### Pyramids, chain letters, exponential growth etc.

The basic scheme claims exponential growth will help you make a fortune. Modeling
exponential growth is one of a physicist's strong points, so here goes:

For illustration purposes I'll invent the following scheme (typical of pyramid & mail schemes you will find):

- Send $1 to each of the five names on the list.
- Make a new list with the top name scratched off and your name at #5.
- Send the new list to 10 friends.

The claim... your spend $5. The first round of people sends you $10, the next round sends you $100... the fifth round (just before your name drops off) sends you $100,000.
This is pretty good even if a lot of people don't participate, right? WRONG! Here's what happens even if everybody participates:
Round #1:

Person starts the list - sends it off to 10 people.

Round #2:

Originator makes $10

list goes to 100 new people

Round #3:

Originator makes $100

round #2 people make $10

list goes to 1000 new people

Round #4:

Originator makes $1,000

round #2 people make $100

round #3 people make $10

list goes to 10000 new people

Round #5:

Originator makes $10,000

round #2 people make $1,000

round #3 people make $100

round #4 people make $10

list goes to 100,000 new people

Round #6:

Originator makes $100,000

round #2 people make $10,000

round #3 people make $1,000

round #4 people make $100

round #5 people make $10

list goes to 100,000 new people

Round #7:

round #2 people $100,000

round #3 people make $10,000

round #4 people make $1,000

round #5 people make $100

round #6 people make $10

list goes to 1,000,000 new people

Round #8:

round #3 people $100,000

round #4 people make $10,000

round #5 people make $1,000

round #6 people make $100

round #7 people make $10

list goes to 10,000,000 new people

Round #9:

round #4 people $100,000

round #5 people make $10,000

round #6 people make $1,000

round #7 people make $100

round #8 people make $10

list goes to 100,000,000 new people

Round #10:

round #5 people $100,000

round #6 people make $10,000

round #7 people make $1,000

round #8 people make $100

round #9 people make $10

list goes to 1,000,000,000 new people

Round #11:

round #6 people $100,000

round #7 people make $10,000

round #8 people make $1,000

round #9 people make $100

round #10 people make $10

list goes to 10,000,000,000 new people

... except that there aren't 10 billion people on earth.
Here is where either it ends, or in a few days you
find yourself sending millions of letters per day.
Sooner or later you will run out of new people even
if everybody participates. In the end many people have
made money yes, but many more have lost money.

You may have noticed the web is flooded with banners like the Google Ads banner that appear in the DC Physics ad rotation.
Is such advertising a route to fast money from your web pages? Again a bit of analysis is needed.
Here we are not talking scam - there is a genuine service (advertising) being offered
to earn the money. But how much money can you earn? Banners are available
for any website through various "affiliate" schemes. Details vary - some are commission on sales,
some are pay-per-click, some are pay per display (usually counted in the thousands).
I have personally had little luck with commission banners, I mostly use
pay-per-click. Now, the hard sell approach goes something like this:

*...join this plan and make 5 cents per click. Imagine you put 6 banners on every page and
***only 50%** of your page visitors click on them... you average 15 cents per visitor. Even if you
only get 1,000 visitors per week, that's $150/wk for doing nothing!!!.

Are you sold? If so, review the assumptions.

* how many people will bother with a page that has 6 banners on it?

* what is a typical click-rate?

A typical click-rate is around 1% (I get up to 10% with a few very good banners), and people
won't click on more than one banner per page so don't dilute the real content of your page with
extra banners. At 1%, this 5 cents per click translates into 10 clicks per thousand page
displays, or $0.50. You are hardly into big easy money, but there is potential if you choose
good banners with high pay-outs and work at developing a site that will generate a good amount of traffic.
If you eventually get really big traffic - say a million page displays per month - you can get into a
whole new ballpark for ad revenue via companies such as DoubleClick.