I'm curious - are you comparing Facebook, the company with nearly 5 years of success as a public company based on strategic decisions, to someone who wins a random chance lottery?
Because just like with lotteries, there are a lot of blanks, few small wins and a tiny amount of never-work-again wins: Many startups don't net the investor much, some make quite a bit after being acquired, and very few - such as facebook - turn out to be really successfull.
Your phrasing suggests that you compare Facebook (now) with lottery as a system. You should rather see Facebook as a lottery ticket that turned out to be the jackpot.
Every lottery ticket has the same odds of winning, no matter the "strategy" employed in picking numbers, location of buying the ticket, etc. Facebook is not in any way a analogue, unless you are arguing that its success was entirely random, and would have stood an equal chance of happening if I had started it at a community college, then put the headquarters in Alaska, which is false.
You can: Assuming that Powerball simply collects all earnings and pays them to the winner (they don't and keep a share), simply regard your lottery ticket as your share and deposit the price you pay in your savings account.
You seem to deliberately ignoring the fact that Facebook is a publicly traded company.
You can't go up to the lottery winner and offer to buy part of their winning ticket. You can buy shares of Facebook today (in fact, at a nice discount currently).
Look at the operating margin and net income increase in just 1 year: https://twitter.com/mbesto/status/793921076820459520
That makes investors absolutely drool.