Math Playground
Money

Insurance

Pool small premiums, pay big claims — risk-sharing as maths.

Insurance pools small premiums from many people to pay big claims for the few who suffer losses.

Quick check

Insurance has a negative expected value for the buyer on average. Why buy it anyway?

Key terms

  • Premium — what you pay (monthly or yearly) for cover.
  • Deductible / excess — the slice of any claim you pay yourself first.
  • Claim — a request for payout after a covered loss.
  • Coverage limit — the most the insurer will pay.
Try it

A 1-in-500 chance of a $50,000 loss. What's the 'fair' yearly premium?

Expected loss = 50,000 / 500 = $100/year. A real premium is higher — that gap covers the insurer's costs and profit.

Insure what you can't afford to lose (home, health, income); self-insure the small stuff by raising deductibles to cut premiums.

Expected payout per dollar of premium is always less than 1 — that's how insurers stay in business. You're paying for risk transfer, not expected gain.