1) I get that to get the first users, you have to go out and recruit them. That's the advertisement part. So yeah, I get how you get users by advertising.
2) I get that when you have a million customers, they become the advertisement and they are the ones who are bringing you new customers. Your product "ad surface" is way bigger than simple banners through them.
Now what I have a hard time to understand is how 300 users procures the same effect as 2) (or even 3000). I get that they gonna get you 30 more customers by talking about your product to their "friends" who, if everything goes fine, at their turn gonna bring you 3 more customers who gonna bring you 1 more customers, for a grand total of 34 more customers. And that's the end of it. That wont grow much bigger. So basically, you would have to go back to 1) to get new users.
What am I missing? Does a user have to bring you n more new customers, n > 1? How many customers do you need via advertising so that the compound growth effect kicks in?
edit: I can see actually 2 types of compound growth effects: a) a user explicitly recruit another user (ex: "hey my friend, come play to this game"), b) a non user "see" other people using the product and he tells himself that might be a good idea to try it. Anyway, so basically, what I see is that, early on, you can rely only on a) so, in average, your customers have to get you n more new customers, n > 1, by explicitly recruiting them for you. Which, if Im correct here, would give an idea how badass the product must be.