Katrina Griffiths
Senior editor
Published on: 06.07.2026
Kingsborough Professor Examines Trade-Off Between Bet Size and House Edge
Christopher Ingrassia, Asst. Professor, Mathematics and Computer Science at New York’s Kingsborough Community College (part of CUNY, City University of New York), presented his research examining the trade-off recreational gamblers make between odds and table minimums at an academic conference in Las Vegas.
The International Conference on Gambling & Risk Taking is held every three years by the International Gaming Institute (IGI) of the University of Nevada in Las Vegas (UNLV) and brings together leading academics from all over the world to showcase their research in the field, including experts in psychology, mathematics, economics, industry, and public policy to explore gambling theory and practice.
Ingrassia presented at the conference’s 19th edition, held at the Bellagio Hotel on the Las Vegas Strip, with his study titled: “Should Recreational Gamblers Seek Better Odds at Higher Table Minimums?”
Breaking Gambling Conventions
For decades, casino gamblers have been taught a simple lesson: always choose the game with the lowest house edge. On paper, that advice makes perfect sense. The lower the house edge, the less money a player is expected to lose over time. Yet in a real casino, the decision is often more complicated than comparing percentages.
Many of the games with the best odds now come with significantly higher table minimums. A player might be able to wager $10 per spin on a triple-zero roulette wheel, but it costs $100 per spin to play on the single-zero European roulette table. While the latter offers better odds, it also forces players to risk their bankroll much more aggressively. This raises an interesting question: Does a better game automatically produce better outcomes for recreational gamblers?
Ingrassia’s study did not just examine the mathematical expectations for game results; it also accounted for recreational gamblers with lower bankrolls. The results show that the house edge is only one factor in the larger equation.
The Modern Reality of Casino Games
The study begins by highlighting a trend that many gamblers already know: casinos are quietly becoming less favourable to players. Blackjack tables that once paid 3:2 on natural blackjacks increasingly pay 6:5. Roulette has seen the introduction of triple-zero wheels that increase the casino’s advantage.
These changes create a familiar pattern. It is still possible to find and play the most advantageous games, but they are now more likely to be behind higher limits that make your minimum stake much larger.
In practical terms, it means players are left with a choice:
- Better odds with larger required bets
- Worse odds with smaller required bets
Traditional gambling advice often boils down to a simple equation: choosing the best odds is always beneficial. However, recreational players are often limited by smaller bankrolls and less time, which alters the calculations.
Roulette Highlights the Challenge
Roulette was chosen for the study because it removes many of the variables present in other casino games. It has a simple betting structure, and the gameplay loop is entirely based on random chance with no player decision-making. This simplicity made it a perfect candidate for the study and pinpointing the relationship between two factors, house edge and bet size.
Ingrassia’s comparison looked at two scenarios:
- Triple-zero roulette with a $10 wager per spin
- Single-zero European roulette with a $100 wager per spin
Single-zero roulette offers significantly better odds, but players need to bet 10 times as much on each spin. Triple-zero roulette dramatically tilts the odds in favour of the house but is much more affordable to play. This raises the question: which of these two options delivers the better outcomes for recreational gamblers with smaller bankrolls?
What Does the Trade-Off Mean?
Single-zero roulette has a significantly lower house edge than triple-zero roulette, so over an extremely long period of play, the player would be expected to lose money more slowly. It does seem that the answer to the problem is obvious, and the lower house edge option is still the best choice in the long term.
The problem is that most recreational gamblers do not play indefinitely. They arrive with a very fixed bankroll, gamble for a few hours, and then leave when they run out of money or hit a specific profit. Under those conditions, the size of each wager becomes just as important as the underlying game rules.
A player risking $100 per spin can experience dramatic swings in bankroll within minutes. Risking $10 each spin will deliver smaller swings and allow the player to survive longer. This leads to tension between mathematical outcomes and bankroll management.
How the Simulations Work
Realizing there was a tension, Ingrassia used computer simulations rather than relying solely on standard probability models. The simulations used realistic conditions for a recreational gambler, with bankrolls ranging from $500 to $3,000 in increments of $500.
Player goals were given as a percentage of the starting bankroll, from 20% up to 100%, with the latter meaning the player would double their original bankroll in profit. Each simulation run had a cap of 600 roulette spins, which equates to roughly ten hours of play at a rate of one spin per minute.
In terms of bet structure, the research covered even-money wagers (red/black and odd/even) and 2-to-1 wagers (dozens and columns). A total of 10,000 simulation trials were run for each scenario.
