One interesting argument I've seen is that there is a serious demand for lotteries and gambling, and that making them illegal won't stop them (as it hasn't for drugs or prostitution). Instead, it just creates a black market for gambling, which is even more problematic than a well-regulated state one with a predictable and reasonable house rake. We may be trying to fight the human psyche itself here, for which making things illegal tends not to work.

But at the very least the states shouldn't be advertising the damn things!