You're making the (probably) false assumption that your lottery is as broken as the Ontario one. I question your detachment if you are calling gambling an "investment" at all. If you want to win at probability games, look at what any professional gambler does and stick your money down only when you can prove or reasonably expect to see a positive expected value given your odds. That's how basic strategy in blackjack…
Numbers games (lotteries) are run by governments now because organized crime was running them in inner cities. People still played then. See Wikipedia: http://en.wikipedia.org/wiki/Numbers_game At least the "tax" from lottery proceeds often goes to benefit social goods like public school systems.