Should recreational gamblers seek better odds at higher table minimums? This is the title of a study conducted by Christopher Ingrassia, a professor of mathematics and computer science at New York’s Kingsborough Community College (part of CUNY, City University of New York).
Ingrassia was particularly interested in the trade-off faced by casual table-game players with smaller bankrolls, who come to play with the aim of entertainment.
"With a very small bankroll, bettors playing at lower-minimum tables will potentially afford more game sessions, even if the game offers worse odds," Ingrassia recently told Covers. "Still, a player in this scenario is unlikely to really feel the full brunt of the higher house edge."
Research challenges the house edge convention
Be it high rollers or novice, casual gamblers, casino players of all types have always been operating under one key notion: Always look for games that give you the best chances to win.
The main indicator most players use is the house edge, which is the statistical percentage the casino will keep in the long run from player losses. For example, a double-zero roulette wheel has a theoretical return to player of 94.74%, giving the casino a 5.26% house edge. That is, every $1 bet will generate an average loss of 5.26 cents, which the casino will keep as the house edge. And thus, the lower the house edge, the better off a player will be in the long run.
Enjoying Covers content? Add us as a preferred source on your Google account
Adding more factors to the mix
Professor Ingrassia, who holds a Ph.D. in Biomedical Engineering, a Master’s in Mathematics, and a Bachelor’s in Computer Science, found that this isn’t always the case for casual players with a smaller bankroll.
In most cases, casinos will protect themselves by setting higher table minimums on games that offer better odds to the player. So, you might be able to place a $10 bet on a spin of a triple-zero American Roulette wheel. But walk a few tables down to the single-zero, European Roulette table, which statistically offers a much better chance to win, and you will discover that the same bet may cost $100 per spin.
Ingrassia explained that while the latter offers better odds, it also forces players to risk their bankroll much more aggressively. In his research, he examines this trade-off and raises an interesting question: Does a better game automatically produce better outcomes for recreational gamblers?
Researching players with smaller bankrolls
Ingrassia’s study didn’t only examine the mathematical expectations for game results, but it also accounted for recreational gamblers with lower bankrolls.
"Large portions of my research are specifically aimed at these smaller players. In fact, with respect to table games, I usually fall into that category myself," he told Covers. "I simulated initial bankrolls ranging from $500 to $3,000, but let's suppose you only had $100. In the high-limit room, that would typically give you just one bet."
While accounting for lower bankrolls, which increase the likelihood that a single loss ends a gaming session, Ingrassia stressed that events should be treated independently and that the house edge won’t usually play as a crucial factor for casual bettors.
"Losing that first bet is just a consequence of the probability associated with that isolated independent event. I would not, however, attribute this type of 'one-and-out' failure to house edge," he said. "House edge is felt over a much longer time span that most recreational players fall short of."
How to view the trade-off at the roulette table
It seems obvious that single-zero roulette has a lower house edge than triple-zero roulette. Therefore, over an extremely long period of play, the player would be expected to lose money more slowly. So, the lower house edge option is still the best game to choose over the long term.
But the issue Ingrassia’s research highlights is that most recreational gamblers play for a relatively short period of time. They arrive with a fixed budget, gamble for a few hours, and then leave when they run out of money or hit a specific profit goal. 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 the psychological aspects of bankroll management.
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 pinpointing the relationship between 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 has significantly better odds, but players need to spend 10 times more on each spin. Games with a triple-zero dramatically tilt the odds toward the house but are much more affordable to play. This raises the question: Which of these two options delivers the better outcomes for recreational gamblers with smaller bankrolls?
Casinos quietly shifting the goalposts
The study begins by highlighting a trend that many gamblers already know exists: casinos quietly changing rules to protect their profits. For example, 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.
We asked Professor Ingrassia about how casinos introduce these new rules and whether players are aware of the disadvantages that follow.
"Truthfully, most casual players are totally oblivious to the subtle differences between the many variants of roulette and those of the other table games," he said.
"None of these new elements are designed to give the public an edge," Ingrassia added. "It doesn't help that these detrimental twists are either advertised to the absolute legal minimum or completely disguised altogether."
He used roulette as an example, which was a primary subject of his studies.
"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," he said. "I wonder how many players are even aware that placing chips on the hotel logo is a valid betting option."
When asked if it’s entirely up to the casino, he responded: "Although I do believe this practice is a bit deceptive, I cannot blame the casinos entirely. They only do it because there isn't enough resistance. When the whales and sharks look for better waters, things may change."
But he is optimistic about players fighting back and casinos responding.
"In fact, the tide may already be rolling back. On my last trip to Las Vegas, I noticed many more 3-to-2 blackjack tables than I did last year. Finally, the public got wise and the casinos took notice. It only took a decade-and-a-half!"
Research methodology
Ingrassia used computer simulations in addition to standard probability models. The simulations used realistic conditions for a recreational gambler, with bankrolls ranging from $500 to $3,000 in increments of $500.
Performance goals
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 10 hours of play at a rate of one spin per minute.
Structure
The research covered even-money wagers, such as red/black and odd/even bets, and 2-to-1 wagers, such as dozens and columns. A total of 10,000 simulation trials were run for each scenario.
Result tracking
While many casino game math models work on theoretical expected value, Ingrassia’s study also 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
The approach produced a more realistic overview of recreational gambling behavior than traditional models that only work on unlimited play.
Triple-zero table results
One finding that stands out is that betting the lower $10 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 because long sessions without much movement in the bankroll is what many recreational gamblers want. More spins equals more entertainment, more gameplay, and more time at the casino. However, looking more closely at the details shows that reality may be less encouraging.
That’s because around 95% of these timeout sessions ended on the losing side. Players did stay in the action for many hours but would almost always end with less money than they started with. The lower betting limit did not stop losses; it just made them slower to arrive. 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 took 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 held true whether players selected even-money 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.
Odds don’t always equal outcome
One of the most valuable insights from the study is that "better odds" and "better outcomes" are not always identical concepts.
"House edge still matters, but more so in theoretical models where there is unlimited time and bankroll, which real-life gamblers don’t have," he said.
Recreational gamblers especially should also consider session length, bankroll amount, game volatility, table minimums, and their own personal goals. The results suggest games with a higher house edge, but low minimums may allow players to stay in the action longer. It appears no option is automatically better than the other, with outcomes largely dependent on what the player wants to accomplish.
A player focusing purely on entertainment may prefer lower minimum tables. While the house edge is higher, the smaller stakes do seem to deliver longer sessions. Someone who wants to mix in profits with entertainment may benefit from the lower-edge game despite the higher minimum bet.
Marketing high-limit tables as premium products
The study offers 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 behavioral tools.
A game with higher minimums but better odds means 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 understand this and balance their game ecosystem to reflect it. Casinos market high-limit tables with better odds as premium products. Lower-limit tables with higher house edges are the entry point for casual visitors.
Key findings
Professor Ingrassia's research points to a more complex relationship between house edge and odds than 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 for a longer time, but financial loss is 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. Instead, it highlights that house edge shouldn't be the only factor when choosing a game.
"Treat gambling as an entertainment expense. If you have the choice, always play the better game," Ingrassia said.
"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."
