Tim Hortons Roll Up to Win no match for stats-slinging Waterloo prof

When Tim Hortons moved its annual Roll Up to Win" contest online during pandemic-plagued 2020, it didn't count on University of Waterloo statistics prof Michael Wallace cracking the code to win.

I played 96 times and won 94," says the easygoing mathematician of his inaugural-year winning streak that landed him more coffee and doughnuts than he knew what to do with.

I had like a 98 per cent win rate.''

When Tims tweaked its contest the following year, his winning strategy fell apart, but climbed back to an impressive 40 per cent after he rejigged his data in 2022.

And then he got a break, this year, when the company began posting the number of prizes won in real time, allowing the determined Rim-buster to plot a graph that pinpointed, with clinical precision, the best time to play.

We've sort of known since the game moved to the app that the best time to play is when other people aren't," notes Wallace, who pegs his current winning streak at 80 per cent.

So in previous seasons I was playing at 4:30 a.m. because that was my guess. But this season Tims is actually publishing data I was able to throw a bunch of math stats at."

The results were unequivocal: if you want to win one of the 13 million coffee or doughnut instant prizes, the optimal time to play is 3:16 a.m. EST., when most people are asleep, while the worst time to play is 11:46 a.m., right around peak lunch hour.

What I'm basically able to do is take the data Tims is giving us and draw a graph that shows you an approximation of when people are playing the game," says Wallace.

It's very low in the middle of the night and then, around like 5 or 6 a.m., it starts to pick up and gets really busy once you get past 9 a.m., and stays busy."

There are other factors to consider, including mounting evidence that fewer people play on Sundays and during the week-long lag between the contest end date, which is on Sunday, and April 9, when all previously won digital rolls must be played.

They can sit in your account from now until the end of the week after next," points out Wallace. In the past, that window has been a good time to play because fewer people are doing it."

To maximize your chances, he suggests buying single items online, rather than multiple, because you get a bonus roll with each.

And while he says bigger prizes like cars and gift certificates are so rare his statistical model can't accurately predict a win, it's worth keeping an eye on the numbers, especially in that final week.

There's nothing you can do to increase your odds of winning a car, specifically," says Wallace, whose wins have all been for coffee products, along with one solitary doughnut."

All you can do is increase your odds of winning a prize, which does, of course, increase your odds of winning a car. But even if you win every single time, your chances of winning a car are pretty small, just to put that in perspective."

Given the media attention that has accompanied his statistical findings, and the way word of mouth spreads on social media, he cautions this ploy could easily backfire.

It's going to be very interesting, because the other thing we're probably going to see are a lot of people saving their rolls until that last week, because this has worked in the past. It's going to be very hard to predict."

At the end of the day, Wallace won't lose any sleep. As a statistician who enjoys bringing real-world examples into his classroom, Roll Up to Win is a win-win proposition.

This isn't some weird scam I'm trying to pull," he notes. I'm just doing an experiment, demonstrating that with this contest, there's some strategy to it. It's using math and stats in the real world to maybe slightly change the odds in your favour."

He laughs. If as a side-effect of that, you get an extra free coffee, that's just a bonus."

While his personal goal is to win back more than I spent to enter," he's not worried about Tims cracking down on his mathematical end-run.

I feel like if you work at a Tim Hortons, you know, you've seen it all," says Wallace, something the company's media relations team confirmed in a statement capped with an exclamation point.

We know there are many Roll Up superfans like Professor Wallace who enjoy strategizing on how to best play the game, and we appreciate their passion for playing Canada's favourite game!"

If there's an irony to his experiment, it's that England-born Wallace - who bought 15 coffees to win 16 coffee equivalent prizes - is actually more of a tea drinker.

I don't actually drink so much coffee, 'cause it's not great for you," he notes.

I was storing it in my refrigerator for a day or two, but I channeled my upbringing to get me through."

Roll Up to Win continues through Sunday and has, to date, awarded more than 13.8 million prizes, including nine cars.

Joel Rubinoff is a Waterloo Region-based staff reporter and columnist for The Record. Reach him via email: jrubinoff@therecord.com