Insurance converts an uncertain individual loss into a certain small payment. That conversion depends on a statistical property, and understanding it explains what insurers can and cannot cover.
Individual outcomes are unpredictable, group outcomes are not
Whether a particular house burns down in a given year is close to unknowable. What proportion of a large number of similar houses will burn is remarkably stable.
Insurers do not attempt to predict individuals. They estimate the aggregate and charge each participant a share of it, plus costs and a margin.
Accuracy improves as the pool grows, because the variation of an average shrinks as more independent cases are added.
This is why new insurers and new product lines are priced conservatively, since the estimate is drawn from a small pool and the margin for error must be larger.
Independence is the critical assumption
The stability of the aggregate depends on losses being largely unrelated to each other. One house burning tells you little about the next.
Where losses are correlated, the pool provides much less protection, because a single event can trigger claims from a large share of policyholders simultaneously.
This is why floods, earthquakes and windstorms are treated as a distinct problem, and why cover for them is often priced, limited or excluded separately.
Premiums must reflect the risk each participant brings
If everyone paid the same regardless of risk, those with low risk would be subsidising those with high risk and would eventually leave the pool.
Their departure would raise the average risk of the remainder, requiring higher premiums, which would drive out the next-lowest tier in turn.
Insurers therefore classify applicants into groups with similar expected losses, and the sophistication of that classification is much of what distinguishes one insurer from another.
Information asymmetry works against the pool
Applicants generally know more about their own risk than the insurer does, and those who know they are high risk have most reason to buy cover.
Left unaddressed, this pushes the pool toward worse-than-expected risks, which is why insurers ask detailed questions and why answers must be accurate.
Waiting periods, exclusions for pre-existing conditions and medical underwriting all exist to manage the same problem from different directions.
Behaviour changes once cover exists
Being insured reduces the personal cost of a loss, which can reduce the care taken to avoid one. Insurers treat this as a design problem rather than as dishonesty.
Deductibles, co-payments and limits all leave the policyholder exposed to part of the loss, which preserves the incentive to avoid it.
Those features are therefore structural rather than merely cost-saving, and a policy without any of them would be considerably more expensive than the losses alone imply.