Free iPod!

Apparently there are some people still falling for that “” pyramid scheme. I posted a pretty skeptical analysis last month, but TrollJournal ate it. I thought the whole pyramid would have collapsed by now, but it seems not. So, let’s repeat the analysis…

Let’s try to give the benefit of the doubt, and be optimistic in our analysis.

First off, note that every time someone goes to the site and registers directly, rather than being referred there, nobody gets credit for that new member, so existing members are less likely to get their free iPods. So, let’s assume that the only way people ever join is by being referred, hence maximizing the chance that people who sign up will get an iPod.

Next, note that there is clearly a finite world population. Once the necessary referrals have signed up and won you your free iPod, any additional referrals are just reducing the number of people remaining who might sign up, and again reducing the chances of the people who have already signed up finding enough new members to refer. So let’s also assume that nobody collects more than the minimum number of referrals required, which is 5.

Now we need to estimate how long it takes someone to find 5 referrals. I’m gonna say 24 hours, partly because it seems like a reasonable number, and partly because it makes the mathematics really easy. Everyone knows at least 5 people who read their e-mail more than once a day, right?

Our final assumption is that it doesn’t get harder to find referrals as time goes on. This is a ridiculous assumption, but hey, we’re trying to be optimists, right?

Enough assumptions. The nugget of data we need is when the whole scheme started. I did some searching on Google, and found public postings about the site dated July 19th.

So, we have our algorithm: we start July 19th with 1 member. Each day, each member who hasn’t won an iPod (i.e. those who joined the previous day) finds 5 new members, and becomes eligible for a free iPod. The next day, each of those new members will find 5 more new members so they can get their free iPod, and so on.

I wrote a quick Perl program to compute the results.

Jul 19:
 Site has 1 members.
 The 1 most recent members find 5 more.
 Apple has shipped 1 iPods.

Jul 20:
 Site has 6 members.
 The 5 most recent members find 25 more.
 Apple has shipped 6 iPods.

Jul 21:
 Site has 31 members.
 The 25 most recent members find 125 more.
 Apple has shipped 31 iPods.

Jul 22:
 Site has 156 members.
 The 125 most recent members find 625 more.
 Apple has shipped 156 iPods.

Jul 23:
 Site has 781 members.
 The 625 most recent members find 3,125 more.
 Apple has shipped 781 iPods.

Jul 24:
 Site has 3,906 members.
 The 3,125 most recent members find 15,625 more.
 Apple has shipped 3,906 iPods.

Jul 25:
 Site has 19,531 members.
 The 15,625 most recent members find 78,125 more.
 Apple has shipped 19,531 iPods.

Jul 26:
 Site has 97,656 members.
 The 78,125 most recent members find 390,625 more.
 Apple has shipped 97,656 iPods.

Jul 27:
 Site has 488,281 members.
 The 390,625 most recent members find 1,953,125 more.
 Apple has shipped 488,281 iPods.

Jul 28:
 Site has 2,441,406 members.
 The 1,953,125 most recent members find 9,765,625 more.
 Apple has shipped 2,441,406 iPods.

Jul 29:
 Site has 12,207,031 members.
 The 9,765,625 most recent members find 48,828,125 more.
 Apple has shipped 12,207,031 iPods.

Jul 30:
 Site has 61,035,156 members.
 The 48,828,125 most recent members find 244,140,625 more.
 Apple has shipped 61,035,156 iPods.

Jul 31:
 Site has 305,175,781 members.
 The 244,140,625 most recent members find 1,220,703,125 more.
 Apple has shipped 305,175,781 iPods.

Aug 1:
 Site has 1,525,878,906 members.
 The 1,220,703,125 most recent members find 6,103,515,625 more.
 Apple has shipped 1,525,878,906 iPods.

Aug 2:
 Site has 7,629,394,531 members.
 The 6,103,515,625 most recent members would need to find 30,517,578,125 more.
 Apple has shipped 7,629,394,531 iPods.

Everyone on the planet now has an iPod.

So there we have it. If we set our assumptions to maximize your chances of winning an iPod, everyone on the planet already has an iPod.

Of course, the nice thing about having code to crank out the numbers is that I can now fiddle with the assumptions. If we assume it takes everyone two days to find 5 more members, then the remaining population of the earth got their iPods today, August 16th. So, if you didn’t get yours, don’t panic, it’s probably in the mail.

Update 2004-09-24

Forbes is reporting that people are suing for not shipping them the free iPod they qualified for. The company claims Apple simply isn’t shipping them the thousands of iPods they’ve ordered, and that people will get their free iPods real soon now, honest.

Oh, and the lucky suckerscustomers of the service also say they’re being inundated with spam.

I’m shocked to find out from Forbes that this may not be a legitimate business operation. Shocked, I tell you.