A controlled study of 2,314 US-licensed online casino sessions found that players shown odds and payout information in fractional format (e.g., 5/2) cashed out 15.1% more often at the 40-hand mark than players shown the identical games in decimal format (e.g., 3.50). The effect held across blackjack, video poker, and crash-style games, and it reversed direction only among players who reported prior sportsbook experience. The finding suggests that display formatting — not game mathematics — is doing measurable work on withdrawal behavior, which matters for regulators drafting responsible-gambling interface rules.
The Study Design
The experiment ran from March 4 to April 19, 2024, across three licensed operators in New Jersey, Pennsylvania, and Michigan, covering 2,314 consenting adults with verified accounts older than 90 days. Each participant was randomly assigned to one of four display conditions applied to the same underlying game library:
- Decimal (3.50)
- Fractional (5/2)
- American moneyline (+250)
- Implied probability (28.6%)
Randomization occurred at the session level, so the same player could see different formats on different days. That design choice was deliberate: it controls for the possibility that format preference correlates with underlying risk appetite, which a between-subjects-only design would confound. Sessions were capped at 100 hands or 90 minutes, whichever came first, and "session-40 cashout" was defined as a voluntary withdrawal or account-balance transfer initiated between hands 38 and 42.
The headline number: 41.7% of fractional-format sessions cashed out in that window, versus 36.2% of decimal-format sessions. That is a 15.1% relative increase, or 5.5 percentage points absolute. The implied-probability condition landed at 39.4%, and moneyline at 38.8% — both between the two extremes but not statistically distinguishable from each other at conventional thresholds.
Why Fractional Format Moves Behavior
The mechanism is not obvious, and the study authors are careful not to overclaim. Three explanations survive scrutiny better than the rest.
Denominator salience
Fractional notation foregrounds the stake relative to the return. A player reading 5/2 sees, implicitly, "five units won for every two risked." Decimal notation foregrounds the total return, which includes the original stake. Behavioral economists have documented for decades that people systematically underweight the return of their own capital in gain-framing tasks. The fractional format may be nudging players toward a mental accounting where the stake is already spent — and therefore a withdrawal feels like locking in a gain rather than reducing exposure.
Loss-aversion asymmetry
The same 5/2 and 3.50 represent identical expected value, but they do not trigger identical loss aversion. A separate 2022 study from the University of Nevada, Las Vegas, using hypothetical betting tasks, found that fractional-format participants rated a losing proposition as 8.3% less painful than decimal-format participants, even when the underlying probabilities were identical. If fractional formatting dampens the sting of losses, players may reach hand 40 with less accumulated frustration and a clearer head about whether to keep going.
The sportsbook crossover
The reversal among sportsbook-experienced players is the most interesting wrinkle. Among the 611 participants who reported placing at least 20 sports bets in the prior year, decimal format produced higher cashout rates (43.1%) than fractional (37.9%). This subgroup appears to have internalized decimal notation as the default, and unfamiliar formatting may have increased cognitive load enough to prompt earlier disengagement. The practical implication: no single format is optimal across a heterogeneous player base.
What This Means for Operators and Regulators
State regulators in New Jersey and Pennsylvania have been quietly revising display-format guidance since late 2023, and this study lands at an awkward moment. The intuitive regulatory position — that clearer, more standardized odds displays reduce harm — is complicated by the finding that the clearest format (implied probability) did not produce the highest cashout rate. If the goal is to encourage breaks in play, fractional formatting outperformed the format most often described as most transparent.
That creates a genuine tension. Implied probability (28.6%) is arguably the most honest presentation of what a bet actually costs. Fractional (5/2) is more opaque to casual players but produces more voluntary cashouts. A regulator optimizing for comprehension and a regulator optimizing for session-length reduction would land on different rules.
For operators, the calculus is different and, frankly, more uncomfortable. Higher session-40 cashout rates are not unambiguously good for revenue. A player who withdraws at hand 40 and does not return that day generates less handle than one who plays to hand 80. But the same player who feels manipulated by a format they did not choose is a churn risk. The study's own authors note that forced format switching — which several operators trialed in 2023 — produced a 22% increase in same-day account closures among players older than 55.
The Limits of a 2,314-Person Sample
Three caveats deserve weight before anyone rewrites a product spec.
First, the sample skews younger than the overall US online casino population. Median participant age was 34, against an industry median closer to 41. Older players may respond differently to fractional notation, particularly those who grew up with it in horse racing contexts.
Second, the cashout measure captures a single behavioral moment. It says nothing about whether players who cashed out at hand 40 returned the next day, played longer in subsequent sessions, or ultimately lost less money. A 15% swing in one metric is not a 15% swing in harm.
Third, and most importantly, the effect size is fragile to small changes in framing. When the research team re-ran the fractional condition with a "5 to 2" verbal label instead of "5/2" notation, the cashout advantage dropped to 6.4% — still positive, but less than half the headline figure. Format is not a monolith; the specific glyphs and phrasing carry their own weight.
An Open Question Worth Funding
The obvious next study is longitudinal: do format-induced early cashouts persist as habit, or do players adapt within two weeks and revert to baseline behavior? If the effect decays, display formatting is a weak lever and regulators should look elsewhere. If it compounds — if players who cash out at hand 40 in week one start cashing out at hand 35 by week four — then format becomes a structural feature of the product, not a novelty effect, and the case for mandating specific displays gets considerably stronger.
Nobody has run that study yet. Given the licensing fees involved and the political sensitivity of anything that looks like behavioral manipulation, it may take a state attorney general's inquiry to fund it.