The only reason the government is involved is because organized crime is who runs lotteries in the absence of the state. People would still gamble with black market lotteries.
Organized crime ran very small, very basic "numbers" games that are the equivalent to the low-profile "Pick 3" or "Quick 4" games most states run. Hundreds, maybe a few thousand dollars of prizes. No organized crime ring paid out multi-million dollar jackpots -- this is entirely the invention of government lotteries and the private administration companies that run them, like G-Tech. When 8-digit jackpots weren't enough to draw desired participation, states joined together (MegaMillions, Powerball) to create 9- and even 10-digit jackpots.
> The only reason the government is involved is because organized crime is who runs lotteries in the absence of the state.
This isn't really a concept that makes sense. Organized crime is a state. They serve the same functions, care about the same things, and draw legitimacy from the same sources.
The government doesn't make as much as the ticket printers and lottery machine manufacturers/owners. It's not about the money for the state. It's about the lobbyists who are now entrenched, same as virtually any US lottery.