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Will paper cups help you 'Roll Up to Win'?
Biostatistics professor and serial winner Michael Wallace on maximizing your odds in annual Tim Hortons contest
Biostatistics professor and serial winner Michael Wallace on maximizing your odds in annual Tim Hortons contest
By Melodie Roschman Faculty of MathematicsPaper cups are back for this year’s Tim Hortons Roll Up to Win sweepstakes — and so is high-profile winner, Dr. Michael Wallace.
Wallace, an associate professor of biostatistics, made headlines in 2020 when he figured out how to win the coffee chain’s newly digital Roll Up game 98 per cent of the time. That winning streak was the result of playing all his accumulated rolls in the middle of the night on the last day of the promotion. Though he only won free coffee and donuts, his high win rate got the attention of Tim Hortons. When they changed their algorithm, he kept playing, developing a new strategy in 2023 that resulted in another winning streak, and another round of media coverage.
Wallace, who plays mostly because the contest provides a great case study for his undergraduate students, took the year off last year. “Like an athlete taking a season off to rest,” he jokes.
Now, with the return of paper cups, the game has changed again. This year, Tim Hortons will offer customers two options: if they bring in a reusable mug for their coffee or buy another participating menu item, they will receive two digital “rolls” to be redeemed on the Tim Hortons app. If they buy their coffee in a paper cup, they’ll receive one digital “roll” in addition to the cup itself, which may or may not be a winner.
“The cups are back, I think, mostly because of nostalgia,” Wallace says. “When it comes to games of chance and gambling, we kind of inherently trust physical objects more.” If a customer chooses a paper cup, they either receive a winning cup or they don’t. “Your odds of winning something are fixed at 1 in 6,” he adds.
Using the app, however, is far more variable — a trait that he has exploited in years past to achieve his winning streaks. “If the app works the way it has in previous years, you’re competing directly against all the other customer for prizes,” he says. “The time of day will likely affect your win rate: you’re less likely to win if you’re playing at the same time as a lot of other people, like lunchtime.”
Wallace also cautions players enthusiastic about receiving two rolls per purchase that this does not necessarily translate to double the chance of winning compared to previous years. “With each drink purchase earning two contest entries, players can rack up rolls at a much quicker rate than in some previous years.” While this means more competition for each prize, Wallace notes that Tim Hortons has more than doubled the number of free coffees and donuts available compared to last year’s contest. “More prizes should mean more winners, so I’ll certainly be taking advantage of those extra entries.”
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