I know a couple of people that did just that. With the lowered barrier to entry (free), people have been able to buy say a single share per paycheck instead of having to hold on for months to get a cost effective amount of cash to make it worth the trade. Not only this, but you can effectively dollar cost average your way into the market to minimize losing to bad timing. The trade fees were always absolute and not a percentage so it just never accessible to a lot of people -- and now, a lot of the big discount brokers went to 0-1¢ fees.

> people have been able to buy say a single share per paycheck instead of having to hold on for months to get a cost effective amount of cash to make it worth the trade

This is the problem solved by ETFs. Small amounts of money buying lots of diversification.

Not when it's $5 to trade 2 shares of SCHB because that's all the extra you can afford per paycheck.

> Same with gambling, I imagine. The utility of 107% guaranteed of this dollar is less than a less than one in a billion chance at a billion dollars.

Is this really true — from a rational perspective, and not one where someone idolizes wealth or being able to purchase "whatever they want?"

The utility of anything — including money — diminishes as you have more of it. The utility of the next hundred million dollars is less than the first hundred million.

So I don't think a rational actor would take the gamble.

Utility is a function of the person, the environment, and the thing. There is no 'utility of a dollar'. There is only 'utility of a dollar to me in this circumstance'.

So if one idolizes wealth then clearly they have assigned high utility to money in a non-diminishing returns sense. It is then rational for them to match their utility curve. Life is full of threshold systems. Given that, it would be very unusual for utility curves to not be deformed by them.

It's easy to construct a few scenarios with locally convex curves:

* You're in debt to the mafia and you will die if you don't pay them your $100k debt. You have $10k dollars. Do you spend the $10k to try a long shot of making $100k?

* You're poor and make $15/hr. If you save you will have an extra $1000 a year in savings. You will never own a home. You will never have time to study for a better job. The magic of compound interest with contributions is in the regularity, not so much in the amount. Put $1000/yr in a calculator and $998/yr in a calculator (assume it compounds 3% every year) and see the difference you get over 60 years. It is insignificant on a 60 year horizon. $2 will buy you a powerball ticket, and maybe out of this life.

* You're an immigrant. You need a few million dollars for your investor visa. Your current visa runs out next year and then you return to a slum.

If a person doesn't see a way out of slaving at or near minimum wage till they retire, even a moderate windfall of a couple million would completely replace their lifetime earnings and give them the freedom to pursue their passions (be it a family, surfing, painting, etc) while they're young and healthy enough to enjoy doing so.

I tend to agree with your point for larger sums like a billion dollars, but maybe you're really passionate about the potential for EVs to positively impact our growing climate problem and need an enormous pile of cash to get that off the ground. People are complicated.