I'm not sure what you mean by 'expectation of one case' here, but just to clarify: rolling a ten-sided dice, 10 times, gives a 65% chance of rolling at least one 10. So you still have a 35% chance of zero 'wins'.
I can't comment on the rest of your model, but its worth keeping in mind how the binomials shake out.
Ack, you're absolutely right. Don't know where I was going with the hypothetical example but my math was totally wrong.
Re:TLDR Stock Options
by waterhouse on Thursday June 01, 2017 @10:06PM
(#14466895)
Actually, your statement was entirely correct. "Let's say 10% of start-ups succeed ... You would need to join 10 of these start-ups ... to have an expectation of one case [of success]."
It is a true statement that the expected number of successes after 10 tries would be 1. It is also a true statement that your chance of zero successes after 10 tries is 34.8%. (The balance comes from the outcomes that include multiple successes.) It may be that the latter is the more relevant and interesting statement to make, but your math was totally right.
;-)
Imagine what kind of stock investments you'd make if you were only allowed to invest in one stock at a time.
Let's say 10% of start-ups succeed to the point where employee 100 makes "a bunch of money", which I think is very generous. You would need to join 10 of these start-ups throughout your career (and of course remain at each for the 3-5 years it takes to learn if the lottery ticket pays off) to have an expectation of one case where you end up that bunch of money.
So yea. Risk adjusted. While the EV might look good, the variance makes it a losing game.