You are confusing expected value with probability of "winning".
The purpose is to trade EV for a small probability of high payout. It's less extreme than the big ticket lotteries but more extreme than a scratcher. If that's not for you, don't do it
Also your last point is either obviously not true (if you're talking about big lottery winnings) or trivially true (if you're talking about $1000 scratcher prizes). More people made life changing money from a single company (Facebook) than all California lottery winners combined across all time
I think you are confusing how lotteries work, most lotteries have additional prizes not just the big grand prize. There are a range of prizes.
as an aside, I got to reading some lottery winning tips (https://www.smartluck.com/free-lottery-tips/california-fanta...). A real interesting hodge podge of statistical fallacies and other wishful thinkings but at the same time it does pull at our brains somehow. Like for example even though I know a run of numbers in a row are just as likely to happen as any other number I'm really unlikely to actually pick it as my guess - I suppose my brain just thinks I need some "balance" or the likelihood of this pattern happening is low. Randomness is hard.
Pick a prize amount that is anywhere in the same order of magnitude as any engineers total compensation. For any such amount, there are more people receiving prizes above this amount from startups than lotteries
But why can't you win n smaller prizes, money being fungible and all we can just tot up the smaller prizes.
The total number of lottery winners who have won, in total, an amount of say 50,000 USD is at least 2 orders of magnitude smaller than the number of people who have received that amount or more from startup equity
You are making an empirical claim that can be made rigorous, it's just off by several orders of magnitude
Less than half of startups have exits…
But most startup people don’t work at most startups.
I've worked at startups that have had exits and the employees got zilch. I think even in the startups with exits the probability of an employee having their equity turn into cash money is very low (also I doubt 50% of startups have exits - I hear a number of 10% more often and even that seems high, I'd imagine 10% of YC startups have an exit and they are the most likely to succeed so I imagine when you add in all the other startups that percentage gets far far lower).
Skill issue
I thought this was sarcasm initially, but I think on looking at the rest of your comments that you are actually being serious. wow. Glad I've never had the pleasure of working with you.
If you think about the amount of money given up as a startup employee you will definitely get some winnings.
For example, say as a startup employee you are earning/being compensated 80,000 a year in equity. If you bought $80,000 of lottery ticket’s each year how much would you win. Depends on the lottery but most lottery’s have a rough payout of approximately 50-70%. Let’s say it’s 50%. So you would expect to receive back $40,000 per year.
Do half of all startups equity turn into cash, I think not. So probably more likely to make money from the lottery.