[Please read the OP before voting. Special voting rules apply.]

Buying a lottery ticket every now and then is not irrational. Unless you have thoroughly optimized the conversion of every dollar you own into utility-yielding investments and expenses, the exposure to large positive tail risk netted by spending a few dollars on lottery tickets can still be rational.

Phrased another way, when you buy a lottery ticket you aren't buying an investment, you're buying a possibility that is not available otherwise.