# Gaming the game: Ontario professor has advice on how to win Tim Hortons Roll Up the Rim

For the second time in four years, a professor at the University of Waterloo has developed a strategy for improving the odds at winning Tim Hortons Roll Up to Win contest.

Michael Wallace, an associate professor specializing in statistics at the University of Waterloo, studied the contest and believes that the best time to play is at 3:16 a.m. while the worst time to roll is between 11 a.m. and 12 p.m.

“I played 30 rolls at what I calculated to be the best time that I played, 30 rolls of what I calculated to be the worst time,” he explained. “And so at the worst time, I won five times out of 30, so about one in six. And at the best time I won 23 times out of 30.

“So my win rate was about five times higher playing at the optimal time or nearly 80 per cent.”

Wallace cautions that these times may change now that he has let the cat out of the bag.

“Because I’m now telling people when to play, we’re in an interesting situation as this is actually an example of a kind of game theory problem where if everyone knows the best time to play is 3:16 a.m., that could make it the worst time to play,” he said.

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This is not the professor’s first experience with Roll Up to Win.

When the coffee chain first switched from rolling up the rim to punching in numbers online, it piqued his interest.

“The way it worked on the app was you buy a coffee, you earn what they call a digital roll,” Wallace explained.

“And the way prizes are awarded is that every single prize in the game is attached to what they call, like a little winning window, a winning time frame. So there’s a 10th-of-a-second window open and then closed during which someone could win like a coffee or a doughnut or maybe even a car.”

But if no one claimed a prize, they did not disappear but would be pushed back to a later window.

“That led me to a hypothesis, as statisticians are wont to do, and I thought, ‘I bet if I wait till the very last day and play very early in the morning, there’ll be lots and lots of prizes sort of piled up over this time,’” Wallace said.

“And that was also because it was during COVID. So, you know, sales in restaurants and stuff were super low, so fewer people were playing.”

So he entered 96 times in 2020 and 94 of those entries came up as a winner.

Naturally, word of Wallace’s winning streak spread, with the venerable coffee chain even reaching out to talk to him about their setup for the contest.

“So I actually had some meetings with them. They wanted to talk to me, sort of pick my brain a bit to see what see what I saw, and they made some changes,” he explained.

“I can’t comment on whether or not those changes were a result of what I did, but certainly they affected what I did.”

The following fall, he steered clear of the game before he decided to test a new theory in 2022.

“So last year I wanted to look at playing on different days of the week because I wanted to see if maybe you play on a Monday morning or a Sunday morning, maybe that makes a difference to your chances to win,” he explained.

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That theory did not pay off for him in 2022 as he was only able to pull off seven wins in 30 tries.

Things changed again this year, though, as he says that Tim Hortons actually began to publish the times when people were winning this year.

“Tim’s started giving us data that was very, very useful to someone like me because they were publishing to their website, to the roll-up game, the number of prizes that had been awarded,” he explained, noting that they had done it in previous years but in 2023 the data was updated in real-time.

“So, for example, I tracked it between, say, 11 a.m. and 12 p.m., which is a really busy time for Tim’s,” he said.

“They gave away about 40-45,000 prizes during that one hour and then on the same day between 3 a.m. and 4 a.m., they only gave away about 5,000 prizes.”

When he put his theory to the test, that was when he proved his hypothesis with the major win rate early in the morning.

While he has won a lot of coffees, he has not managed to take home any of the coffee contest’s major prizes — like a car.

“I think I am a good lesson in how you have to get very, very lucky to win the really big prizes,” he noted, explaining that there are around 20 million prizes but only 15 of those are cars.

“So if I can guarantee that my next play will be a winner, the probability that I win a car in that situation is still less than one in a million.”