Decide whether a specific insurance policy is genuinely worth the premium. Compare annual cost against the probability and size of a claim to see the expected value and whether the cover makes financial sense.
Insurance is mathematically a negative expected value proposition by definition — insurers profit from the difference between collected premiums and paid claims. The rational reason to buy insurance is not to "win" financially on average, but to transfer risk you cannot afford to absorb. The question is not "do I expect to make a claim?" but "could I financially survive this loss without insurance?".
Self-insurance (not buying cover and retaining the risk yourself) is rational when: the maximum potential loss is affordable without financial hardship, the premium is high relative to expected claims, and you have sufficient savings to absorb the loss. Example: travel insurance for a £500 trip you can afford to lose — probably rational to self-insure if healthy. Travel insurance for a £5,000 trip with £150 medical cover — essential. The size of the potential loss relative to your savings determines whether self-insurance is sensible.
Insurance may not be worth buying when: (1) The maximum loss is affordable without financial hardship; (2) The premium is very high relative to the risk (excess warranty contracts are often extremely poor value); (3) You would never claim due to excess level or experience. Extended warranties on appliances, phone insurance on older phones, and excess waivers on car hire are commonly cited as poor value insurance products. Use the expected value test: if annual premium significantly exceeds claim probability × net payout, consider self-insuring.