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Why buy insurance?
For big values the loss becomes negligible. Say you have a 10% chance to get 10 million $/€/Whatever, expected value 1m. You sell that chance for 990k, which loses you 10k of expected income. Why would you throw away 10k? Because in the face of getting almost 1m the 10k are insignificant, 1m and 990k will make you roughly equally rich. Also the richness increase from 1m to 10m is less than 10x since 1m gives you maybe 90% of the freedom that 10m does (depending on how well you can make 10m work for you, most people will just let it rot in the bank). Another way to look at it is to look at bankruptcy risk. Say I have 10k in the bank, which is nice. Those 10k cannot pay for a new house or 2 cars (mine and the one I hit), so I have a small risk of significant loss. If I buy an insurance I reduce my chance of going bankrupt from maybe 0.001% to 0% for a fairly small price. Usually you can buy insurance fairly cheap if you raise your deductible to maybe 5k (both for the house and the car) so that you shoulder the risk you can (shouldering risk = gaining money) and paying an insurance to shoulder the rest for you. That way you minimize the cost to remove the risk of bankruptcy. It makes sense to shoulder as much risk as you can (unless a fixed fee of the insurance makes in unfeasible) before paying others to do it for you so you can optimize your income while removing fatal risks.