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## Unlucky Odds in the Free Coke Game

One spring, oh, about 10 or 11 years ago, I bought a 20 oz. Coke from the vending machine at Lake View Country Club. I looked under the cap and saw that I won a free 20 oz. Coke - yay! I used the lid to get my free Coke and won another! The cycle repeated itself quite frequently, and I think I spent about ten dollars all summer and won at least 75 free Cokes. Nearly every Coke I got was a winner. That was back when you had a 1 in 3 chance of winning.

This year, Cokes offer a 1 in 12 chance of winning, or an 11/12 chance of not winning. From the Country Fair less than a mile from my house, Carey and I have purchased at least 100 Cokes. Not a single one has produced a winner. What are the odds?

Doing the math, we take the odds of not winning (11/12) and raise it to the number of times I've not won in a row: `(11/12)^100 = 0.0001663963943`. That's roughly 1 in 6000 odds I would not win 100 times in a row.

Needless to say, Carey and I question both Coke and Country Fair. The summer I won a bunch of Cokes it was as if every bottle was a winner, and I seriously wondered (after just five consecutive winners) if the bottling plant had screwed up and sent cases of winners to one location and cases of non-winners elsewhere. Basically, perhaps they forgot to randomize the caps?

Well, this summer I wonder the same thing. One in 6,000 odds are pretty steep when the odds are supposed to be 1 in 12.

### 7 Responses to "Unlucky Odds in the Free Coke Game"

1. While the 1/6000 is true of not winning hundred cokes in a row, the chance of not winning the next one isn't 0.000152530028, (or approximately 1/6550) but still 11/12.

That's the thing. Each one you don't win, doesn't change the odds of you not winning the next one. Well, not really. We're of course assuming an infinite supply of coke. Which is a practical assumption. In reality each coke you drink, reduces the pool of non-winners and thereby increases the chance of winning. But from a practical standpoint, because of the hugeacity (damn, that should be a word) of the pool, it can be treated as infinite.

2. I think it was about 10 years when I had a similar experience. Someone bought me a Coke from the little store down the road, and the cap was good for a free Coke. Eventually, I had won 21 free Cokes, all from the same storeâ€¦

3. Yeah, I know the odds on the next one are the same as the first. Still sucks that I've been ripped off all year. 😉

4. I had a similar issue about 20 years ago when I like 8 years old. However it was potato chips. We were at my Aunt's wedding at this very upscale hotel that had snack bar.

My dad went down to the snack bar and bought like 10 bags of chips for all the kids because there was no "kid" (junk) food at the wedding. Of the 5 bags we openned , 4 were winners. We kept on winning free bags of chips. To the point where the snack bar TRIED to refuse us a bag of free chips.

When we told my parents about all the free bags they had conculded that maybe the potato company put all the free winners here at the hotel because they A) probably did not sell many chips here and B) The kind of people staying at this hotel would normally think its below them to go back and get another bag of free chips.

The following week we wanted to see if our parents were full of it, so we went to the local 7eleven by our school and bought 10 bags over the week and I think maybe we got 1 free bag!

5. You are merely evening out the sample.. last year your 1 in 3 odds were probably BETTER than what they had announced as the official odds... was coke really giving away 3 cokes for the price of 2?

(I typically wait until EVENT weekends, like the superbowl, etc to find good price per unit ratios, when cokes are used as loss leaders, then stock up as much as is allowed) In the past month, I have found 12 ounce cans for around 20 cents or less. Or a case for four dollars, when they were trying out 24 pack packaging. CostCo pricing is usually around seven dollars a case.

Of course, buying the big bottles is even cheaper, but that goes flat, unless you are drinking it fast enough.

Regarding contest caps, some people really lucked out in the Pepsi/iTunes promo as well, where others, did not at all. The bottles with the winning caps themselves were NOT randomly distributed to all markets. This is probably what happened to you your summer of free Cokes.

6. strangely I've bought about a dozen cokes in the past few months and I won once.

7. I bought another today and didn't win. Where have you bought yours, Ron? Probably not at Country Fair. 🙂