By Ezra Ivudria

Student Writer

Roulette is a thrilling, high-stakes game made popular through Las Vegas-set movies and TV shows. The game is popular because of how easy it is to grasp: Players place a bet on a winning number, set of numbers or color, and then a ball is placed in a spinning wheel. The number it lands on determines whether any bettors win.

It appears to be all about luck, but senior math major Imani Ballou wanted to know whether there was a winning strategy casinogoers could employ to increase their odds. Ballou, who will graduate tomorrow, teamed up with math professor Dr. Kayla Javier-Joyner to find out during a Reeves Summer Research project this year. Tomorrow's commencement exercises begin at 10 a.m. in Cuddy Arena.

Dr. Kayla Javier-Joyner

As a freshman, Ballou was taken with the idea of studying roulette for a required research paper for Honors College students. The concept of probability fascinated her, especially as someone who admits she "doesn't really trust casinos." She questioned how casino games, specifically roulette, really benefit the players.

When Ballou was a freshman in Javier-Joyner's Math 209 course, the professor recalls being impressed by Ballou's early idea and the ambition behind it, but she advised her to wait until she had completed a few more courses before pursuing the project. After strengthening her foundation in math and computer science, Ballou returned to the project with new confidence. She built a roulette simulation program from scratch to study how probability plays out over repeated spins. With the groundwork prepared, Javier-Joyner and Ballou formally began their research journey together.

Despite the countless myths surrounding roulette, the results of their study revealed a reality far less glamorous than the casino floor suggests. After running thousands of simulated spins, they discovered that there is no strategy capable of consistently beating the wheel. As Ballou says, "You have to be very lucky to win," because no matter how creative the betting method or how aggressive the risk, the numbers remained unforgiving.

One of the most striking findings was the expected payout per spin. Javier-Joyner explains that, on average, a player loses about five cents for every dollar they bet, a return that holds true across every betting style they tested. Whether a player chose red or black, odd or even, the return was always negative. Ballou says that although supposedly safer group bets were supposed to be the winning formula, the outcome remained the same: There is no scenario in which the odds tilt toward the player.

Ballou presented some of her research during the spring Wellspring Symposium.

Ballou says that her results align closely with studies from industry experts, which all point to the same mathematical truth: Players should always expect a smaller payout than what they invest. Roulette may feel unpredictable, but it is designed to ensure that, in the long run, the advantage rests firmly with the casino.

"Many players believe they can read the wheel or recognize patterns in the chaos," Ballou says. The simulation proved the opposite. Luck, and only luck, is the deciding factor in every outcome. Skill cannot change the trajectory of the ball. Strategy cannot outsmart probability. At the end of the day, the house always wins, because the math is structured that way.

For Ballou, the takeaway is clear: "If you know the math, it doesn't add up." Understanding the numbers is not about finding a way to beat roulette. It is about knowing how the game beats you. The research ultimately emphasized a simple but crucial lesson for anyone tempted by the spinning wheel: Know when to stop. No system can guarantee victory, but understanding the math can protect players from chasing losses that were never mathematically recoverable to begin with.

So what does it all mean? What was the point? Javier-Joyner says that for mathematicians, the unknown is always unsettling. Ballou shares this feeling. The outcomes of these games are unpredictable, and as mathematicians they believe that inputs should produce predictable results. Roulette, however, is a game of chance, and their research highlights exactly that. Recognizing that you are not likely to get lucky, and that you may receive a lower payout than expected, can reduce the risks that come with gambling.

In January, Ballou will present her findings at the Joint Mathematics Meeting in Washington, D.C. She'll be in the area anyway, having lined up a job teaching middle- and high-school math in her native Maryland after graduation. She believes that her research will help her make math work for her students. "Many people don't realize that understanding probabilities could help them make more informed decisions, such as about how they handle their money," she says.

At the heart of this project is a genuine curiosity about the unknown and a testament to the resilience required to seek solutions to the problems people face. Roulette may not be solvable, but Ballou and Javier-Joyner provide a clearer understanding of why.

Dec. 12, 2025