There are stories of pressing national importance, and then there's Tim Hortons' Roll Up The Rim To Win contest, a veritable Canadian preoccupation and one so rife with rumours of conspiracy that it begs for an, ahem, journalistic investigation.

To wit, do residents of certain parts of Canada have better odds of winning the top prizes — 40 Toyota Rav4s — based on the regional distribution of cups? Are Tim Hortons employees rolling up cup lids before sale, scooping the prize winners and passing off the please-play-agains to their customers

And the question du jour: Are you more likely to win a prize if you buy a larger size drink? It’s a question on the minds of many frustrated small- and medium-size cup drinkers who, after countless coffees and teas, feel the one-in-six odds of winning a food prize don’t seem to apply to them.

Alexandra Cygal, senior manager of public affairs for Tim Hortons, gave a categorical "no" when we asked her if the odds change depending on cup size.

The "conspiracy theorists are wrong," she said in an email. "Our prizes are distributed randomly across all eligible cup sizes so large cups don’t necessarily mean better odds."

But we're a skeptical bunch of hard-nosed journalists at The Huffington Post Canada. Could we take Tim Hortons at their word?

Of course not.

So we challenged members of our talented newsrooms to take part in a journalistically questionable, unreliable and completely unscientific experiment: We asked them to drink a swimming pool's worth of coffee over a week and keep their cups. Sure, we knew the results would be skewed by all kinds of factors, beginning with the small sample size and ending with the fact that most cups were bought in Toronto.

Still, guess what we found? Our staff, which consumed 92 beverages over the week, were far more likely to win a prize if they purchased an extra large drink than a small drink. The numbers:

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  • Do The Odds Change?

    Are you more likely to win a Roll Up The Rim To Win prize if you buy a larger size drink? It’s a question on the minds of many frustrated small- and medium-size cup drinkers who, after countless coffees and teas, feel the <a href="http://forums.beyond.ca/showthread/t-121304.html" target="_hplink">one-in-six odds don’t seem to apply</a> to them. Tim Hortons says a categorical no, that prizes are distributed randomly across all cup sizes.

  • The Challenge

    So we challenged members of our talented newsrooms to take part in a journalistically questionable, unreliable and completely unscientific experiment: We asked them to drink a load of coffee over a week and keep their cups. Sure, we knew the results would be skewed by all kinds of factors, beginning with the small sample size and ending with the fact that most cups were bought in Toronto. Still, the results were interesting:

  • Small Cups

    38 Small Cups: 4 wins, 34 losses (10.5 per cent winners or one-in-9.5 odds)

  • Medium Cups

    18 Medium Cups: 3 wins, 15 losses (16.6 per cent winners or one-in-six odds)

  • Large Cups

    18 Large Cups: 3 wins, 15 losses (16.6 per cent winners or one-in-six odds)

  • Extra Large Cups

    18 Extra Large Cups: 5 wins; 13 losses (27.7 per cent winners or one-in-3.5 odds)

  • Roll up the Rim to Win: A History

    Here are nine important, fun or just plain random facts about Tim Hortons’ Roll Up The Rim To Win Contest.

  • This is the guy who invented it

    Ron Buist was the marketing director for Tim Hortons when the chain rolled out its first Roll up the Rim to Win contest. Buist says he came up with the idea because of cost constraints. The chain didn’t have enough money to make cups for a scratch-and-win contest, so he came up with the idea of rolling up the cup’s rim instead. "<a href="http://www.thepeterboroughexaminer.com/2012/05/01/roll-up-the-rim-inventor-among-judges-at-may-12-bears-lair-finale">Like any invention, one person comes up with it, but it's the company that makes it work</a>," Buist said.

  • There's a novel about it

    Giller Prize-nominated writer Leo MacKay Jr.’s novel <em>Roll up the Rim</em> is “<a href="http://www.indiegogo.com/rolluptherim">a comic tale of obsession, redemption, divine intervention, and Timbits</a>.” MacKay is selling the book directly, and depending on how much money you send him, you can get the book autographed, get a reading from the author via Skype, or even get an in-person reading. Now that’s dedication.

  • A hot commodity among thieves

    Some retailers who carry Tim Hortons coffee have reported customers doubling or even tripling up on roll-up-the-rim cups. Some brazen wannabe winners are going so far as to take entire stacks of cups out of stores. Retailers have <a href="http://www.torontosun.com/2012/02/25/thieves-stealing-roll-up-the-rim-cups">taken to hiding the cups behind the counter to keep people from stealing them</a>.

  • Dude, where’s my Toyota?

    A winning Timmies cup became the centre of acrimony in 2006 when a 10-year-old Montreal girl found a cup in a garbage can. With the help of a 12-year-old friend, the girl discovered that the cup was a Toyota RAV4 winner. But the contest win turned into a battle between two families when the 12-year-old’s parents claimed the prize for their own. And the whole issue became even more complicated when a custodian at the girls’ school claimed he had thrown the cup away. In the end, <a href="http://www.cbc.ca/news/canada/story/2006/04/19/hortons-cup-060419.html">Timmies gave the car to the 10-year-old</a>, as the rules stipulate whoever hands in the cup wins the prize.

