That depends on the policy. But you are right that my analysis only really applies for repeat players. So if you have two insurance providers with the same wr

That depends on the policy. But you are right that my analysis only really applies for repeat players. So if you have two insurance providers with the same written down policies, but one provider A usually pays out, and the other B fights it tooth and nail, then provider A has an easier time selling their services for a higher price. Reputation matters. Thus in the end (assuming some competition) the actual policies as implemented matter more than what's written down.