Tuesday, February 26, 2013

The Economics of Roll Up the Rim to Win

Roll up the Rim is a great Canadian tradition. Once a year Canadians flock to Tim Horton's to buy their coffees in the hopes of winning something wonderful.

According to this year's statistics, just by buying a cup of coffee at Tim Horton's you could win one of:
  • 40 2013 Toyota RAV4 Vehicles
  • 100 $5,000 MasterCard Prepaid Cards
  • 1,000 Napoleon Gourmet Grills
  • 25,000 $100 Tim Cards
  • 10,873,327 Donuts, or
  • 32,619,980 Coffees
This is out of a total of 260,959,840 printed RUTR cups, making the odds of you winning something just slightly higher than 1/6.

Looking at the numbers, you have about a 1/8 chance of winning a coffee on any given cup you buy (ignoring regional variation). With these odds, you would need to buy 6 cups of coffee before expecting a greater than 50% chance of winning one. Assuming, then, that you got the largest size coffee you could as your freebie, and the smallest sizes possible for each attempt, this whole adventure would cost you a net $2.08. Six cups of coffee would gain you an expected $4.52 in winnings (including the chance of donuts and Barbecues, etc.), but would cost $6.60. Fascinatingly, as the largest coffee costs $3.89*, you may actually end up ahead after trying this.

What if your goal was to win a donut? You would expect to buy 17 cups of coffee before having a 50% chance of getting one of those. During this adventure you'd expect to win at least 2 coffees, and your net cost to try this would be $8.04.

Let's ramp it up. How many coffees would you need to buy to get a $100 Tim's Card? 7235. Oof. Not impossible, but a team effort would be required - that's 107 cups of coffee per day of the contest. You'd expect to win about 900 coffees and 300 donuts, but including winnings this would cost a net $3,646.27.

I like Barbecues. I don't think I'd like them enough to buy 180,883 cups of coffee just for the chance to win one, though. Sure, I'd likely get 17 of the Tim's Cards, 22,600 free coffees, and 7,500 donuts, but at a cost of $91,597.23 I think I'd rather just buy one...

It would take 1,808,833 cups of coffee before you'd have more than a 50% chance of winning one of those elusive $5000 MasterCards. In that time you'd likely win 7 barbecues that you could sell for $5,000. I really don't know why you'd bother past that... Anyway, this would lose you $917,747.41.

And what if you really like cars? You'd have to buy at least 5,522,083 coffees to have a reasonable chance at one of those Toyotas. This process would get you 2 MasterCards, 21 Barbecues, 530 Tim's Cards, 690,260 free coffees, and 230,100 donuts, but would cost you $2,801,508.19. For that price, you could just buy 85 of the cars yourself.

More importantly, this would involve you purchasing about 1.3 million liters of coffee over two months. If you think that sounds like a lot, just remember that's only about as much as the amount of oil spilled in the Deepwater Horizon oil spill every three hours.

So is Roll up the Rim worth it? Sure. If you already like Timmy's coffee, then go for it. If you're in it for the prizes, though, you may want to re-think things...

*Values for coffee and donuts based on ranges given in Tim Horton's website, and may not reflect prices at your local store. If you try anything mentioned above and it's more/less expensive than I say, don't blame me*


G said...

Way to release the air from the tires of my new Rav4. Damn you!

Anonymous said...

I guess you didn't read the lawsuit against McDonald's that showed all of the original monopoly winners were hand picked by the company that was paid to administer the game?