  • Timmies employees sneaking and peeking?

    A Newfoundland man told the press in 2008 he suspected Timmies employees of sneaking and peeking at cups to suss out winners, then passing along the losing cups to customers. Bernard Delaney said he got a cup that looked like the rim had already been rolled up, and the cup, he said, even had teeth marks. Tim Hortons said <a href="http://www.stcatharinesstandard.ca/2008/03/26/manufacturer-blamed-for-faulty-roll-up-rims-man-says-his-cup-looked-like-it-had-teeth-marks-on-it">a manufacturing problem was to blame for the cup</a>, and denied anyone had bitten into the cup or sneaked a look under the rim.

  • Environmentalists vs. Roll up the Rim

    The Toronto Environmental Alliance criticized the Roll up the Rim contest in 2010, noting that disposable coffee cups of the sort Tim Hortons uses are wasteful and harmful to the environment. "A lot of resources go into making a coffee cup and too often they end up going into garbage. . . . it's a pretty significant waste of resources,” the group said. Tim Hortons <a href="http://www.lfpress.com/news/canada/2010/03/01/13076551.html">said they were looking into alternatives, but hadn’t found one yet that works</a>.

  • Regional divides

    Tim Hortons took some criticism when it emerged in 2009 that <a href="http://www.cbc.ca/news/canada/new-brunswick/story/2009/03/11/nb-tim-hortons-rims-629.html">your odds of winning are worse in some provinces than others</a>. CBC reported that, though 52.5 per cent of Roll up the Rim purchases took place in Canada’s largest province, Ontario only received 43 per cent of prizes. The best odds of winning were in British Columbia, where the odds of winning were nearly double that of Ontario.

  • Counterfeit cups?

    Vancouver Island house painter Matthew de Jong walked into a Tim Hortons in 2009 and presented a winning cup for a Toyota Venza. A week later, the company <a href="http://www.cbc.ca/news/canada/british-columbia/story/2009/05/15/bc-roll-up-the-rim-fraud.html">informed de Jong he wouldn’t be getting his prize because his cup was a fake</a>. Tim Hortons even suggested it could bring charges against de Jong. But when the story hit the news, a 12-year-old girl who lived in the house de Jong was painting came forward to admit she had made a fake winning cup as part of an April Fools prank. Tim Hortons dropped the matter.

  • Bad for business??!!

    In 2011, when Tim Hortons missed quarterly earnings projections, the company blamed the bad performance on “<a href="http://www.theglobeandmail.com/globe-investor/tim-hortons-blames-roll-up-the-rim/article591364/">significantly increased food and beverage prize redemptions</a>.” The company estimated Roll up the Rim had cut about a third off of same-store sales growth that quarter. But the company also noted that a coffee promotion at McDonald’s during that year’s Roll up the Rim may have cut into sales.

  • 18 Extra Large Cups: 5 wins; 13 losses (27.7 per cent winners or one-in-3.5 odds)
  • 18 Large Cups: 3 wins, 15 losses (16.6 per cent winners or one-in-six odds)
  • 18 Medium Cups: 3 wins, 15 losses (16.6 per cent winners or one-in-six odds)
  • 38 Small Cups: 4 wins, 34 losses (10.5 per cent winners or one-in-9.5 odds)

For the record, the winning prizes were 11 coffees and four doughnuts. No gourmet grill or Rav4 for us. And the overall number of prizes-to-cups is pretty much one-in-six (16.3 per cent), as advertised, though certainly not if you break it down by individual cup sizes.

UPDATE: Our readers respond to our survey and size does matter.

By the way, if you think odds of one-in-six mean you’re due a prize after buying six drinks, a crash course in probability theory is warranted.

As Wai Kong (John) Yuen, a math professor at Ontario's Brock University says, "it only means that in the long run, if you buy a large number of coffees, say 600 cups, you are expected to win around 100 times. However, anything can happen if you only buy six."

Think of what happens when you roll dice. There's a one-in-six chance the die will turn up a six. The odds essentially "reset" on the next roll. Says Vadim Kaimanovich, the Canada Research Chair in Analysis and Probability at University of Ottawa, "The result doesn’t depend on what happened before or what happens after."

"What difference does it make to the dice that you rolled it some way in the past?" adds Jeremy Quastel, a math professor at University of Toronto.

Roll Up The Rim, he notes, "is a tiny bit different with the coffee cups, because the odds don't completely reset each time. There are a fixed number of winning cups, so after you buy a losing cup there is the tiniest improvement of your chances the next time. But it is way too small to make any real difference."

Regional differences do exist, according to Yuen, who crunched the numbers for HuffPost. The odds for small prizes aren’t disclosed, but it’s reasonable to assume that it’s one in six everywhere, he said.

However, your chances of winning a car are best in the Atlantic provinces, Yuen found. You’re more likely to win a BBQ in Ontario. The best chance to win a $5,000 pre-paid Mastercard or $100 "Tim Card" is to buy your Timmies in — gasp — the United States.

Again, the big prizes are few and far between. As our friends at WalletPop Canada note, the odds of winning one of the cars on Roll Up The Rim is one in 6.5 million. You’d have far more luck winning the grand prize home in one of those charity lotteries.