On the other side, as an early employee you can have a much bigger impact on the odds of success than an investor. If you think a company has huge potential, but it's missing X/Y/Z, and you're an expert in X/Y/Z, then you have both a unique insight and unique leverage to make a success out of something that might not have been without you. Looking for situations where you make the difference is perhaps one way to have the whole thing feel like less of a lottery.
I think this is a good point. If you are the ‘secret sauce’ than you may have an edge over an investor. There is perhaps the question of how you know that the company has huge potential with any confidence but I can think of a number of situations where it may be generally indicated. You should also command a stiff premium for catalyzing the company’s success. =)