What you are buying with an insurance is ease of mind. You are buying the ability to sleep at night, because you don't need to worry about the big catastrophe to happen which bankrupts you. The crucial difference between winning the lottery and "winning the insurance" (by having a damage event) is that the insurance gives you the big check at the time where you need it the most.
Transfering this to a lottery ticket, what you are buying with the ticket is hope. The slim hope that your numbers are correct and all your financial troubles are solved for the rest of your life. However, that's a dangerous mindset. The chance to win the lottery is extremely small. So what you are actually buying is false hope. Even worse, it might distract you from actively working towards your life goals. You are in danger of convincing yourself that you do not need to work on your career or learn a marketable skill or find a smart investment or build your own business because one day you win the lottery and get all the stuff you dreamed about anyway.
No, life is not fair, and we are not all born with the same privileges. But it's up to us how we play the cards we were dealt. If you want to improve your life, you need a reliable long term plan and you need to work on it. You can't assume that good luck will come to those who wait for it.
Further, the few people who actually win multi-million lottery prices often do not end up as happy as you would expect. They often realize that:
- Their social life often becomes worse, not better, thanks to their newfound wealth.
- Sudden access to that amount of money can generate anxiety.
- They might suffer from imposter syndrome, because they realize that they didn't actually do anything worthwhile to deserve that amount of money.
- They lack the experience to work with any larger amount of money, so they might invest it badly or spend it much quicker than they should.
- They don't know what kind of things really make them happy, so they might end up spending it in ways which do not really bring them as much of an emotional benefit as they think it would. They soon realize that just because something is the most expensive thing they can buy doesn't mean it's the best thing for them to buy.
But if you are not interested in my armchair psychology and want to read some cold hard numbers instead: The payout rate of the US Powerball lottery (money they collect with ticket sales vs. money paid to winners) is 50%. Other state-run lotteries have similar payout rates. The profit margin of insurances varies a lot, but is usually in the one-digit percent area. The payout rate is likely smaller than 90% due to administrative overhead which needs to be paid by the insurance company, but should still be far larger than 50% for most insurances.
So from a purely statistical cost/benefit analysis, the expected loss on lottery tickets is usually higher than the expected loss on insurances.
If you really want to gamble with minimal losses, then I recommend to learn how to play Black Jack and go to a casino. When you memorize the rules for the ideal strategy, your expected loss is just 0.28%.