Meet the statistician who cracked Tim Hortons' digital Roll Up the Rim and won 67 free coffees

Thanks to the COVID-19 pandemic, Tim Hortons launched its annual Roll Up The Rim contest without the cups.

Instead, the game went online where patrons could "unroll" their rims on the coffee chain's loyalty app.

Bleary-eyed coffee drinkers may not have realized that this new system also changed some of the conditions for winning the game. And if you're a statistician, that's an opportunity to have some fun. 

"Like everyone else, I'm home and I'm kind of looking for things to do. And so I was pretty delighted when an academic publication asked me if I'd be interested in writing about the new Roll Up the Rim game," said Michael Wallace, assistant professor of Statistics at the University of Waterloo.

But Wallace didn't just write about the contest — he cracked it.

"I managed to win 67 free coffees and 27 free doughnuts," he said. 

Normally, winning hangs on whether you arrived at the front of the line at just the right time to be handed a winning cup.

This time around, whether or not you win depends not on the coffee cup you bought, but when you unroll the digital rim in the app.

According to the new rules, coffee drinkers were able to accumulate their virtual rims and unroll them whenever they wanted during the contest period.

"This change, in a sense, meant that you started to compete with other players," Wallace said. 

Rolled over prizes

Wallace figured that if you happened to unroll your entries on your phone when lots of other people were doing the same thing, there's a good chance someone will sneak in ahead of you, tap their phone first and win the prize. 

This made it wise to avoid playing when lots of other people online are doing the same thing.

But it was also just as important what happens if no one was playing online when a prize had become available. 

"Rather generously, Tim Hortons said if a prize appeared and disappeared because no one claimed it, it wouldn't be gone," Wallace said.

"It would instead be re-randomized to a point later in the contest period. And this could keep happening — a prize could get rolled over, over and over again, until that very last day."

Given the pandemic lockdown, Wallace also figured that sales were probably lower for Tim Hortons, which meant many prizes had become available online, but were rolled over because no one claimed them. 

"So on that last day of the competition, there would be a huge number of prizes available, giving yourself the best chance to win," he said. 

Winning and winning again 

By the contest's April 21 deadline, Wallace had accumulated 96 chances to win.

That day, he woke up before the crack of dawn. 

"I set an alarm for 5 a.m. ET. I thought that's when fewer people would be up in Canada playing those rolls on their app," he said. 

Once he started tapping his phone to unroll the rims, the prizes kept coming. 

"The first one was a free coffee, the second one was a free coffee, the third one was a free doughnut. And it just kept going and going."

 After about 15 minutes of tapping his phone, Wallace had won 94 out of 96 times.

'I am British — I can drink a lot of tea'

But once he had the stash, Wallace wasn't sure what to do with it. 

"I hadn't really thought that far ahead about what I would do if I suddenly had dozens of doughnuts to eat," he said. 

He thought it might be nice to donate his winnings to frontline workers at a hospital, so he got in touch with Tim Hortons. 

"I was a bit worried they'd be upset with me for doing this to their game, but they were actually fantastic," he said. 

Tim Hortons wasn't able to donate his prizes directly to a hospital because the winnings are locked in his app. But the coffee chain promised Wallace it would make a donation to the Jewish General Hospital in Montreal on his behalf.

That still leaves Wallace with a lot of coffees and doughnuts. 

"I'm a statistics professor with 67 coffees and 27 doughnuts, which honestly sounds like an exam question I might write for my probabilities students," he said. 

"The worst case scenario, I've decided, is that from reading the rules again, I know those coffees could be turned into teas. And I am British — I can drink a lot of tea."

Written and produced by Yamri Taddese.

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