Canadian statistics professor Tim Hortons competes for 80-98% wins – Ars Technica

Tim Hortons signs with maple leaf signs in the style of the Canadian flag
Zoom in / Tim Hortons is a coffee and donut chain popular with Canadians, the US contiguous to Canada, and statistics professors.

Roberto Machado Noah/LightRocket via Getty Images

All you had to do if you really wanted free coffee and donuts was wake up around 3am every day and click on some virtual Tim Hortons coffee cups.

It was actually 3:16 a.m. that gave a University of Waterloo professor an estimated 80 percent win in the Tim Hortons Roll Up To Win game. It wasn’t as good as the 98 percent scored by Michael Wallace in early 2020 when he discovered a quirk in the coffee chain’s prize distribution scheme, but it still led to great lessons for his students.

“I really like the fact that you can take real-world data, run it through some math and find patterns that describe what you’re seeing,” Wallace told his university’s news service. “It’s a kind of magic.”

For those unfamiliar, Tim Hortons is a coffee and donut chain with more than 4,000 locations in Canada and over 500 in the US, most of them in areas near Canada. The chain was founded and named after a famous hockey player, and its brand can inspire devotion, to the point where Snopes offers a page debunking the myth that Tim Hortons put nicotine in its coffee.

Among the loyalty-inspiring aspects of Tim Hortons is the annual Roll Up To Win contest. Formerly known as Roll Up the Rim to Win, the competition previously involved unfolding the rolled up paper rim of a coffee cup to see if a prize claim was printed on the underside to be picked up at a store location . When the COVID-19 pandemic hit North America, the chain wisely decided that its employees might not want to handle cups that customers had placed in their mouths and then pressed with their fingertips. So Roll Up went online and that’s when the statistics professor started paying attention.

When this was a physical cup-based game, roughly one in six cups had a prize below the rim, a set number that would be offered while supplies last. As Wallace wrote soon after the game’s transition at the start of COVID, the new game was something like a slot machine, with each prize available to virtual players for a set amount of time, sometimes as little as 0.1 seconds. Given that some prizes may go unclaimed, Tim Hortons has specified in its policies that unclaimed prizes will be carried over to another day, up until the last day to claim.

Tim Hortons donuts and coffee from the pre-Covid era when gift giving with edges could be controlled at the print shop.
Zoom in / Tim Hortons donuts and coffee from the pre-Covid era when gift giving with edges could be controlled at the print shop.

Brent Lewin/Bloomberg/Getty Images

With coffee sales likely down during the early pandemic and with 96 entries accumulated, Wallace figured that at 5 a.m. on the last day to redeem the rewards, nearly two weeks after the in-store promotion ended, he would have the best a chance. He played 96 times and won 67 coffees and 27 donuts, losing only twice. As he noted in Maclean’s, the maximum value of his prizes was about $500 (and he hoped to donate them), but turning a game with an 11 percent published win rate into a 98 percent windfall was also free course content for a statistics professor.

Tim Hortons contacted Wallace to find out how he won (“They were very kind,” he told Waterloo, “despite the fact that I probably caused some pretty stressful meetings”). His winning percentage dropped after the coffee chain changed the game mechanics, but he was still able to use the weather and Canada’s multiple time zones to raise his percentage to 40 percent in 2022, he told The Record of Waterloo.

Then this year, Tim Hortons—seemingly unable to go it alone or possess institutional knowledge—added real-time data to its website showing how many prizes were won at any given moment. Wallace enlisted several friends to help him record the prize data over hours and days; the competition prohibits computer scripts.

That’s how Wallace determined that 3:16 a.m. ET was the best time to play, giving him an 80 percent win. The worst time was 11:46 a.m. ET, when, he said in Waterloo, customers in eastern Canada are at an early lunch and western Canadians are still on their morning commute. If you still have Rolls to redeem, you can do so until April 9, and that lag period between award availability and final redemption is usually slow, Wallace found. Sunday is also happier.

Asked about Wallace’s continued success, Tim Hortons issued a typically Canadian statement of respect to The Record. “We know there are many Roll Up super fans like Professor Wallace who love to strategize on how best to play the game, and we appreciate their passion for playing Canada’s favorite game!”

Wallace may be enthusiastic about the game, but the coffee is just a sign. As he told The Record, he was born in England and drinks mostly tea.

List image by Tara Walton/Toronto Star via Getty Images

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