Why are pyramid scams doomed to fail? Because, quite simply, they cannot support themselves. Think about it, say 10 people are in a pyramid scam where they each have to give a dollar to join. That means there are 10 dollars. How can everyone be a winner? Dividing equally means everyone gets a refund, so you could try giving most of it to one person, but then others lose out.

Say each person has to give a dollar to the person above them to join, and each person refers 5 people.
A
//|
BC D EF

So far, A has 5 dollars, and B C D E and F are broke. Let's say the pyramid continues.

If this keeps going, it's obvious that soon, someone won't be able to refer 5 people. By the third 'level', there are already 31 people in the group. The next levels go like this:

4: 156
5: 781
6: 3,906
7: 19,531
8: 97,656
9: 488,281
10: 2,441,406
11: 12,207,031
12: 61,035,156
13: 305,175,781
14: 1,525,878,906
15: More than the population in the world.

So it's clear, by the 10th level or so, the pyramid will fall apart, and everyone will run. I think if the pyramid gets to the 7th level, it's too much.

So the pyramid scheme is bust. On average, about 1/5 of the people who play this one 'win' and about 4/5 lose. Sure, you might think to join first, and screw the rest, but think about it: If you join by the 8th level, would you feel comfortable letting your mother/children into the 9th? How about your extended family into the 10th? Hope that the scheme lived to level 11? I doubt it.

All of the other mechanisms, such as having the people who are at the top rejoin at the bottom, etc, are also forced to lose by this simple reason: You can't make money from nothing. You have to either win by ripping someone off, or lose by being ripped off. There is no escape. All of these schemes are bound to make you lose, or make the people you refered lose. All that risk for a possible 5x what you pay? I think not!