Mastering the Challenge: Insight from an Ontario Academic on Achieving Victory in Tim Hortons Roll Up the Rim

In a repeat of history, a professor from the University of Waterloo has devised a strategy to enhance the chances of winning the renowned Tim Hortons Roll Up to Win contest, marking the second instance in four years.

Michael Wallace, an associate professor specializing in statistics at the University, extensively examined the contest and concluded that the most favorable time to participate is at 3:16 a.m., while the least opportune time is between 11 a.m. and 12 p.m.

"I engaged in 30 rolls during what I determined to be the optimal time and played another 30 rolls during what I determined to be the worst time," he clarified. "During the worst time, I emerged victorious in five out of the 30 rolls, approximately a one in six chance. However, during the best time, I won 23 out of the 30 rolls."

Wallace emphasizes that these designated times may no longer hold true now that he has divulged this secret. "By sharing the best time to play, we find ourselves in an intriguing scenario. It becomes an exemplification of a game theory problem where if everyone is aware that 3:16 a.m. is the prime time to play, it could potentially become the worst time," he explained.

This is not the professor's inaugural encounter with Roll Up to Win. When the coffee chain transitioned from physical rolling to online number selection, Wallace's curiosity was piqued. "In the app, the process involved purchasing a coffee, earning what they refer to as a digital roll," Wallace elucidated.

The awarding of prizes is tied to specific intervals of time known as winning windows, where a tenth of a second is allotted for participants to secure prizes such as coffee, doughnuts, or even cars. Unclaimed prizes from a window are not discarded but rather shifted to a subsequent window.

"This led me to form a hypothesis, as statisticians are inclined to do. I speculated that if I waited until the final day and played during the early hours of the morning, numerous prizes would have accumulated during that time frame," Wallace shared. "This notion was further reinforced by the circumstances of the COVID-19 pandemic, which resulted in reduced sales and subsequently fewer players."

In 2020, he made a total of 96 entries, with 94 of them proving successful. Naturally, news of Wallace's impressive winning streak spread, prompting the esteemed coffee chain to engage in discussions with him regarding their contest setup.

"They reached out to me and we had a series of meetings. They were interested in tapping into my insights and making some alterations based on my observations," he revealed.

Following these developments, the professor abstained from participating in the game until he devised a fresh theory to test in 2022.

In order to explore the potential impact of playing on different days of the week on one's chances of winning, I embarked on an investigation last year. My intention was to determine if participating in the game on a Monday morning or a Sunday morning would yield any noticeable differences in winning probabilities," he elucidated.

A customer from Ontario, Tim Hortons, is currently suing for $500K due to burns sustained while visiting the establishment at 2:13. Unfortunately, this theory did not prove fruitful for him in 2022, as he only managed to secure seven victories out of 30 attempts.

However, circumstances took a turn this year as Tim Hortons unexpectedly started divulging the times when winners were emerging. This development proved to be exceedingly valuable for individuals such as myself who were interested in analyzing the data for strategic purposes. They began publishing the number of prizes awarded in real-time on their website and the roll-up game.

"I monitored the data closely within the one-hour timeframe from 11 a.m. to 12 p.m., which is typically a bustling period for Tim Hortons," he revealed.

When I tested my hypothesis, I uncovered a significant increase in the win rate during the early morning hours, thus confirming my theory.

Despite attaining numerous complimentary coffees, securing one of the coveted grand prizes, like a car, has remained elusive for me.

"I believe my experience serves as a valuable lesson in the extraordinary stroke of luck required to win these top-tier prizes," he remarked. It is worth noting that there are approximately 20 million prizes available, but only 15 of them are cars.

"So, even if I were to guarantee that my next play would result in a win, the probability of winning a car in that scenario would still be less than one in a million."

Nevertheless, this aspect does not significantly bother me since I primarily view my participation in the contest as an educational tool.

"I am not driven by the prospect of free coffee, or in my case, tea," affirmed the British-Canadian educator.

He further shared that he incorporates his experimentation from the previous year into his introductory statistics class.

One of the paramount objectives of utilizing these examples is to demonstrate to my students how statistical thinking can be employed to analyze real-world problems. I encourage them to ponder the type of information required to address a particular question, explore methods for obtaining that information, and subsequently employ statistical reasoning to interpret the obtained results.