Trick to winning Tim Hortons’ Roll up to Win: Play during the middle of the night

Tim Horton’s legendary roll-up-the-rim competition began in 1985 and has remained largely unchanged for 25 years. The format was simple: buy a coffee, roll up the rim of the paper cup and see if you won a prize. But that changed in 2020.

Amid the onset of a global pandemic, the game went digital. Purchasing Tim Hortons products still earned you entries to the competition, but these have now been saved in the company’s loyalty app. It was then up to you when to play these so-called “digital roles”. Since players no longer actually roll up the rim of a coffee cup, the competition is now called Roll up to Win.

My approach sounds simple – play when other people aren’t – but it took data, determination and a lot of coffee to find the optimal approach.

Here’s the history of the stats behind the headlines.

The digital element changes the odds

So when do the fewest people play?

On the surface, that seems simple: play in the middle of the night when most Canadians are asleep. But in a country that spans six time zones, finding the best time is a difficult math.

In previous competitions, I’ve assumed that 4:30 am Eastern is the optimal time: not too late and not too early. But an educated guess is still a guess, and if I wanted to find the true Goldilocks zone of free coffee, I’d need data.

This year, Tim Hortons gave me just that.

Retrieving data from the app

When I logged into the app on the first day of the competition on March 6th, a big message caught my attention: “More than 308,619 prizes already awarded!” That’s an enticement to play – so many winners already! – but it is also valuable information.

I waited five minutes and refreshed the page. The message changed: “More than 309,949 prizes already awarded!” Another 1,330 prizes were won.

That gave me an idea.

I have updated the page regularly and logged the time and number of prizes awarded. My theory: The number of prizes won should correlate with the number of players. By tracking this data, I was able to model Roll up to Win player behavior and thereby calculate exactly when to play.

Online data tracking is common in scientific research, often using software to automatically download information. However, automated procedures usually break the rules of such competitions, and Roll up to Win was no exception. So I entered the data manually.

I updated the site myself during the day – and night – and was able to roughly track the prices. But I had other things to do, so there were gaps in my logs. Statistically, I had so-called missing data.

Missing data is common in real analysis. Examples include unreturned or incomplete surveys, patients missing doctor appointments, or even misplaced or corrupted data files.

Statistical Challenges

This can present statistical challenges depending on how – and why – we have gaps in our records. A patient could miss their appointment because they were unwell to travel or perhaps simply because their car wouldn’t start. These two scenarios provide different information and require different solutions.

My problem with missing data was comparatively simple. My goal was to fill in the gaps left by sleeping, traveling, or otherwise away from my keyboard.

With the data I had, I looked for patterns. Most prizes were won between 9:00 am and 1:00 pm Eastern Time, with the fewest around 3:00 am. This repeated itself every day and I was able to use this to my advantage.

In order to map our mathematical models to the real world, statisticians often make assumptions. I assumed that the behavioral patterns of the players would be similar in everyday life. That was a pretty strong assumption – I had some indication of a slightly later start on Sunday morning – but it seemed a reasonable one for my problem.

weighting of the data

This turned my educated guess of the past few years into a data-backed estimate. The best time to play was 3:16 am Eastern – over an hour earlier than I’ve played in the past – and the worst was 11:46 am for the highest and lowest odds.

There was one last step: I had to test my results. My analysis was based on a different assumption: that the number of prizes available was constant throughout the day. Maybe at 3am fewer people were winning because there were fewer prizes, not fewer players. Fortunately, this was an assumption I could test.

3:16 am is the golden hour

I collected 60 rolls and split them in half, playing 30 at the 3:16 mark and the rest just before noon. I won 23 times in the early hours, later only 5 times. No big prizes – mostly lots of free coffee – but I got the result I was hoping for: statistically strong evidence that my theory was correct.

I reached out to a local journalist who had worked with me in the past. I thought this might be a fun little story about applying statistics to the real world, with a touch of local flavor as a University of Waterloo professor. Then things went uphill. By the end of the week, I had appeared on countless radio stations and even national television shows, including CTV’s Your Morning and CBC’s The National.

While the interviews were a great opportunity to show that statistics can be more than just equations in a textbook, many outlets spotted a potential flaw. If everyone starts playing at 3:16, won’t the strategy change?

However, I don’t think everyone will get up in the middle of the night to win a free coffee, so it should remain a good time to play.

I’ll get up in the early hours and follow the data for the final week of the competition – all entries must be played by April 9th ​​- to see if the strategy needs an update. It’s still a few long nights, but I think I’ve got enough caffeine for it.