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Is this a "should" as in "is it in my own selfish interests" question, or a "should" as in "is it right to harass my friends in order to marginally promote my own interests as part of yet another goddamn evil viral marketing scheme for yet another goddamn internet startup" question?
Earlier quoted context omitted.
Exactly. The comment at the end "Now imagine there are hundreds of other entrants, even further decreasing your odds" makes no sense. Those hundreds (actually, more like you said: tens of thousands) of other entrants make the negative effect of inviting your own friends negligible. Example: let's assume there 10,000 entrants including you, maintain the assumption that "a new person will sign up each day based on your…
That ignores the effect of your friends sharing with their friends and so on. I added the final graph to illustrate this point - yes, having 2 entries is better than having 1, but the network effect of your friends pulling in their friends eventually kills your odds.
If I were really to invite 5 of my friends, their most likely response is:
a) not to join at all
b) not to share (that's extra work)
c) or being generous: invite one or two people
But let's roll with the post's bizarro assumptions that each accepted invite results in 2 more and see what happens if there are just 6 other entrants initially (this problem favors your argument with less entrants, not the other way around).
Your chances without sharing (remember, those other entrants are going to be able to bring in a billion persons each):
1/(1 + 2 * 6 * 2^30)
Your chances with sharing (you get two extra entries):
(1 + 2)/(2 * 7 * 2^30)
That's right. Every human being alive has joined. Only 6 other people started in the contest and you still improve your chances 157% by sharing.
The absolute only case in which it makes sense not to share is when you're the only person in the contest. And I would hope most people know not to try to improve on 100% odds.
First, the case in which you are the only entrant is irrelevant. Your chances are already 100%... why share?
For all other cases, think about this:
-Getting one extra entry DOUBLES your chances of winning.
-Supposedly, the network effect of inviting friends offsets the above. Think about what that means. The number of people you are able to get to join through invites has to be MORE THAN HALF of the total number of final entrants (if there are 10,000 entrants already, you have to cause at least 10,000 more to join to offset the doubling above).
The author is essentially stating that by the end of the contest the majority of the entrants will have been caused by you. There is no universe in which this makes sense.