Insurance 101

Insurance companies providing service which they were paid for challenge [IMPOSSIBLE]

Insurance companies work like casinos. You are a guaranteed small win every month but there is a small odd that you could ask for a lot of money each month (so they lose). The standard model should be they simply balance the odds and only take bets where they gain more money each month than is likely to be lost (given out in claims). However the optimal strategy is to simply refuse to pay meaning you just lose less so long as it doesn’t significantly reduce the amount of wins (income) each month to a greater degree than what is made by refusing to lose (denying claims).

It all makes really brutal logical sense from a probability and game theory perspective. This is also why most insurance companies hire people who are good at math because then you understand how poker and other chance games work.