Getting a bigger chance of winning in a government lottery? I don't know about your country's government-sponsored lottery but here in mine, government lotteries have millions of entries per day. That makes your chances of winning very little. But the jackpot prizes are really huge that many think it's worth trying. And each ticket is cheaper, too.
Aside from having low probability of winning, even lower than getting struck by lightning, there's always the suspicion of corruption and fraud. For one, it's being run by the most corrupt institution in the country, the government. Also, because they only announce that the jackpot is won without naming the winner, many doubt its integrity.
Government lotteries may not be profit-oriented but if you think this is a reason for them to be generous in their prizes, you're wrong. Here in my country, although the jackpot prizes are so big, actually only 55% of tickets sales go to the prizes.