[Zarel]

I don't think it's about who's at fault, it's about what risks you're willing to tolerate.

Insurance is always a trade-off of EV for tail risk. In exchange for losing money on average (the insurance company has to earn money somehow, after all), you're protected from the worst case scenario. You can think of it like, yourself from parallel universe where you don't get into a crash, pays yourself in the parallel universe where you do get into a crash. And the insurance company skims a little off the top as payment for the service of sending money across parallel universes.

But if you can afford to just eat the cost of a crash, you don't need to pay the insurance company for that service. And maybe you can eat the costs of some crashes but not others: If you crash into a rich guy's car, maybe you can't afford those costs, but damage to your own car is capped at the price of your own car. So that's all Dan's doing: insuring the costs he can't pay (damage to others) but not the ones he can (damage to his own car).

The math isn't affected by his chances of being found at fault, or how good of a driver he is, at all.

[kristofferc]

It's my understanding that most insurance companies earn most of their money by investing their float, not by paying out less than they bring in from customers.

[xapata]

No, it's the injuries you can't afford. Property damage doesn't add up to much (for some definitions of "much").