Pyramid schemes for kids

I have twice now been invited to join pyramid schemes for my child. The other day we got a letter in the mail from a friend soliciting us to join a “sticker club” (a few months ago, it was a “book club”). Two other children’s names and addresses were on the page, with the instructions that we were to send a pack of stickers to each kid. Then, we were to make twelve copies of a blank version of the letter; on six, we were to move up the name of child #2 to the spot of child #1, then insert our child’s name; finally we were to send the letter plus a blank to six friends.

The promise was that for our efforts to send two packs of stickers, we would then get 36 from others in the “sticker club”. This is, of course, a classic pyramid scheme. I recognized it immediately because there was one operating out of my tennis club when I was a teenager, though real money was at stake not stickers.

The problem is that this set-up cannot perpetuate itself for long. In round one, there is one kid sending out six letters, which jumps to 36 in round two, and so on. Here is the progression:

6
36
216
1,296
7,776

At this point, after only five rounds, the numbers still seem plausible. But it is after this point that things quickly go off the rails:

46,656
279,936
1,679,616
10,077,696
60,466,176
362,797,056
2,176,782,336
13,060,694,016

As should be obvious, the “sticker club” in short order includes every child on the planet (by round 12). Even if we allow for kids to “join” multiple times, and even if not every letter sent results in stickers, the club cannot continue. And at 51 cents per letter sent, the costs of running the game would consume the collective resources of the entire economy (although Canada Post might be very happy).

This is why pyramid schemes are illegal. You could also think of the scheme as a “bubble”, which shows quite clearly what happens with runaway growth. And it is also the old parable about the rice grains on the checkerboard.

The tough part is that it would be nice for my child to receive lots of stickers from all over the place. And the letter does warn “If you cannot do this within six days, please let me know. It isn’t fair to those kids who have already participated if you don’t follow”. But the structure of the game is such that it cannot be fair – someone down the line will not get their stickers.

So I will pass on stickers to #1 and #2, but I will not pass on the letter.