You can look at gambling and insurance from a portfolio theory perspective. You want to hold the portfolio that maximizes return for the level of risk (variabil

You can look at gambling and insurance from a portfolio theory perspective. You want to hold the portfolio that maximizes return for the level of risk (variability) you're willing to take. Both insurance and gambling lower your returns, but the change in variability for insurance has a -1 correlation with a risk you currently have (canceling it out), therefore significantly reducing the overall variability of your portfolio. Gambling isn't related to any other risk you already have, therefore introducing more variability into your portfolio. So insurance is just a form of gambling where the payout is correlated with a risk you currently carry, instead of being "random".