The Expected Value of Tim Horton's Roll Up The Rim To Win® Cup

Tim Horton's® is running there Roll Up The Rim To Win contest right now, with a chance to win $77,571,230 in prizes, although we calculated it to be at least $90,153,176 in prizes.  There are a variety of prizes including donuts, coffee, $100 Tim cards, 55" LG 4K TVs, $5,000 CIBC prepaid cards and forty Honda Civics.  The bigger prizes are what gets people excited, but it is the smaller prizes that have a larger expected value.


Tim Horton's® Roll Up The Rim To Win Expected Value on Each Cup

Prize

Prizes Available

Individual Prize Value

Total Prize Value

Expected Value

55" LG 4K UHD TV

150

$1,599

$239,850

$0.000816

$5,000 CIBC Prepaid Cards

100

$5,000

$500,000

$0.001700

Honda Civic

40

$23,290

$931,600

$0.003168

$100 Tim Cards

24,000

$100

$2,400,000

$0.008161

Instant Win Food and Drinks

49,007,531

$0.70 - $4.29

$73,499,780

$0.249940

Our Instant Win Food and Drinks*

49,007,531

$0.99 - $2.09

$86,081,726

$0.292726

Total

49,031,821

$0.70 - $23,290

$77,571,230

$0.263785

Our Total*

49,031,821

$0.99 - $23,290

$90,153,176

$0.306571


* This is our estimated value, not Tim Horton's estimated value, see below for more details.


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Total Expect Value

The total approximate value for all available prizes is $77,571,230 and there are at a minimum of 294,069,480 cups available according to the Roll Up The Rim To Win website.  The expected value of all prizes would be $77,571,230 ÷ 294,069,480 = $0.263785 or about 26 cents a cup.
    We consider that to be too conservative of a number.  Tim Horton's calculated their food prize value based on the lowest retail price of medium coffee and lowest retail price of donut/cookie within each regional allocation.  There is 49,007,531 food and drink prizes with 65% being coffee, 25% being donuts/muffins and 10% being wedges.  The numbers we are going to use is $2 for coffee, $0.99 for donuts and $2.09 for potato wedges.  Using these values, we get (49,007,531 x 0.65 x $2) + (49,007,531 x 0.25 x $0.99) + (49,007,531 x 0.1 x $2.09) = $86,081,726 in food prizes.  Using our prize value the expected value of a cup would be $90,153,176 ÷ 294,069,480 = $0.306571 or about 31 cents.
    That is a reasonable expected value amount for a free chance to win, but you could value it more if you place the same payout ratio as a lottery ticket.  Sure, the expected value is around 26 or 31 cents a cup, but if the contest was a paid lottery with a 45% payout ratio, you would pay around $0.59 or $0.68 for each cup.  ($0.263785 x 100/45 = $0.586188) or (0.306571 x 100/45 = $0.681269)
    If you don't value the food prizes as a lottery, then the expected value would be ($0.263785 - $0.249940) x 100/45 + $0.249940 = $0.280707 or around 28 cents per cup using Tim Horton's numbers.  The EV using our number would be ($0.306571 - $0.292726) x 100/45 + $0.306571 = $0.337338 or around 34 cents per cup.



Roll Up The Rim To Win Rules and Redemption
Roll Up The Rim To Win Website