Tim Hortons lovers across Canada are rolling up rims of coffee cups and, although millions dream of seeing a shiny new car reveal itself under the lid, documents show that's not likely to happen — especially if they live in Ontario.

Debra Deveau, a Tim Hortons server in Saint John, N.B., watches traffic at the popular coffee shop mushroom during the annual "Roll Up the Rim to Win" contest, where customers can roll up the rim of their cups to see potential prizes.

'You'll get six, eight, 10 ... cups of large coffees from people who will come in the run of a day, compared to when the contest is not running.' — Debra Deveau, Tim Hortons worker

"I've seen people come in and buy tons and tons of larges," Deveau said.

"You'll get six, eight, 10 ... cups of large coffees from people who will come in the run of a day, compared to when the contest is not running."

Tim Hortons has issued 281.7 million special contest cups for its popular springtime contest, which runs across Canada and in 11 American states.

The average Canadian adult will roll up a rim 10 times before the company closes the promotion May 1.

Top prize is a $32,000 Toyota Venza and is hidden beneath the rim of 35 of the cups, but company documents show they are not distributed equally across the country.

For example, although 52.5 per cent of all contest cups will be sold in Ontario, only 15 of those 35 grand prize cups — or 43 per cent — have been allotted to the country's most populated province.

That's three fewer than provincial coffee drinkers could have expected under a proportional distribution of top prizes.

Extra cars slipped into B.C., Quebec, Atlantic

Instead, those three cups have been slipped, one each, into stores in British Columbia, Quebec and Atlantic Canada. 

Tim Hortons lists the overall chances of winning a Toyota Venza as slightly more than one in eight million.

But because of the distribution of cups those odds vary across the country.  The best chance to win big is in British Columbia (one in 5.9 million) and the worst is in Ontario (1 in 9.9 million).

Tim Hortons gives no reason in its contest documents for the uneven placement of the car cups around the country.

All other prizes are distributed proportionately.

A call to Tim Hortons headquarters in Oakville, Ont., about the issue was not returned.

Still, many customers say they have their sights set lower than the grand prize anyway.

Katie Burtt, a student at the University of New Brunswick in Saint John, said she would happily celebrate a free doughnut.

"I keep a tally. I've had 26 coffees and won nothing," Burtt said.