Comment by xelxebar
3 days ago
Insurance can actually be a win-win if you keep your money sitting anywhere else other than a literal piggy bank.
Basically, it takes just as much time for your investments to go from 10,000 USD to 50,000 USD as it does for 50,000 USD to go to 250,000 USD. So a setback of 5,000 USD has a disproportionate impact on your future financials the less money you start off with.
In other words, if your total wealth is low enough, the premiums can set you back much less than the expected loss from the insured event, and at the same time make insurance companies a profit.
I'm still learning about this stuff, but here's an article that breaks it down in more detail and more clearly than I have: https://news.ycombinator.com/item?id=26834333
In general it's worth it if a) you can't afford to replace the item in question (and the Kelly criterion gives you a precise definition of 'afford' if you really want to model it out), or b) you think the risk of losing the item is higher than the insurance company does (which is rare outside of cases of outright fraud, but might happen)
Another advantage of insurance is that if your insurer is responsible for the rectification then you benefit from collective bargaining at a time when you may be unable to do so yourself.
For example, if my car breaks down in the middle of nowhere at 3am, I expect I'll end up paying far more for recovery were I self-insured than a breakdown insurer will.
I think the article you linked is flawed because it presents a mathematical solution without taking this into account.