While many casino game math models work on theoretical expected value, Ingrassia’s study tracked practical results, including:
- How often players reach their target profit
- How often they lost their entire bankroll
- How many sessions timed out after 600 spins
- Whether players finished ahead or behind when time expired
This approach produced a more realistic overview of recreational gambling behaviour than traditional models that only work on unlimited play.
Triple-Zero Table Results
One finding that stands out in the research is that betting the lower $10 per spin resulted in almost all simulations passing the 600-spin limit before reaching a winning or losing target. This suggests that even with a higher house edge, players on these tables are likely to maintain a playable bankroll over a long period.
This appears to be an obvious positive, as long sessions with little movement in bankroll are what many recreational gamblers want. More spins = more entertainment, more gameplay, and more time at the casino. However, a closer look at the details suggests that reality may be less encouraging.
That’s because around 95% of these time-out sessions ended on the losing side. Players stayed in the action for many hours but would almost always end up with less money than they started with. The lower betting limit did not stop losses; it just made them slower. So, the takeaway is that surviving longer lets you play longer, but it’s not the same as winning more often.
Single-Zero Table Results
The results were considerably different for the $100 single-zero scenario. Each wager was taking a bigger percentage of the player’s bankroll, so limits were hit much faster. It was less likely that a session would reach the 600-spin boundary, with players mostly hitting profit or loss targets within the time.
More importantly, the study found several situations where players with modest goals had positive results. This was true regardless of whether the player selected even-money bets or 2-to-1 bets. Betting more money does increase volatility, but players had access to the superior odds offered by the single-zero wheel.
Ingrassia’s simulations suggest that a player with a modest profit target, such as 20% of bankroll, has a realistic chance of hitting their goal before the house edge takes over. This flips the results from the triple-zero players, whose longer sessions usually ended with gradual bankroll losses.
When we asked him about the biggest misconception players have when choosing between different versions of roulette, he said, “Most casual players are totally oblivious to the subtle differences between the many variants of roulette and those of the other table games. None of these new elements are designed to give the public an edge. It doesn’t help that these detrimental twists are either advertised to the absolute legal minimum or completely disguised altogether. An example of the latter is happening right now up and down the Vegas strip, as many casinos are using their logo instead of ‘000’ on roulette wheels and layouts.”
Why Better Odds Do Not Always Mean Better Outcomes
One of the most valuable insights from the study is that “better odds” and “better outcomes” are not always identical concepts. House edge definitely still matters, especially in models with unlimited time and bankroll.
However, real players do not have either of those things. Recreational gamblers, especially, should also consider session length, bankroll size, game volatility, table minimums, and their personal goals.
The results suggest that games with a higher house edge, but lower minimums may allow players to stay in the action for longer. It appears no option is automatically better than the other, with outcomes largely depending on what the player wants to accomplish.
When asked whether the house edge or bet cost matters more in reality, Ingrassia told us, “With a very small bankroll, playing at a lower minimum will afford a bettor more rounds of a game with worse odds. Still, a player in this scenario is unlikely to really feel the full brunt of the house’s edge. When playing games of pure chance, we rely much more on experiencing positive swings of fortune, which are often fleeting if they come at all. If we zoom out far enough, the overall trend is always a downward slope, which is the house’s edge.”
What This Means for Casino Design
The study provides insight into casino strategy, where operators view table minimums as necessary or as price points for customers. One interesting takeaway from Ingrassia’s research is that they also work as behavioural tools.
A game with higher minimums but better odds mean players must make trade-offs, with many viewing the table as a premium product. Lower minimum games are accessible to all types of players, but the long-term economics may lead to more losses.
Casinos already understand this and balance their game ecosystems accordingly. Casinos market high-limit tables with better odds as premium products. Lower-limit tables with higher house edges are the entry-point games for casual visitors.
Conclusion
Ingrassia’s research points to a more complex relationship between house edge and table minimums than many gamblers assume. Playing with a lower house edge remains the best option for mathematical returns, but higher table minimums mean there is a clear compromise for players.
Low-stakes games like triple-zero roulette often allow players to remain in the action longer, but financial losses are likely. Higher-stakes single-zero roulette produces faster outcomes and offers realistic opportunities for modest profit targets.
For recreational gamblers, this study is not about making it easier to choose which game to play. It is about highlighting that the house edge should not be the only reason you choose a game.
Ingrassia’s takeaway is to “treat gambling as an entertainment expense. If you have the choice, always play the better game. It is shocking how often I am able to find multiple empty seats at a 3-to-2 blackjack table, while the neighboring table offering 6-to-5 with the same minimum is packed.”
