A University of Waterloo professor is using statistics to analyze how to win the Tim Hortons ‘Roll up to Win’ contest

A Tim Hortons cup is shown in Toronto on Thursday, February 3, 2017. Police say two more people have been arrested in connection with the thefts of several boxes of "roll up the rim to win" cups from a Tim Hortons in Belleville, Ont. THE CANADIAN PRESS/Nathan Denette

Tim Hortons’ “Roll up to Win” contest is back this year and a biostatistics professor at the University of Waterloo is once again rolling up his sleeves to dive into the statistics of winning.

Michael Wallace’s area of expertise is statistical theory questions motivated by health problems and he collaborates with researchers in nutrition, oncology, and eye diseases.

In 2020, when Tim Horton scrapped the longtime practice of rolling up the rim on your cup and turned the contest into a strictly online game amid the COVID-19 pandemic, Wallace used his statistical knowledge to win 94 out of 96 times, a 98 per cent win rate – most of his prizes were for free coffee and donuts.

Now, with the return of physical contest cups alongside the online game, Wallace is planning to take another look at the numbers.

In the past, Wallace says that he has found that players can improve their chance of winning by logging on and playing the online game at off-peak hours.

“If you played your rolls when lots of other people were playing, your chances of winning were lower, whereas if you played your rolls when fewer people were playing, your chances of winning were higher,” he said.

“Another aspect of that first year was that prizes that went unclaimed over time would gradually be re-randomized to later in the contest, causing kind of a big pile up right at the end.”

Wallace discovered in 2020 that when he redeemed his rolls using the Tim Hortons app had a big impact on his success rate.

He found that by playing early in the morning, usually at round 3 a.m., his win rate increased by 50 per cent. But if he played mid-morning his win percentage decreased by 10 per cent.

He also found that the number of winners increased quickly during the day and slower at night, indicating different types of player behaviour.

However, Tim Hortons has now updated the rules to level out the game by using a mathematical equation to even the odds based on player behaviour.

Analysis of the new strategy by Tim Hortons

Wallace said that he’s planning to run experiment over a span of a week, covering weekdays and weekends to determine if the chances of winning vary, depending on the time of day and the day of the week.

He believes there still may be opportunities to gain a slight advantage depending on several factors that he will test.

“It will depend less somewhat on the time of day you play, but also with the day of the week you play, because they’ve taken data from previous years, and they basically treat it every day as if it’s the same,” Wallace said.

Although, the return of the physical cups can affect the rates of winning.

Customers who bring in their own reusable cup get two entries on the app, while the ones who buy the cup get one on the app, and one on the cup.

“I want to see if you can do better than one in six odds playing on the app than on the physical cups, because that would be an interesting comparison,” he said.

Wallace hopes to determine whether the app could have better odds than the physical cups.

“People can play on the cups without ever interacting with the app. So, there’s a chance that people playing on the cups may reduce the number of people playing on the app, because people may choose not to engage with [it],” Wallace said, adding that he plans to buy a lot of soup to acquire digital entries, since customers can get entries on the Tim Hortons app by purchasing various products at some grocery stores.

“That’s another way in which the return of the game in changing is there may be more people playing the app because of all these new avenues to secure rolls, but that is hard for us to know,” he said.

Public interest about his winning streak

Wallace says that he has received a lot of attention and lots of request for tips since his initial findings were made public in 2020.

He recalls the time he helped the parents of a PhD student improve their odds.

“They tried this strategy of playing sort of very early in the morning, and it worked for them,” he said.

With the return of the cups this year, people have asked him for advice on whether the cups or the digital app gives them better odds of winning.

Wallace said he may have an answer about the probability of winning this time around by next week.

The physical cups are back only for a limited time and will only be available while the supplies last.

This year’s prizes include gift cards, free coffee, free donuts, all-inclusive vacations, Samsung TVs, smartphones and a 2025 all-electric Volkswagon.

The contest ends on March 23, and the winners have until April 29 to redeem their prizes, while winners can claim their food prizes at any Tim Hortons outlet until April 9.

CTV News reached out to Tim Hortons for a comment but did not hear back by time of publication.