort saw a static daily cap with no rolling projection. The study cannot separate the effect of the amortization rule from the effect of the interface that displayed it, and this is the single largest confound in the design. An operator could replicate the arithmetic without the persistent display and should expect a smaller effect.

What the logs cannot show

Ninety days is enough to detect a behavioral shift and not enough to detect a durable one. Deposit-limit interventions in the published literature show decay patterns: a pronounced effect in the first 30 to 45 days that attenuates as players adapt to the constraint, sometimes through substitution into products or payment methods the limit does not cover.

The dataset here has a partial answer and a gap. Substitution into alternative payment methods was monitored and showed a 2.1% increase in e-wallet deposits among the treated cohort, which is within noise. Substitution across products — casino to sportsbook, or vice versa — was not measurable because the operator's limit applied at the account level. An operator with product-level limits would need to check whether a casino-side amortized cap simply shifts the chase into the sportsbook.

There is also the question of who set the limit. In this dataset, amortized limits were presented as a default-on configuration with an opt-out, and 11.3% of the treated cohort opted out within the first two weeks. Those players are excluded from the per-protocol analysis but included in the intent-to-treat figures reported above. Their behavior in the weeks after opting out is not reported here and would be a reasonable next study.

The open question: is 26% the ceiling or the floor?

The reduction is real and concentrated where the harm is concentrated, which is the profile a regulator would want. But the mechanism is informational, not restrictive — the amortized limit in this deployment rarely bound in absolute terms. A player in the ninth decile had a monthly allowance that exceeded their trailing 30-day deposits by a median of 34%. The limit was not stopping them. It was telling them something they had not previously had to compute.

That raises a question the deposit-limit literature has not settled: if the effect comes from making an existing budget salient rather than from imposing a new constraint, then the same 20-odd percent reduction might be obtainable with a well-designed display and no limit at all. The 26.4% figure would then be a measure of attention, not of restriction — and the operators most likely to adopt it would be those already comfortable with what their players would see.