• ## [Computational Complexity] Pepsi Math

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• I bought a Diet Pepsi yesterday and the label described a bottle top promotion: One in six wins Buy One Get One Free . Suppose you drink a large amount of
Message 1 of 1 , Nov 16, 2006
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I bought a Diet Pepsi yesterday and the label described a bottle top promotion: One in six wins "Buy One Get One Free". Suppose you drink a large amount of Diet Pepsi, what is your asymptotic expected discount?

If you buy six bottles then you expect to have one winning bottle top enabling you to get the next two bottles for the price of one, or eight bottles total for the price of seven. But bottles seven and eight have bottle tops too which may be winners. One can continue this process and take the limit but is there a simpler argument?

Soda bottles are interchangeable, a free soda in the future can be exchanged for your current soda. So you can assume that when you get the "Buy One Get One Free" bottle top, your current soda is free. That means you get one free soda from every six, a discount of 16 2/3%.

You get the same discount if the bottle top said "Buy Two Get One Free" or simply "Get One Free". But if the bottle top said "50% off next purchase" which seems equivalent to the original promotion, the discount is only 8 1/3%.

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Posted by Lance to Computational Complexity at 11/16/2006 04:19:00 PM

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