But why is reducing variance desirable? It's exactly because there is utility of money function which is concave. Variance being undesirable comes from the shape of utility of money function.

Yes that’s one factor. But there’s also a “going bust” factor which is kind of a fundamental dynamic as well.

Think of it in terms of life. Once you are dead you’re dead, it’s the end. If the variance in your life outcomes “crosses the zero line” then the game ends, even if it’s just for an hour.

You could bend your argument to cover that by arguing that the utility of that last little fraction tends to infinity. Like what would you exchange for the drink of water that would save your life if you were minutes from death?

But it’s a bit strained, especially as a way to explain it to someone for whom utility is not already intuitive.

I think it’s pretty easy to understand that excessive variance leads to death or very negative outcomes.

All you need to demonstrate it is a houseplant and a supply of water, air, and sunshine. If you increase the variance of any of those three things sufficiently you quickly don’t have a houseplant any more, regardless of the average total supply.

And at some point that function bends hard once you hit bankruptcy, for instance many places in US you go to jail if you run out of money, especially if you have children with someone to whom you're not currently married.

Variance can be good though. Imagine you want some expensive service like a waterline for your house that's difficult to steal but you live under rules of gangsters or oppressive government so holding anything more than a little money at a time is risky.

You gamble every paycheck knowing eventually you will get a big payout. You quickly pay for the waterline and now you don't have to walk 300 ft to the well everyday.

Another example could be needing money for life saving expensive treatment for either yourself or a loved one.

That's why I mentioned that "avoiding variance" in itself is not a good argument. You avoid it for a reason and that reason is that (u(x - a) + (u + a)) / 2 < u(x) for vast majority of life scenarios.

That's a very contrived scenario and your hypothetical response is very unrealistic. For one thing, the gangsters either wait outside the gambling joint or simply take it outright and farm the rake. For another, real communities with such dynamics don't accumulate cash, they might accumulate tangible goods or a little infrastructure but they are not going to have large sums of cash-equivalents lying around. For all kinds of reasons you need either a high-trust society or an army to accumulate liquid wealth.

Informal gambling between low tier non gangster class people outside a joint is common amongst the lower class most everywhere and the whole scenario was about minimizing liquid wealth and dealing with cash intensive problems in places where cash is risky.

In the Philippines they even have a pooling system 'paluwagan' like this to make it possible for people to buy big things without a bank account or having to store large sums for large period of time which can be risky there.

Thanks for the example.

Maybe but when you see seemingly irrational behavior by "the underclass" it's always worth spending a little more time trying to understand what kinds of issues they may be facing that you're not intuitively aware of.

If you've been in the position where every dollar you make gets somehow taken from you without warning for years you'd act differently. Goes from things like avoiding banks due to various fees or garnishments, up to practices of wearing expensive jewelry because it's a fairly efficient way to carry value on your person, and because you often get to keep it even when you get arrested, unlike the cash in your pocket.